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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Future Transp.</journal-id>
<journal-title>Frontiers in Future Transportation</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Future Transp.</abbrev-journal-title>
<issn pub-type="epub">2673-5210</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">1600739</article-id>
<article-id pub-id-type="doi">10.3389/ffutr.2025.1600739</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Future Transportation</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Traffic capacity constraints from level 3 control transitions</article-title>
<alt-title alt-title-type="left-running-head">Alms and Wagner</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/ffutr.2025.1600739">10.3389/ffutr.2025.1600739</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Alms</surname>
<given-names>Robert</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<xref ref-type="author-notes" rid="fn1">
<sup>&#x2020;</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/3017072/overview"/>
<role content-type="https://credit.niso.org/contributor-roles/conceptualization/"/>
<role content-type="https://credit.niso.org/contributor-roles/data-curation/"/>
<role content-type="https://credit.niso.org/contributor-roles/formal-analysis/"/>
<role content-type="https://credit.niso.org/contributor-roles/investigation/"/>
<role content-type="https://credit.niso.org/contributor-roles/methodology/"/>
<role content-type="https://credit.niso.org/contributor-roles/software/"/>
<role content-type="https://credit.niso.org/contributor-roles/validation/"/>
<role content-type="https://credit.niso.org/contributor-roles/visualization/"/>
<role content-type="https://credit.niso.org/contributor-roles/writing-original-draft/"/>
<role content-type="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Wagner</surname>
<given-names>Peter</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="author-notes" rid="fn1">
<sup>&#x2020;</sup>
</xref>
<role content-type="https://credit.niso.org/contributor-roles/conceptualization/"/>
<role content-type="https://credit.niso.org/contributor-roles/methodology/"/>
<role content-type="https://credit.niso.org/contributor-roles/supervision/"/>
<role content-type="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/"/>
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<aff id="aff1">
<sup>1</sup>
<institution>Institute of Transportation Systems</institution>, <institution>German Aerospace Center (DLR)</institution>, <addr-line>Berlin</addr-line>, <country>Germany</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>Institute of Land and Sea Transport Systems</institution>, <institution>TU Berlin</institution>, <addr-line>Berlin</addr-line>, <country>Germany</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/946658/overview">Aleksandar Stevanovic</ext-link>, University of Pittsburgh, United States</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/3021121/overview">Haifei Yang</ext-link>, Hohai University, China</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/3080391/overview">Zeynel Baran Y&#x131;ld&#x131;r&#x131;m</ext-link>, Adana Science and Technology University, T&#xfc;rkiye</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/3080728/overview">Changshuai Wang</ext-link>, Southeast University, China</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/3081439/overview">Jana Sarran</ext-link>, University of Guyana, Guyana</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Robert Alms, <email>Robert.Alms@dlr.de</email>
</corresp>
<fn fn-type="other" id="fn1">
<label>
<sup>&#x2020;</sup>
</label>
<p>ORCID: Robert Alms, <ext-link ext-link-type="uri" xlink:href="http://orcid.org/0000-0001-9950-3596">orcid.org/0000-0001-9950-3596</ext-link>; Peter Wagner, <ext-link ext-link-type="uri" xlink:href="http://orcid.org/0000-0001-9097-8026">orcid.org/0000-0001-9097-8026</ext-link>
</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>07</day>
<month>07</month>
<year>2025</year>
</pub-date>
<pub-date pub-type="collection">
<year>2025</year>
</pub-date>
<volume>6</volume>
<elocation-id>1600739</elocation-id>
<history>
<date date-type="received">
<day>26</day>
<month>03</month>
<year>2025</year>
</date>
<date date-type="accepted">
<day>16</day>
<month>06</month>
<year>2025</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2025 Alms and Wagner.</copyright-statement>
<copyright-year>2025</copyright-year>
<copyright-holder>Alms and Wagner</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>With the increasing integration of conditionally automated Level 3 systems into real-world traffic, concerns about their impact on traffic efficiency and capacity have emerged. When such systems reach their operational limits, mandatory control transitions could disrupt traffic flow and reduce overall capacity. This study employs large-scale simulations and numerical experiments to analyze these effects and quantify potential capacity constraints. The results of the two-lane highway scenario show an experimental capacity reduction of up to <inline-formula id="inf1">
<mml:math id="m1">
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</inline-formula> in an almost fully automated but unmanaged traffic mix, corresponding to a loss of about <inline-formula id="inf2">
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<mml:mrow>
<mml:mn>60</mml:mn>
<mml:mi>%</mml:mi>
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</inline-formula>. Control transition-related effects become increasingly pronounced at a Level 3 penetration rate between <inline-formula id="inf3">
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<mml:mrow>
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<mml:mrow>
<mml:mn>20</mml:mn>
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</inline-formula>. Estimated capacity reductions suggest that the maxima in time headway increments during the transition phase contribute most to these effects.</p>
</abstract>
<kwd-group>
<kwd>automated vehicles (AVs)</kwd>
<kwd>level 3 automation</kwd>
<kwd>mixed-autonomy traffic</kwd>
<kwd>traffic capacity</kwd>
<kwd>transition of control (ToC)</kwd>
</kwd-group>
<custom-meta-wrap>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Transportation Systems Modeling</meta-value>
</custom-meta>
</custom-meta-wrap>
</article-meta>
</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>As manufacturers begin to introduce Level 3 automated driving systems to the market, the potential impact of such systems on overall traffic flow and capacity needs to be investigated. A key challenge arises from the fact that Level 3 systems require human drivers to take over control when reaching system limits, leading to so-called transitions of control (ToC), which may disrupt traffic flow and reduce road capacity. Despite regulatory advancements concerning Level 3 systems (R157 by <xref ref-type="bibr" rid="B32">UNECE (2023)</xref>), the macroscopic impact of such procedural ToC effects on traffic conditions remains insufficiently explored. This raises the general question of how Level 3 control transitions in conditionally automated vehicles (AVs) affect traffic capacity and, more specifically, what characteristics of procedural ToC-induced time headway increments in vehicle strings contribute to this effect. To investigate this, we conduct a large-scale simulation-based analysis and complement it with simplified numerical experiments to estimate macroscopic capacity impacts. Our study also explores the underlying mechanisms of the transition phase in greater detail. Existing research on potential capacity gains from AVs, as exemplified by <xref ref-type="bibr" rid="B13">Friedrich (2016)</xref> and <xref ref-type="bibr" rid="B23">Park et al. (2021)</xref>, has primarily focused on higher automation levels (4&#x2013;5) under optimistic assumptions of short time headways, e.g., <inline-formula id="inf5">
<mml:math id="m5">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3c4;</mml:mi>
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<mml:mrow>
<mml:mi>A</mml:mi>
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</mml:mrow>
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<mml:mo>&#x3d;</mml:mo>
<mml:mn>0.5</mml:mn>
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</inline-formula> s, in contrast to observed headways in manually driven vehicles of at least <inline-formula id="inf6">
<mml:math id="m6">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mtext>&#x2003;</mml:mtext>
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</inline-formula> in freeway traffic, depending on vehicle speed, as shown by <xref ref-type="bibr" rid="B35">Wagner (2012)</xref>. Our previous work in <xref ref-type="bibr" rid="B1">Alms et al. (2022)</xref> and <xref ref-type="bibr" rid="B2">Alms and Wagner (2024)</xref> touched on ToC-related capacity effects but lacked a comprehensive quantification of resulting capacity losses. This study addresses these gaps by (i) adopting a macroscopic perspective using realistic, R157-compliant time headways of <inline-formula id="inf7">
<mml:math id="m7">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3c4;</mml:mi>
</mml:mrow>
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<mml:mi>A</mml:mi>
<mml:mi>V</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1.6</mml:mn>
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</mml:math>
</inline-formula> s, and (ii) introducing an exploratory estimation approach that explicitly accounts for Level 3 disengagements in road capacity assessment.</p>
<p>The rest of the paper is organized as follows: <xref ref-type="sec" rid="s2">Section 2</xref> introduces the conceptual aspects of ToCs in Level 3 automated systems. In <xref ref-type="sec" rid="s3">Section 3</xref>, we present a highway scenario calibration based on real-world detector data. <xref ref-type="sec" rid="s4">Section 4</xref> details our methodology for investigating ToC-related capacity effects in a simulation study, while <xref ref-type="sec" rid="s5">Section 5</xref> presents and discusses our results, comparing simulated and estimated capacity reductions. Lastly, <xref ref-type="sec" rid="s6">Section 6</xref> offers our perspective on the interpretation and limitations of this study.</p>
</sec>
<sec id="s2">
<title>2 Transitions of control in level 3 automated driving</title>
<p>The six levels of driving automation, defined by <xref ref-type="bibr" rid="B26">SAE International (2021)</xref>, not only classify automated driving functions and capabilities but also specify the human driver&#x2019;s role in terms of engagement and responsibility, as illustrated in <xref ref-type="fig" rid="F1">Figure 1</xref>. Conditional automated driving (Level 3, highlighted with a purple frame in <xref ref-type="fig" rid="F1">Figure 1</xref>) represents a fundamental shift toward automated vehicle operation within defined Operational Design Domains (ODD), specified in <xref ref-type="bibr" rid="B9">British Standards Institution (2020)</xref>, allowing human drivers to disengage from the primary driving task. However, if the Level 3 system requires the driver to resume control, a takeover request (ToR) is issued, initiating a critical transfer of authority: these procedures are referred to as transitions of control (ToC, plural: ToCs). Detailed insights into various aspects of ToCs are available through a comprehensive literature review on takeovers in automated driving (<xref ref-type="bibr" rid="B20">McDonald et al., 2019</xref>). Further studies examine the intricacies of modeling human factors, such as situational awareness and task demand (<xref ref-type="bibr" rid="B34">Van Lint and Calvert, 2018</xref>; <xref ref-type="bibr" rid="B10">Calvert and van Arem, 2020</xref>), or reduced driver performance (<xref ref-type="bibr" rid="B38">Wang et al., 2025b</xref>), during ToCs.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Excerpt from <xref ref-type="bibr" rid="B30">Shuttleworth (2019)</xref>&#x2019;s illustration of the SAE Levels of Driving Automation (<xref ref-type="bibr" rid="B26">SAE International, 2021</xref>), with Level 3 highlighted by a purple frame.</p>
</caption>
<graphic xlink:href="ffutr-06-1600739-g001.tif">
<alt-text content-type="machine-generated">Chart detailing SAE Levels of vehicle automation. Levels zero to two require driver supervision and engagement. Levels three to five involve automated driving, with level three indicating conditional driver intervention upon request, and levels four and five involving full automation without driver takeover.</alt-text>
</graphic>
</fig>
<p>The current regulations R157 from <xref ref-type="bibr" rid="B32">UNECE (2023)</xref> specify technical requirements for the certification of Level 3 Automated Lane Keeping Systems (ALKS) and set the time range <inline-formula id="inf8">
<mml:math id="m8">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>lead</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
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</inline-formula> to <inline-formula id="inf9">
<mml:math id="m9">
<mml:mrow>
<mml:mn>10</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>s</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula> before a failed transition escalates to a minimum risk maneuver (MRM), which is critical for the process of control transitions. Within the context of the EC project (<xref ref-type="bibr" rid="B31">TransAID, 2021</xref>; <xref ref-type="bibr" rid="B18">L&#xfc;cken et al., 2019</xref>; <xref ref-type="bibr" rid="B22">Mintsis et al., 2019</xref>) introduced a novel ToC model, which is fully parametrizable to align with these later-established UNECE specifications and for which a detailed description of the model&#x2019;s implementation is provided. The operationalization of ToCs is further specified in the ongoing EC project Hi-Drive (<xref ref-type="bibr" rid="B7">Bolovinou et al., 2023</xref>; <xref ref-type="bibr" rid="B27">Sauvaget et al., 2023</xref>) and demonstrated in <xref ref-type="bibr" rid="B29">Schulte-Tigges et al. (2023)</xref>.</p>
<p>
<xref ref-type="fig" rid="F2">Figure 2</xref> illustrates the basic mechanisms of the ToC model for successful and failed control transitions implemented in the microscopic traffic simulation SUMO (<xref ref-type="bibr" rid="B4">Alvarez Lopez et al., 2018</xref>). After a ToR, the AV enters a preparatory phase characterized by headway enlargement and disabled lane changing. Automated driving continues for the limited lead time, after which either the driver resumes control in time (successful transition), or, if not, the AV initiates an MRM (failed transition). For failed transitions, the AV initiates a phase of constant deceleration and may come to a full stop if the human driver does not respond. Although such events are rare, they can have a high impact and are the subject of extensive safety investigations based on disengagement reports (e.g., (<xref ref-type="bibr" rid="B39">Ward, 2024</xref>; <xref ref-type="bibr" rid="B16">Kohanpour et al., 2025</xref>)). However, this aspect is not the focus of the present work. In the case of a successful transition, the driver state model accounts for a phase of reduced human driving performance, with recent studies gaining further insights into both post-ToC durations (<xref ref-type="bibr" rid="B37">Wang et al., 2025a</xref>) and potential negative impacts on traffic stability (<xref ref-type="bibr" rid="B36">Wang et al., 2024</xref>).</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>ToC model operation modes illustrated in a representative speed-time diagram for: <bold>(a)</bold> successful transition and <bold>(b)</bold> failed transition.</p>
</caption>
<graphic xlink:href="ffutr-06-1600739-g002.tif">
<alt-text content-type="machine-generated">Graph illustrating two scenarios: (a) Successful Transition and (b) Failed Transition. In both, speed decreases from automated to manual mode. The successful transition shows a smooth shift from automated to manual with a post-transition phase. The failed transition shows a drop to a minimal risk maneuver (MRM) after an unsuccessful transition attempt. Both scenarios depict phases labeled as Normal Operation, Prep ToC Phase, and Post ToC or MRM Phase.</alt-text>
</graphic>
</fig>
<p>In <xref ref-type="bibr" rid="B19">Maerivoet et al. (2019)</xref> and <xref ref-type="bibr" rid="B18">L&#xfc;cken et al. (2019)</xref> principal transition phase effects of consecutive, quasi-synchronous ToCs in a platoon of Level 3 automated vehicles were previously demonstrated. <xref ref-type="fig" rid="F3">Figure 3a</xref>, which depicts speed and time headways for a string of five AVs disengaging at the same location, illustrates this effect in a simplified simulation experiment with identical vehicle parametrization. The increased time headways, and consequently the cumulative speed reduction, are caused by the preparatory headway increment of the vehicle automation to facilitate a safe takeover (<italic>cf.</italic> <xref ref-type="fig" rid="F2">Figure 2</xref>, <italic>Prep ToC Phase</italic>). <xref ref-type="fig" rid="F3">Figure 3b</xref> extends this analysis by showing acceleration profiles for a larger platoon of up to 32 vehicles&#x2014;the maximum size at which the last AV still manages to prevent a complete stop&#x2014;using SUMO&#x2019;s ACC model for AVs, based on <xref ref-type="bibr" rid="B40">Xiao et al. (2017)</xref>. The main observed effects in the vehicle decelerations include:<list list-type="simple">
<list-item>
<p>
<inline-formula id="inf10">
<mml:math id="m10">
<mml:mrow>
<mml:mo>&#x2022;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> With a moderate default deceleration of <inline-formula id="inf11">
<mml:math id="m11">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:msup>
<mml:mrow>
<mml:mtext>m/s</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> during the <inline-formula id="inf12">
<mml:math id="m12">
<mml:mrow>
<mml:mn>10</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>s</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula> transition phase specified by R157, maintaining safe gaps in AV platoons is not feasible without initiating deceleration earlier. Panel (b-2) in <xref ref-type="fig" rid="F3">Figure 3b</xref> illustrates that, starting with the first vehicle behind AV.1 (dark blue line), SUMO&#x2019;s gap controller begins to decelerate even before the respective vehicles receive ToRs to initiate their ToC.</p>
</list-item>
<list-item>
<p>
<inline-formula id="inf13">
<mml:math id="m13">
<mml:mrow>
<mml:mo>&#x2022;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> Starting with AV.20, the following vehicles must decelerate more aggressively than their target deceleration of <inline-formula id="inf14">
<mml:math id="m14">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:msup>
<mml:mrow>
<mml:mtext>m/s</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula>. Panel (b-3) in <xref ref-type="fig" rid="F3">Figure 3b</xref> highlights these deceleration overshoots for AV.24&#x2013;28. These overshoots are specific to the ACC model, while similar experiments employing SUMO&#x2019;s default model do not exhibit this behavior. However, that model compensates by initiating deceleration even earlier than the ACC model. The principal accumulation effect of consecutive ToCs remains present in both cases.</p>
</list-item>
</list>
</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Platoon simulations with consecutive ToCs performed at a fixed location. <bold>(a)</bold> shows speed and time headway profiles for a short platoon with five AVs, illustrating the headway increment effect. <bold>(b)</bold> depicts acceleration profiles for a platoon of 32 AVs, showing an escalating headway increment effect with SUMO&#x2019;s ACC model.</p>
</caption>
<graphic xlink:href="ffutr-06-1600739-g003.tif">
<alt-text content-type="machine-generated">Figure a shows two graphs: (a-1) depicts speed over time for a leader and four autonomous vehicles (AV), showing a drop and recovery in speed. (a-2) illustrates time headways, highlighting fluctuations. Figure b contains acceleration data: (b-1) presents various vehicles&#x2019; acceleration over time, with highlighted sections. Insets (b-2) and (b-3) zoom in on specific time ranges. Different line colors represent diverse vehicle IDs.</alt-text>
</graphic>
</fig>
<p>These numerical experiments are highly simplified due to identical vehicle parametrizations, yet they effectively illustrate the isolated ToC effects discussed. Given the cumulative deceleration patterns observed, we expect that ToC-induced disturbances may lead to noticeable reductions in traffic capacity. To examine whether these effects also manifest under more realistic traffic flow conditions, we calibrate a SUMO simulation scenario to detector data in <xref ref-type="sec" rid="s3">Section 3</xref>.</p>
</sec>
<sec id="s3">
<title>3 Calibrating SUMO for a highway traffic scenario</title>
<p>To analyze the impact of ToCs on traffic capacity, we use real-world detector data from a German highway west of Berlin as a reference for SUMO calibration. The following sections detail the dataset and simulation setup.</p>
<sec id="s3-1">
<title>3.1 AVUS detector data</title>
<p>
<xref ref-type="fig" rid="F4">Figure 4a</xref> shows a section of the Bundesautobahn A115, referred to as AVUS, which was occasionally used as a motor racing track in the past and is a highly frequented highway with up to 80.000 vehicles per day. We hypothesize a potential ODD zone for Level 3 automated driving in the inbound segment of the road (<italic>cf.</italic> <xref ref-type="fig" rid="F4">Figure 4a</xref>, panel (a)), which is a two-lane highway with speed limits of <inline-formula id="inf15">
<mml:math id="m15">
<mml:mrow>
<mml:mn>80</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
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</mml:mrow>
</mml:math>
</inline-formula> starting at an interchange section and increasing to <inline-formula id="inf16">
<mml:math id="m16">
<mml:mrow>
<mml:mn>100</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
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</inline-formula> up to the next traffic exit, that is located nearly <inline-formula id="inf17">
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</inline-formula>.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Overview of the AVUS scenario. <bold>(a)</bold> OpenStreetMap view of the AVUS highway with a potential 5 km ODD zone on the two-lane inbound edge highlighted in purple. Zoom displays show traffic detector locations, marked with blue in subpanels <bold>(b)</bold> and <bold>(c)</bold>. Purple arrows indicate the inbound traffic direction. (b) Speed&#x2013;flow scatterplots of yearly AVUS detector data for inbound traffic from detector &#x201c;TE002&#x201d;.</p>
</caption>
<graphic xlink:href="ffutr-06-1600739-g004.tif">
<alt-text content-type="machine-generated">Map illustrating an &#x22;ODD Zone&#x22; in the Grunewald area, with insets showing detailed sections of the zone near Halensee and Steglitz-Zehlendorf. Below the map, graphs display vehicle speed against flow for the years 2017, 2019, 2023, and 2024, with scatter plots showing hourly counts and a van Aerde fit line.</alt-text>
</graphic>
</fig>
<p>
<xref ref-type="fig" rid="F4">Figure 4b</xref> displays speed&#x2014;flow relations for several years of the AVUS between 2015 and 2022, as scatterplots based on data from <xref ref-type="bibr" rid="B11">Digitale Plattform Stadtverkehr Berlin (2024)</xref>. These data are originally tagged as hourly flows with corresponding average speeds per hour, but we suspect that this is not accurate. While the number of vehicles is accumulated over a full hour, the high variations in speeds at lower flow rates suggest that these data points from the detector database might actually represent speed averages over intervals of 1&#xa0;minute or less. We were unable to verify this suspicion directly with the publisher of the data, but we argue that the actual speed value recorded in the database is likely the last entry of a full hour &#x2014; possibly for efficiency and memory-saving reasons in data processing &#x2014; rather than the average speed over the entire hour. This ultimately results in a notably wider distribution of speed values at lower flow rates than expected for true hourly data. For reference, we also added the model fit developed by <xref ref-type="bibr" rid="B33">Van Aerde (1995)</xref> to each plot.</p>
<p>
<xref ref-type="table" rid="T1">Table 1</xref> lists the yearly maximum flows <inline-formula id="inf21">
<mml:math id="m21">
<mml:mrow>
<mml:mi>q</mml:mi>
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<mml:math id="m22">
<mml:mrow>
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</inline-formula> and <inline-formula id="inf23">
<mml:math id="m23">
<mml:mrow>
<mml:mn>9</mml:mn>
<mml:msup>
<mml:mrow>
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<mml:mtext>th</mml:mtext>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> percentiles as suggested by <xref ref-type="bibr" rid="B8">Brilon and Geistefeldt (2010)</xref>, and the deterministic capacity derived from the van Aerde model, as well as the corresponding shares for heavy good vehicles (HGVs) extracted from the raw detector data between 2016 and 2024. Additionally, data provided by the <xref ref-type="bibr" rid="B6">BASt (2025)</xref> from a detector downstream of the AVUS at &#x201c;Eichkamp&#x201d; are also included in the table for comparison (<italic>cf.</italic> <xref ref-type="fig" rid="F4">Figure 4a</xref>, panel (b)). Note that 2024 shows an oddly high HGV share, which we consider very unlikely and attribute to recent technical changes in sensor-based detection and data processing by the provider. The report from <xref ref-type="bibr" rid="B5">BASt (2021)</xref> stated a nationwide HGV share of <inline-formula id="inf24">
<mml:math id="m24">
<mml:mrow>
<mml:mn>18.1</mml:mn>
<mml:mi>%</mml:mi>
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</inline-formula> in 2021 on Germany&#x2019;s highways.</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Yearly flow metrics and HGV shares for AVUS inbound traffic.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Year</th>
<th align="center">2016</th>
<th align="center">2017</th>
<th align="center">2018</th>
<th align="center">2019</th>
<th align="center">2020</th>
<th align="center">2021</th>
<th align="center">2022</th>
<th align="center">2023</th>
<th align="center">2024</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Max <inline-formula id="inf25">
<mml:math id="m25">
<mml:mrow>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">3,477</td>
<td align="center">3,472</td>
<td align="center">3,497</td>
<td align="center">3,447</td>
<td align="center">3,528</td>
<td align="center">3,226</td>
<td align="center">3,284</td>
<td align="center">3,396</td>
<td align="center">3,763</td>
</tr>
<tr>
<td align="left">99%ile</td>
<td align="center">3,212</td>
<td align="center">3,155</td>
<td align="center">3,116</td>
<td align="center">3,142</td>
<td align="center">3,104</td>
<td align="center">2,865</td>
<td align="center">2,837</td>
<td align="center">2,943</td>
<td align="center">3,018</td>
</tr>
<tr>
<td align="left">95%ile</td>
<td align="center">2,818</td>
<td align="center">2,751</td>
<td align="center">2,708</td>
<td align="center">2,766</td>
<td align="center">2,677</td>
<td align="center">2,434</td>
<td align="center">2,530</td>
<td align="center">2,514</td>
<td align="center">2,541</td>
</tr>
<tr>
<td align="left">van Aerde <inline-formula id="inf26">
<mml:math id="m26">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>c</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>F</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">3,070</td>
<td align="center">3,011</td>
<td align="center">3,013</td>
<td align="center">2,915</td>
<td align="center">2,971</td>
<td align="center">2,687</td>
<td align="center">2,622</td>
<td align="center">2,733</td>
<td align="center">2,766</td>
</tr>
<tr>
<td align="left">raw HGV (%)</td>
<td align="center">5.94</td>
<td align="center">5.74</td>
<td align="center">5.92</td>
<td align="center">5.55</td>
<td align="center">5.60</td>
<td align="center">4.91</td>
<td align="center">6.37</td>
<td align="center">7.72</td>
<td align="center">&#x2a;28.46</td>
</tr>
<tr>
<td align="left">BASt HGV (%)</td>
<td align="center">6.51</td>
<td align="center">7.21</td>
<td align="center">7.25</td>
<td align="center">6.81</td>
<td align="center">7.24</td>
<td align="center">7.56</td>
<td align="center">7.05</td>
<td align="center">&#x2014;</td>
<td align="center">&#x2014;</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>&#x002A;Outlier value; see main text for discussion</p>
</fn>
</table-wrap-foot>
</table-wrap>
</sec>
<sec id="s3-2">
<title>3.2 Simulation setup for calibration</title>
<p>To investigate the impacts of ToCs in mixed-autonomy traffic, we compose a traffic mix of four different vehicle types: automated passenger vehicles (AVs), manual passenger vehicles (MVs), light goods vehicles (LGVs), and heavy goods vehicles (HGVs). The most relevant parameters for a heterogeneous traffic behavior in this AVUS highway scenario are visualized in <xref ref-type="fig" rid="F5">Figure 5</xref>. Instead of utilizing SUMO&#x2019;s default parameters, vehicle type specific distributions were deployed. <xref ref-type="table" rid="T2">Table 2</xref> presents the full parametrization scheme for all vehicle types.</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Distributions of the main parameters for different vehicle types. SUMO&#x2019;s default is indicated by the black dashed line.</p>
</caption>
<graphic xlink:href="ffutr-06-1600739-g005.tif">
<alt-text content-type="machine-generated">Four density plots compare different vehicle types across acceleration and deceleration (top row), and Tau and speed factor (bottom row). Vehicle types are MV, AV, LGV, HGV, and Default Krauss Passenger, represented by lines and areas in red, blue, green, light blue, and black.</alt-text>
</graphic>
</fig>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Vehicle type definitions. &#x201c;&#x2014;&#x201d; indicates not defined.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Parameter/Attribute</th>
<th align="left">MV</th>
<th align="left">LGV</th>
<th align="left">HGV</th>
<th align="left">AV</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Car-following model</td>
<td align="left">Krauss</td>
<td align="left">Krauss</td>
<td align="left">Krauss</td>
<td align="left">ACC</td>
</tr>
<tr>
<td align="left">sigma</td>
<td align="left">
<inline-formula id="inf27">
<mml:math id="m27">
<mml:mrow>
<mml:mi mathvariant="script">N</mml:mi>
<mml:mrow>
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<mml:mrow>
<mml:mn>0.2</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>0.50</mml:mn>
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<mml:mo stretchy="false">]</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">
<inline-formula id="inf28">
<mml:math id="m28">
<mml:mrow>
<mml:mi mathvariant="script">N</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mn>0.1</mml:mn>
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<mml:mn>0.20</mml:mn>
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<mml:mo stretchy="false">)</mml:mo>
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<mml:mo stretchy="false">]</mml:mo>
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</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">
<inline-formula id="inf29">
<mml:math id="m29">
<mml:mrow>
<mml:mi mathvariant="script">N</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mn>0.1</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>0.20</mml:mn>
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<mml:mo stretchy="false">)</mml:mo>
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<mml:mo>,</mml:mo>
<mml:mspace width="2.77695pt" class="tmspace"/>
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</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">&#x2014;</td>
</tr>
<tr>
<td align="left">tau</td>
<td align="left">
<inline-formula id="inf30">
<mml:math id="m30">
<mml:mrow>
<mml:mi mathvariant="script">N</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mn>1.0</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>0.50</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>,</mml:mo>
<mml:mspace width="2.77695pt" class="tmspace"/>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:mn>0.5</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>1.6</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">]</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">
<inline-formula id="inf31">
<mml:math id="m31">
<mml:mrow>
<mml:mi mathvariant="script">N</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mn>1.0</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>0.30</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>,</mml:mo>
<mml:mspace width="2.77695pt" class="tmspace"/>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:mn>0.7</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>1.6</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">]</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">
<inline-formula id="inf32">
<mml:math id="m32">
<mml:mrow>
<mml:mi mathvariant="script">N</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mn>1.2</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>0.50</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>,</mml:mo>
<mml:mspace width="2.77695pt" class="tmspace"/>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:mn>1.0</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>1.6</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">]</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">
<inline-formula id="inf33">
<mml:math id="m33">
<mml:mrow>
<mml:mi mathvariant="script">N</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mn>1.6</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>0.05</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>,</mml:mo>
<mml:mspace width="2.77695pt" class="tmspace"/>
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<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:mn>1.5</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>1.7</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">]</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
</tr>
<tr>
<td align="left">decel</td>
<td align="left">
<inline-formula id="inf34">
<mml:math id="m34">
<mml:mrow>
<mml:mi mathvariant="script">N</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mn>4.5</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>1.00</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>,</mml:mo>
<mml:mspace width="2.77695pt" class="tmspace"/>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:mn>2.5</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>5.5</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">]</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">
<inline-formula id="inf35">
<mml:math id="m35">
<mml:mrow>
<mml:mi mathvariant="script">N</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mn>4.5</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>1.00</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>,</mml:mo>
<mml:mspace width="2.77695pt" class="tmspace"/>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:mn>2.0</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>5.0</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">]</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">
<inline-formula id="inf36">
<mml:math id="m36">
<mml:mrow>
<mml:mi mathvariant="script">N</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mn>4.0</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>1.00</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>,</mml:mo>
<mml:mspace width="2.77695pt" class="tmspace"/>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:mn>2.0</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>5.0</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">]</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">
<inline-formula id="inf37">
<mml:math id="m37">
<mml:mrow>
<mml:mi mathvariant="script">N</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mn>3.0</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>1.00</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>,</mml:mo>
<mml:mspace width="2.77695pt" class="tmspace"/>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:mn>2.0</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>4.0</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">]</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
</tr>
<tr>
<td align="left">accel</td>
<td align="left">
<inline-formula id="inf38">
<mml:math id="m38">
<mml:mrow>
<mml:mi mathvariant="script">N</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mn>2.0</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>1.00</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>,</mml:mo>
<mml:mspace width="2.77695pt" class="tmspace"/>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:mn>1.0</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>3.5</mml:mn>
</mml:mrow>
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<inline-formula id="inf40">
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<mml:mrow>
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<inline-formula id="inf41">
<mml:math id="m41">
<mml:mrow>
<mml:mi mathvariant="script">N</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mn>1.5</mml:mn>
<mml:mo>,</mml:mo>
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<td align="left">speedFactor</td>
<td align="left">
<inline-formula id="inf42">
<mml:math id="m42">
<mml:mrow>
<mml:mi mathvariant="script">N</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mn>1.1</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>0.20</mml:mn>
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<mml:mo stretchy="false">)</mml:mo>
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<mml:mo>,</mml:mo>
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<mml:mrow>
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<td align="left">
<inline-formula id="inf43">
<mml:math id="m43">
<mml:mrow>
<mml:mi mathvariant="script">N</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mn>1.0</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>0.10</mml:mn>
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<inline-formula id="inf44">
<mml:math id="m44">
<mml:mrow>
<mml:mi mathvariant="script">N</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mn>1.0</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>0.10</mml:mn>
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<td align="left">1.0</td>
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<td align="left">lcAssertive</td>
<td align="left">
<inline-formula id="inf45">
<mml:math id="m45">
<mml:mrow>
<mml:mi mathvariant="script">N</mml:mi>
<mml:mrow>
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<mml:mrow>
<mml:mn>1.3</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>0.40</mml:mn>
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<mml:mo stretchy="false">)</mml:mo>
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<mml:mo>,</mml:mo>
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<td align="left">
<inline-formula id="inf46">
<mml:math id="m46">
<mml:mrow>
<mml:mi mathvariant="script">N</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
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<inline-formula id="inf47">
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<mml:mrow>
<mml:mi mathvariant="script">N</mml:mi>
<mml:mrow>
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<inline-formula id="inf48">
<mml:math id="m48">
<mml:mrow>
<mml:mi mathvariant="script">N</mml:mi>
<mml:mrow>
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<mml:mrow>
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<tr>
<td align="left">vClass</td>
<td align="left">Passenger</td>
<td align="left">Delivery</td>
<td align="left">Truck</td>
<td align="left">Passenger</td>
</tr>
<tr>
<td align="left">length [m]</td>
<td align="left">5.0</td>
<td align="left">8.0</td>
<td align="left">15.0</td>
<td align="left">5.0</td>
</tr>
<tr>
<td align="left">width [m]</td>
<td align="left">1.8</td>
<td align="left">2.0</td>
<td align="left">2.4</td>
<td align="left">1.8</td>
</tr>
<tr>
<td align="left">actionStepLength [s]</td>
<td align="left">0.1</td>
<td align="left">0.1</td>
<td align="left">0.1</td>
<td align="left">0.1</td>
</tr>
<tr>
<td align="left">maxSpeed [m/s]</td>
<td align="left">55.56</td>
<td align="left">27.78</td>
<td align="left">25.0</td>
<td align="left">55.56</td>
</tr>
<tr>
<td align="left">speedDev</td>
<td align="left">0</td>
<td align="left">0</td>
<td align="left">0</td>
<td align="left">0.01</td>
</tr>
<tr>
<td colspan="5" align="left">TOC model&#x2014;moderate parametrization scheme</td>
</tr>
<tr>
<td align="left">TOC device</td>
<td align="left">&#x2014;</td>
<td align="left">&#x2014;</td>
<td align="left">&#x2014;</td>
<td align="left">true</td>
</tr>
<tr>
<td align="left">manualType</td>
<td align="left">&#x2014;</td>
<td align="left">&#x2014;</td>
<td align="left">&#x2014;</td>
<td align="left">MV</td>
</tr>
<tr>
<td align="left">automatedType</td>
<td align="left">&#x2013;</td>
<td align="left">&#x2014;</td>
<td align="left">&#x2014;</td>
<td align="left">AV</td>
</tr>
<tr>
<td align="left">responseTime</td>
<td align="left">&#x2014;</td>
<td align="left">&#x2014;</td>
<td align="left">&#x2014;</td>
<td align="left">
<inline-formula id="inf49">
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<mml:mrow>
<mml:mn>7.0</mml:mn>
<mml:mo>,</mml:mo>
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</mml:mrow>
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</inline-formula>
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<tr>
<td align="left">initialAwareness</td>
<td align="left">&#x2014;</td>
<td align="left">&#x2014;</td>
<td align="left">&#x2014;</td>
<td align="left">
<inline-formula id="inf50">
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<mml:mi mathvariant="script">N</mml:mi>
<mml:mrow>
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<mml:mrow>
<mml:mn>0.5</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>0.30</mml:mn>
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</inline-formula>
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<tr>
<td align="left">recoveryRate</td>
<td align="left">&#x2014;</td>
<td align="left">&#x2014;</td>
<td align="left">&#x2014;</td>
<td align="left">
<inline-formula id="inf51">
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<mml:mrow>
<mml:mi mathvariant="script">N</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mn>0.2</mml:mn>
<mml:mo>,</mml:mo>
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<mml:mo>,</mml:mo>
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<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
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</inline-formula>
</td>
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<tr>
<td align="left">mrmDecel</td>
<td align="left">&#x2014;</td>
<td align="left">&#x2014;</td>
<td align="left">&#x2014;</td>
<td align="left">3.0</td>
</tr>
<tr>
<td align="left">ogNewSpaceHeadway</td>
<td align="left">&#x2014;</td>
<td align="left">&#x2014;</td>
<td align="left">&#x2014;</td>
<td align="left">10.0</td>
</tr>
<tr>
<td align="left">ogNewTimeHeadway</td>
<td align="left">&#x2014;</td>
<td align="left">&#x2014;</td>
<td align="left">&#x2014;</td>
<td align="left">5.0</td>
</tr>
<tr>
<td align="left">ogChangeRate</td>
<td align="left">&#x2014;</td>
<td align="left">&#x2014;</td>
<td align="left">&#x2014;</td>
<td align="left">1.0</td>
</tr>
<tr>
<td align="left">ogMaxDecel</td>
<td align="left">&#x2014;</td>
<td align="left">&#x2014;</td>
<td align="left">&#x2014;</td>
<td align="left">1.0</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>In principle, SUMO&#x2019;s vehicle insertion capacity exceeds that of comparable real-world traffic scenarios. Therefore, we aim to calibrate the simulation primarily to match the maximum flow <inline-formula id="inf52">
<mml:math id="m52">
<mml:mrow>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> in relation to the real-word AVUS data. Besides the general vehicle parametrization, two insertion properties in SUMO heavily effect the overall capacity of a simulation, i.e., the vehicle speed at insertion <monospace>departSpeed</monospace> and lane choice at insertion <monospace>departLane</monospace>. We kept these parameters unchanged for all simulations in the paper. The most important capacity related SUMO options are defined as follows:<list list-type="simple">
<list-item>
<p>
<inline-formula id="inf53">
<mml:math id="m53">
<mml:mrow>
<mml:mo>&#x2022;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> <monospace>departSpeed &#x3d; max</monospace>
</p>
</list-item>
<list-item>
<p>
<inline-formula id="inf54">
<mml:math id="m54">
<mml:mrow>
<mml:mo>&#x2022;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> <monospace>departLane &#x3d; random (AV,MV,LGV)</monospace>
</p>
</list-item>
<list-item>
<p>
<inline-formula id="inf55">
<mml:math id="m55">
<mml:mrow>
<mml:mo>&#x2022;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> <monospace>departLane &#x3d; right (HGV)</monospace>
</p>
</list-item>
<list-item>
<p>
<inline-formula id="inf56">
<mml:math id="m56">
<mml:mrow>
<mml:mo>&#x2022;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> <monospace>extrapolate-departpos &#x3d; true</monospace>
</p>
</list-item>
<list-item>
<p>
<inline-formula id="inf57">
<mml:math id="m57">
<mml:mrow>
<mml:mo>&#x2022;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> <monospace>step-length &#x3d; 0.1 s</monospace>
</p>
</list-item>
</list>
</p>
</sec>
<sec id="s3-3">
<title>3.3 Calibration including ramp flow</title>
<p>In the first step, we ran simulations with increasing demand using MVs only. To better capture the full spectrum of the fundamental diagram in SUMO, we introduced additional vehicle flow on the incoming ramp. This creates a merging scenario, leading to traffic breakdown upstream of the main edge&#x2019;s detector position. <xref ref-type="fig" rid="F6">Figure 6</xref> shows the speed&#x2013;flow relations as scatterplots for (i) real-world detector data from 2024, (ii) SUMO&#x2019;s default parametrization, and (iii) the aggregated main edge data from the final calibration. The graphic also color-codes the demand intensities from the on-ramp and highlights the maximum <inline-formula id="inf58">
<mml:math id="m58">
<mml:mrow>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> of the AVUS detector data 2024. For reference of the expected average speeds defined by the german Highway Capacity Manual&#x2014;referred to as HBS&#x2014;in (<xref ref-type="bibr" rid="B12">FGSV, 2015</xref>, Part A, Figure A3-10) for a two-lane highway (slope <inline-formula id="inf59">
<mml:math id="m59">
<mml:mrow>
<mml:mo>&#x2264;</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>, speed limit <inline-formula id="inf60">
<mml:math id="m60">
<mml:mrow>
<mml:mn>80</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>km/h</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>), a black solid line was added.</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Speed&#x2013;flow relations for the AVUS scenario, including ramp flow, comparing calibrated flows based on the parametrization scheme from <xref ref-type="table" rid="T2">Table 2</xref> versus AVUS detector data from 2024, and SUMO&#x2019;s default. The main edge&#x2019;s demand intensities are color-coded in blue. Ramp demand levels are coded by marker size and style.</p>
</caption>
<graphic xlink:href="ffutr-06-1600739-g006.tif">
<alt-text content-type="machine-generated">Scatter plot illustrating calibrated SUMO main flows for ramp demand intensity, with speed in kilometers per hour on the y-axis and flow in vehicles per hour on the x-axis. Data points are color-coded: light blue plus signs for 0-250, blue squares for 250-500, darker blue crosses for 500-750, and dark blue triangles for 750-1000. A key highlights real data and benchmark lines.</alt-text>
</graphic>
</fig>
<p>The key findings derived from <xref ref-type="fig" rid="F6">Figure 6</xref> are:<list list-type="simple">
<list-item>
<p>1. Comparing the dark gray SUMO default data with the light gray detector data, we identify how far SUMO&#x2019;s default exceeds the actual maximum flow (about 700 vehicles surplus).</p>
</list-item>
<list-item>
<p>2. The calibrated main edge&#x2019;s flow (blue-colored points) is notably lower than SUMO&#x2019;s default. Maximum flows (dark blue points) are much closer to the real-data (about 130 vehicles difference) compared to SUMO&#x2019;s default (dark gray).</p>
</list-item>
<list-item>
<p>3. The overall speed&#x2013;flow relation of the calibrated main edge (blue) is slightly tilted toward higher speeds compared to SUMO&#x2019;s default (dark gray), and the speed gradient more in line of the HBS expectation (black line).</p>
</list-item>
<list-item>
<p>4. The calibrated main edge&#x2019;s traffic breakdown on the congested side of the fundamental diagram (indicated by darker-colored blue points) is much less pronounced than what is to be expected from real-world data (see light gray scatter points).</p>
</list-item>
</list>
</p>
<p>The phenomenon described in point 4 is, in part, a limitation of SUMO&#x2019;s current modeling of cooperative lane-changing behavior between neighboring lanes under traffic breakdown conditions. Correspondingly, <xref ref-type="fig" rid="F7">Figure 7</xref> compares the lane-specific calibrated flows in SUMO with real AVUS data from 2024. We clearly identify the disparate speed levels between the lanes in SUMO (bottom panel), whereas the real-world data (top panel) indicate similar speed&#x2013;flow relations on both lanes. <xref ref-type="bibr" rid="B25">Rummel (2017)</xref> indirectly revealed this issue in his investigation but was unable to unequivocally identify the lane-specific breakdowns as the underlying cause of SUMO&#x2019;s oversaturation compared to the HBS predictions, nor did the report by <xref ref-type="bibr" rid="B14">Geistefeldt et al. (2017)</xref>, which ultimately disregarded SUMO in its analysis for this very reason. While this limitation prevents a full replication of the real-world dynamics, we proceed with the calibration of the scenario as a basis for our analysis and will address this shortcoming in our future work.</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>Lane-specific speed&#x2013;flow relations for real data from 2024 (top panel) and SUMO&#x2019;s calibrated ramp scenario (bottom panel).</p>
</caption>
<graphic xlink:href="ffutr-06-1600739-g007.tif">
<alt-text content-type="machine-generated">Two scatter plots compare lane-specific speed data and calibrated lane flow. The top plot shows real data from AVUS 2024, with right lane in purple and left lane in orange. The bottom plot displays calibrated SUMO lane flows by ramp demand intensity, with four color-coded categories: 0-250, 250-500, 500-750, and 750-1000 vehicles per hour. Speed is on the vertical axis in kilometers per hour, and flow is on the horizontal axis in vehicles per hour.</alt-text>
</graphic>
</fig>
</sec>
<sec id="s3-4">
<title>3.4 Refining calibration by incorporating HGV share</title>
<p>In a second step, based on the parametrization scheme plausibilised for MVs in the ramp scenario (<italic>cf.</italic> <xref ref-type="table" rid="T2">Table 2</xref>), we conducted simulations with different shares of HGVs, LGVs, and MVs, but without any ramp flow. As a result, we can no longer reproduce the entire fundamental diagram for this highway scenario, since SUMO&#x2019;s flow does not naturally lead to a traffic breakdown as observed in real-world highway traffic. The reason we need to disregard the unstable part of the fundamental diagram at this point is technical: SUMO does not maintain precise LGV/HGV shares for vehicle insertions when approaching maximum flow. Instead, the share of LGVs and HGVs declines to zero until SUMO can only insert MVs when the traffic breakdown at capacity is expected. This behavior stems partly from the parametrization of LGVs and HGVs, such as their larger vehicle lengths and time headways.</p>
<p>
<xref ref-type="fig" rid="F8">Figure 8</xref> shows the speed&#x2013;flow relations for the main edge with LGV/HGV shares of <inline-formula id="inf61">
<mml:math id="m61">
<mml:mrow>
<mml:mn>0</mml:mn>
<mml:mi>%</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>5</mml:mn>
<mml:mi>%</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>10</mml:mn>
<mml:mi>%</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, and <inline-formula id="inf62">
<mml:math id="m62">
<mml:mrow>
<mml:mn>15</mml:mn>
<mml:mi>%</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> (LGV/HGV distributed as <inline-formula id="inf63">
<mml:math id="m63">
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mo>/</mml:mo>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> vs. <inline-formula id="inf64">
<mml:math id="m64">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>/</mml:mo>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>), compared to AVUS detector data from 2018. The key findings are as follows:<list list-type="simple">
<list-item>
<p>1. The maximum flow with a <inline-formula id="inf65">
<mml:math id="m65">
<mml:mrow>
<mml:mn>0</mml:mn>
<mml:mi>%</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> HGV share (purple-colored scatter points) is almost the same as in the ramp case (<italic>cf.</italic> <xref ref-type="fig" rid="F6">Figure 6</xref>, purple markers), with a difference of about <inline-formula id="inf66">
<mml:math id="m66">
<mml:mrow>
<mml:mn>50</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>veh/h</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>.</p>
</list-item>
<list-item>
<p>2. The AVUS detector data from 2018 have an HGV share of <inline-formula id="inf67">
<mml:math id="m67">
<mml:mrow>
<mml:mn>6</mml:mn>
<mml:mi>%</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, with a maximum flow of <inline-formula id="inf68">
<mml:math id="m68">
<mml:mrow>
<mml:mn>3497</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>veh/h</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>. The speed variation in the detector data, particularly for lower demands, is very high, which we attribute to factors discussed in <xref ref-type="sec" rid="s3-1">Section 3.1</xref>.</p>
</list-item>
<list-item>
<p>3. The speed variations in all simulation results are relatively large. This is expected, as we deliberately plotted only the average speeds of the last 1-min interval of a full hour, which we suspect is also the case for the real detector data. This illustrates a plausible speed distribution from the calibrated simulations compared to the detector data.</p>
</list-item>
<list-item>
<p>4. The color-coded flows at capacity decrease notably with increasing HGV shares (decline by 260 to <inline-formula id="inf69">
<mml:math id="m69">
<mml:mrow>
<mml:mn>410</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>veh/h</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>).</p>
</list-item>
</list>
</p>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>Speed&#x2013;flow relations for the AVUS scenario based on the parametrization scheme from <xref ref-type="table" rid="T2">Table 2</xref> comparing calibrated main flows considering LGV/HGV shares. Real-world detector data from AVUS 2018; color-coding by LGV/HGV share.</p>
</caption>
<graphic xlink:href="ffutr-06-1600739-g008.tif">
<alt-text content-type="machine-generated">Scatter plot showing calibrated SUMO main flows, color-coded by LGV/HGV share, with speed (km/h) on the y-axis and flow (vehicles per hour) on the x-axis. Various data points are marked by shapes and colors indicating different percentages of LGV/HGV from zero to fifteen percent. A line labeled HBS 2015 and gray circles indicating real data are also present. Reference data is from AVUS 2018.</alt-text>
</graphic>
</fig>
<p>Considering the relatively low deterministic capacities based on the AVUS detector data stated in <xref ref-type="table" rid="T1">Table 1</xref> compared to the expected capacities from the HBS (range from 3,600 to <inline-formula id="inf70">
<mml:math id="m70">
<mml:mrow>
<mml:mn>3900</mml:mn>
<mml:mtext>&#x2003;</mml:mtext>
<mml:mtext>veh/h</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>) for this highway type, we assess our SUMO calibration in terms of capacity as follows:<list list-type="simple">
<list-item>
<p>
<inline-formula id="inf71">
<mml:math id="m71">
<mml:mrow>
<mml:mo>&#x2022;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> The maximum flow in the SUMO ramp scenario without HGV share consideration is <inline-formula id="inf72">
<mml:math id="m72">
<mml:mrow>
<mml:mn>3907</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>veh/h</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>. The 95th and 99th percentile flows are <inline-formula id="inf73">
<mml:math id="m73">
<mml:mrow>
<mml:mn>3853</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>veh/h</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf74">
<mml:math id="m74">
<mml:mrow>
<mml:mn>3882</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>veh/h</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>, respectively. The van Aerde model estimates a maximum flow of <inline-formula id="inf75">
<mml:math id="m75">
<mml:mrow>
<mml:mn>3665</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>veh/h</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula> based on SUMO data. These values are significantly higher than the detector data but do not account for HGV shares in SUMO.</p>
</list-item>
<list-item>
<p>
<inline-formula id="inf76">
<mml:math id="m76">
<mml:mrow>
<mml:mo>&#x2022;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> With HGV share consideration the maximum flows on the stable arm of the fundamental diagram decrease notably between 6.7 to <inline-formula id="inf77">
<mml:math id="m77">
<mml:mrow>
<mml:mn>10.5</mml:mn>
<mml:mi>%</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> as illustrated in <xref ref-type="fig" rid="F8">Figure 8</xref>.</p>
</list-item>
</list>
</p>
<p>Under the assumption that those percentages under HGV consideration scale down proportionally in SUMO with the capacity numbers stated above, we obtain the following deterministic capacity ranges for the calibrated parametrization scheme:<list list-type="simple">
<list-item>
<p>
<inline-formula id="inf78">
<mml:math id="m78">
<mml:mrow>
<mml:mo>&#x2022;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> Max flow: <inline-formula id="inf79">
<mml:math id="m79">
<mml:mrow>
<mml:mn>3497</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>3647</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> veh/h</p>
</list-item>
<list-item>
<p>
<inline-formula id="inf80">
<mml:math id="m80">
<mml:mrow>
<mml:mo>&#x2022;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 95th percentile: <inline-formula id="inf81">
<mml:math id="m81">
<mml:mrow>
<mml:mn>3449</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>3597</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> veh/h</p>
</list-item>
<list-item>
<p>
<inline-formula id="inf82">
<mml:math id="m82">
<mml:mrow>
<mml:mo>&#x2022;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 99th percentile: <inline-formula id="inf83">
<mml:math id="m83">
<mml:mrow>
<mml:mn>3475</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>3624</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> veh/h</p>
</list-item>
<list-item>
<p>
<inline-formula id="inf84">
<mml:math id="m84">
<mml:mrow>
<mml:mo>&#x2022;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> van Aerde model: <inline-formula id="inf85">
<mml:math id="m85">
<mml:mrow>
<mml:mn>3281</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>3421</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> veh/h</p>
</list-item>
</list>
</p>
<p>Even though these capacities are still about <inline-formula id="inf86">
<mml:math id="m86">
<mml:mrow>
<mml:mn>200</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>300</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>veh/h</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula> larger than the detector numbers in <xref ref-type="table" rid="T1">Table 1</xref>, we consider this an adequate calibration, particularly compared to SUMO&#x2019;s default, since the real-world detector flow data are overall lower compared to the HBS range, which we identified to be between 3,600 and <inline-formula id="inf87">
<mml:math id="m87">
<mml:mrow>
<mml:mn>3900</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>veh/h</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>. Other local factors, such as road curvature, slope, shoulder lane width, underpass length, or surface conditions, which might impact the local capacity and could explain the rather low detector-based flows, are unknown to us. While more detailed microscopic calibration using high-resolution trajectory data (e.g., as in <xref ref-type="bibr" rid="B28">Schrader (2024)</xref> or <xref ref-type="bibr" rid="B17">Liu et al. (2024)</xref>) would be desirable, such data were not available for this study.</p>
</sec>
</sec>
<sec id="s4">
<title>4 Methodology to quantify capacity effects of ToCs</title>
<p>To determine ToC-related capacity impacts, we conduct a simulation study with an increasing AV penetration rate and measure the corresponding maximum flows <inline-formula id="inf88">
<mml:math id="m88">
<mml:mrow>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>. Additionally, we estimate the anticipated ToC-induced capacity reduction and later compare these estimates with the measured results from the simulation study.</p>
<sec id="s4-1">
<title>4.1 Simulation experiment</title>
<p>
<statement content-type="algorithm" id="Algorithm_1">
<label>Algorithm 1</label>
<p>Binary search for maximum flow.<list list-type="simple">
<list-item>
<p>1: <bold>Initialize:</bold>
</p>
</list-item>
<list-item>
<p>2:&#x2003;<inline-formula id="inf89">
<mml:math id="m89">
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mi>o</mml:mi>
<mml:mi>w</mml:mi>
<mml:mo>&#x2190;</mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf90">
<mml:math id="m90">
<mml:mrow>
<mml:mi>h</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>g</mml:mi>
<mml:mi>h</mml:mi>
<mml:mo>&#x2190;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> max demand</p>
</list-item>
<list-item>
<p>3:&#x2003;<inline-formula id="inf91">
<mml:math id="m91">
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>x</mml:mi>
<mml:mtext>_</mml:mtext>
<mml:mi>v</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>d</mml:mi>
<mml:mo>&#x2190;</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
</p>
</list-item>
<list-item>
<p>4:&#x2003;<inline-formula id="inf92">
<mml:math id="m92">
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>d</mml:mi>
<mml:mi>s</mml:mi>
<mml:mo>&#x2190;</mml:mo>
<mml:mn>12</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
</p>
</list-item>
<list-item>
<p>5:&#x2003;<inline-formula id="inf93">
<mml:math id="m93">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mi>h</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>s</mml:mi>
<mml:mi>h</mml:mi>
<mml:mi>o</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>d</mml:mi>
<mml:mo>&#x2190;</mml:mo>
<mml:mi>s</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>d</mml:mi>
<mml:mi>s</mml:mi>
<mml:mo>/</mml:mo>
<mml:mn>2</mml:mn>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>6</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
</p>
</list-item>
<list-item>
<p>6:&#x2003;<bold>while</bold> <inline-formula id="inf94">
<mml:math id="m94">
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mi>o</mml:mi>
<mml:mi>w</mml:mi>
<mml:mo>&#x2264;</mml:mo>
<mml:mi>h</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>g</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> <bold>do</bold>
</p>
</list-item>
<list-item>
<p>7:&#x2003;&#x2003;&#x2003;<inline-formula id="inf95">
<mml:math id="m95">
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>d</mml:mi>
<mml:mo>&#x2190;</mml:mo>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mi>o</mml:mi>
<mml:mi>w</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>h</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>g</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
</p>
</list-item>
<list-item>
<p>8:&#x2003;&#x2003;&#x2003;Run simulation at demand <inline-formula id="inf96">
<mml:math id="m96">
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> for each <inline-formula id="inf97">
<mml:math id="m97">
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> in <inline-formula id="inf98">
<mml:math id="m98">
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>d</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
</p>
</list-item>
<list-item>
<p>9:&#x2003;&#x2003;&#x2003;Count valid and invalid results</p>
</list-item>
<list-item>
<p>10:&#x2003;&#x2003;&#x2003;<bold>if</bold> invalid results <inline-formula id="inf99">
<mml:math id="m99">
<mml:mrow>
<mml:mo>&#x2264;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> threshold <bold>then</bold>
</p>
</list-item>
<list-item>
<p>11:&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;<inline-formula id="inf100">
<mml:math id="m100">
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>x</mml:mi>
<mml:mtext>_</mml:mtext>
<mml:mi>v</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>d</mml:mi>
<mml:mo>&#x2190;</mml:mo>
<mml:mi>m</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
</p>
</list-item>
<list-item>
<p>12:&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;Increase <inline-formula id="inf101">
<mml:math id="m101">
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mi>o</mml:mi>
<mml:mi>w</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
</p>
</list-item>
<list-item>
<p>13:&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;Record maximum flow at detector for valid results</p>
</list-item>
<list-item>
<p>14:&#x2003;&#x2003;&#x2003;<bold>else</bold>
</p>
</list-item>
<list-item>
<p>15:&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;Decrease <inline-formula id="inf102">
<mml:math id="m102">
<mml:mrow>
<mml:mi>h</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>g</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
</p>
</list-item>
<list-item>
<p>16:&#x2003;&#x2003;&#x2003;<bold>end if</bold>
</p>
</list-item>
<list-item>
<p>17:&#x2003;<bold>end while</bold>
</p>
</list-item>
<list-item>
<p>18:&#x2003;Save max valid demand and corresponding maximum flow</p>
</list-item>
</list>
</p>
</statement>
</p>
<p>For the simulation study, we define a wide range of traffic shares based on the vehicle types outlined in <xref ref-type="table" rid="T2">Table 2</xref>. The traffic compositions feature increasing AV shares (<monospace>AV00</monospace>&#x2013;<monospace>AV85</monospace>) in <inline-formula id="inf103">
<mml:math id="m103">
<mml:mrow>
<mml:mn>10</mml:mn>
<mml:mi>%</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> increments, with AV increases and MV decreases of equal size, and a constant LGV/HGV share of <inline-formula id="inf104">
<mml:math id="m104">
<mml:mrow>
<mml:mn>15</mml:mn>
<mml:mi>%</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> (split <inline-formula id="inf105">
<mml:math id="m105">
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mo>/</mml:mo>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> LGV, <inline-formula id="inf106">
<mml:math id="m106">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>/</mml:mo>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> HGV). Considering a hypothetical ODD zone on the AVUS inbound highway, as illustrated in <xref ref-type="fig" rid="F4">Figure 4a</xref>, AVs are assumed to be capable of Level 3 automated driving at speeds of up to <inline-formula id="inf107">
<mml:math id="m107">
<mml:mrow>
<mml:mn>100</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>km/h</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula> until reaching the end of the ODD zone. Vehicles enter the network in their respective driving mode at random on one of the two lanes, except for HGVs, which are only inserted on the right lane. They continue their trip until reaching the end of the AVUS, near the detector position highlighted in <xref ref-type="fig" rid="F4">Figure 4a</xref>, panel (b). Four distinct scenarios are examined, differing in how ToCs are facilitated:<list list-type="simple">
<list-item>
<p>1. No ToCs: Simulations without any ToCs.</p>
</list-item>
<list-item>
<p>2. Unmanaged: Simulations with unmanaged ToCs at the end of the ODD zone.</p>
</list-item>
<list-item>
<p>3. Managed: Simulations with ToCs managed by a ToC-dispatch algorithm over the full length of the ODD zone.</p>
</list-item>
<list-item>
<p>4. Unmanaged &#x201c;rightmost95&#x201d;: Simulations with unmanaged ToCs at the end of the ODD zone, emulating the concept of the latest approved manufacturer system by <xref ref-type="bibr" rid="B21">Mercedes-Benz Group (2024)</xref>, operating up to <inline-formula id="inf108">
<mml:math id="m108">
<mml:mrow>
<mml:mn>95</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>km/h</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula> on the rightmost lane, without overtaking.</p>
</list-item>
</list>
</p>
<p>For cases 2&#x2013;4, we additionally run simulations with <inline-formula id="inf109">
<mml:math id="m109">
<mml:mrow>
<mml:mi>&#x3c4;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>-distributions for MVs around <inline-formula id="inf110">
<mml:math id="m110">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3c4;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mi>V</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0.8</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>s</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf111">
<mml:math id="m111">
<mml:mrow>
<mml:mn>1.2</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>s</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>. In case 3, we deploy the heuristic algorithm developed by <xref ref-type="bibr" rid="B18">L&#xfc;cken et al. (2019)</xref>. The control algorithm basically emulates a V2X-based traffic management scheme by dispatching ToRs to AVs in a coordinated manner to mitigate the accumulation effect of consecutive ToCs. For case 4, AVs are only inserted into the simulation on the rightmost lane, overtaking is disabled, and their speed is limited to <inline-formula id="inf112">
<mml:math id="m112">
<mml:mrow>
<mml:mn>95</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>km/h</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>.</p>
<p>To measure the capacity per AV share as precisely as possible, we run the AVUS scenario with 12 seeds per traffic mix, deploying a binary search as illustrated in <xref ref-type="statement" rid="Algorithm_1">Algorithm 1</xref>. To ensure we obtain the correct maximum flow, the results of each run must be checked against the actual traffic share versus the expected share due to SUMO&#x2019;s insertion mechanism, as described in <xref ref-type="sec" rid="s3-4">Section 3.4</xref>. The binary search continues increasing the demand as long as valid traffic shares are observed, until the maximum flow per simulation run is reached.</p>
<p>Simulations run with a <inline-formula id="inf113">
<mml:math id="m113">
<mml:mrow>
<mml:mn>30</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>min</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula> warm-up phase to populate the scenario and then record data for a full hour of simulated time (SUMO version 1.22 from <xref ref-type="bibr" rid="B3">Alvarez Lopez et al. (2025)</xref>). A detector near the end of the ODD zone records speed and flow to identify potential traffic breakdowns and measures the maximum flow. <xref ref-type="fig" rid="F9">Figure 9</xref> exemplarily shows spatiotemporal heatmaps of the ODD zone for speed and flow. <xref ref-type="fig" rid="F9">Figures 9A,B</xref>, result from the same demand level and AV share&#x2014;only the seed values, which determine the randomization process of vehicle insertions, differ.</p>
<fig id="F9" position="float">
<label>FIGURE 9</label>
<caption>
<p>Spatiotemporal heatmaps of the ODD zone for speed and flow. <bold>(a)</bold> Valid run at max capacity: Mix AV60, seed 1053. <bold>(b)</bold> Invalid run: Mix AV60, seed 1055. The traffic breakdown is clearly visible in speed and flow.</p>
</caption>
<graphic xlink:href="ffutr-06-1600739-g009.tif">
<alt-text content-type="machine-generated">Two sets of heatmaps labeled as figures a and b. Each set contains two heatmaps comparing flow and speed over time and position. Figure a: The flow map shows a uniform green color, indicating consistent flow, while the speed map features mostly dark blue with small areas of light blue, reflecting overall high speed with occasional decreases. Figure b: The flow map shows slight variations and black patches, suggesting fluctuations, while the speed map has a red diagonal gradient, indicating significant decreases in speed over time. Both figures are based on a mix AV60 scenario with different seed values.</alt-text>
</graphic>
</fig>
</sec>
<sec id="s4-2">
<title>4.2 Estimating capacity reduction</title>
<p>Considering the <monospace>minGap</monospace> in SUMO as <inline-formula id="inf114">
<mml:math id="m114">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>g</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>min</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, individual vehicle lengths <inline-formula id="inf115">
<mml:math id="m115">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>l</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, type-specific <inline-formula id="inf116">
<mml:math id="m116">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3c4;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, and varying vehicle shares <inline-formula id="inf117">
<mml:math id="m117">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, the theoretical lane capacity <inline-formula id="inf118">
<mml:math id="m118">
<mml:mrow>
<mml:mi>C</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> at speed <inline-formula id="inf119">
<mml:math id="m119">
<mml:mrow>
<mml:mi>v</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is given by:<disp-formula id="e1">
<mml:math id="m120">
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>v</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mo>&#x2211;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x22c5;</mml:mo>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>l</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>g</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>min</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>v</mml:mi>
<mml:msub>
<mml:mrow>
<mml:mo>&#x2211;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x22c5;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3c4;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>
</p>
<p>For the SUMO default <monospace>minGap</monospace> of <inline-formula id="inf120">
<mml:math id="m121">
<mml:mrow>
<mml:mn>2.5</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>m</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, a speed <inline-formula id="inf121">
<mml:math id="m122">
<mml:mrow>
<mml:mi>v</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>100</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>k</mml:mi>
<mml:mi>m</mml:mi>
<mml:mo>/</mml:mo>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, and the respective vehicle lengths and <inline-formula id="inf122">
<mml:math id="m123">
<mml:mrow>
<mml:mi>&#x3c4;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>-values from <xref ref-type="table" rid="T2">Table 2</xref>, we compute lane capacities across all traffic mixes. Assuming a constant time headway <inline-formula id="inf123">
<mml:math id="m124">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3c4;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> for each vehicle type, without considering ToCs, the resulting capacities per mix are shown in <xref ref-type="fig" rid="F10">Figure 10a</xref>. The results demonstrate that as the <inline-formula id="inf124">
<mml:math id="m125">
<mml:mrow>
<mml:mi>&#x3c4;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>-values for MVs increase (<inline-formula id="inf125">
<mml:math id="m126">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3c4;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>MV</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0.8</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>s</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula> to <inline-formula id="inf126">
<mml:math id="m127">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3c4;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>MV</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1.2</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>s</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>), while keeping fixed values for AVs <inline-formula id="inf127">
<mml:math id="m128">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3c4;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>AV</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1.6</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>s</mml:mtext>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>, LGVs <inline-formula id="inf128">
<mml:math id="m129">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3c4;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>LGV</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1.0</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>s</mml:mtext>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>, and HGVs <inline-formula id="inf129">
<mml:math id="m130">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3c4;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>HGV</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1.2</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>s</mml:mtext>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>, the decline in maximum capacity across traffic mixes becomes less pronounced. If MVs had the same <inline-formula id="inf130">
<mml:math id="m131">
<mml:mrow>
<mml:mi>&#x3c4;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>-value as AVs&#x2014;in this case, <inline-formula id="inf131">
<mml:math id="m132">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3c4;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>AV</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1.6</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>s</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula> &#x2014; the lane capacities would remain stable, regardless of the increasing AV share.</p>
<fig id="F10" position="float">
<label>FIGURE 10</label>
<caption>
<p>Estimated lane capacities based on Equation 1 for varied mean &#x03C4;_MV-values. <bold>(a)</bold> shows capacity estimates assuming a constant &#x03C4;_AV (no ToC consideration). <bold>(b)</bold> accounts for increasing &#x03C4;_AV due to ToC effects (with ToC consideration).</p>
</caption>
<graphic xlink:href="ffutr-06-1600739-g010.tif">
<alt-text content-type="machine-generated">Two line graphs labeled \&#x22;a\&#x22; and \&#x22;b\&#x22; show vehicle flow versus vehicle mix. Graph \&#x22;a\&#x22; shows three lines with varying &#x03C4;MV values (0.8, 1.0, 1.2), indicating decreasing flow from over 3000 to down to 2000 vehicles per hour. Graph \&#x22;b\&#x22; also shows lines for &#x03C4;MV values of 0.8, 1.0, and 1.2, with distinctions between mean and max values, demonstrating a steeper downward trend down to 1300.</alt-text>
</graphic>
</fig>
<p>To account for ToC effects in such estimations, we repeat the simplified numerical experiment with the 32-vehicle platoon described in <xref ref-type="sec" rid="s2">Section 2</xref>, this time varying the AV&#x2013;MV share in 10%-intervals between the two vehicle types. The top panel in <xref ref-type="fig" rid="F11">Figure 11a</xref> shows the time headway profiles for a 100% AV share, corresponding to the acceleration profile discussed in <xref ref-type="fig" rid="F3">Figure 3b</xref>. The increasing headways for later-following AVs are clearly identifiable. In the bottom panel (<xref ref-type="fig" rid="F11">Figure 11b</xref>), which depicts a 50&#x2013;50 share, the headway increase is far less pronounced compared to the top panel.</p>
<fig id="F11" position="float">
<label>FIGURE 11</label>
<caption>
<p>Time headways in a platoon experiment with 32 vehicles and varying AV&#x2013;MV shares. Black markers indicate the maximum headway for each vehicle. The vertical blue dashed line marks the onset of system-wide headway stabilization (see text for criterion), after all ToCs are completed. <bold>(a)</bold> 100% AV vs. 0% MV share. <bold>(b)</bold> 50% AV vs. 50% MV share.</p>
</caption>
<graphic xlink:href="ffutr-06-1600739-g011.tif">
<alt-text content-type="machine-generated">Two line graphs labeled a and b, plotting time headways in seconds against time. Both graphs feature multiple colored lines illustrating fluctuations in time headways from 0 to 400 seconds. A prominent vertical dashed blue line at approximately 200 seconds is present in each graph, marking a notable change point. Graphs show similar patterns with increases and stabilization in time headways.</alt-text>
</graphic>
</fig>
<p>Therefore, we introduce two additional estimators. In <xref ref-type="disp-formula" rid="e1">Equation 1</xref>, instead of using a fixed <inline-formula id="inf141">
<mml:math id="m142">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3c4;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>A</mml:mi>
<mml:mi>V</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1.6</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>s</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>, we derive <inline-formula id="inf142">
<mml:math id="m143">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3c4;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> for each share <inline-formula id="inf143">
<mml:math id="m144">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> from the numerical experiments as follows:<list list-type="simple">
<list-item>
<p>
<inline-formula id="inf144">
<mml:math id="m145">
<mml:mrow>
<mml:mo>&#x2022;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> <monospace>Max:</monospace> The black markers in <xref ref-type="fig" rid="F11">Figure 11</xref> denote the maximum time headway of each vehicle in the simulation run. The average of these maximum values serves as <inline-formula id="inf145">
<mml:math id="m146">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3c4;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> for each <inline-formula id="inf146">
<mml:math id="m147">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> in the estimator <monospace>max</monospace>.</p>
</list-item>
<list-item>
<p>
<inline-formula id="inf147">
<mml:math id="m148">
<mml:mrow>
<mml:mo>&#x2022;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> <monospace>Mean:</monospace> The point at which headways have stabilized after all ToCs are completed is marked by the vertical blue dashed line in <xref ref-type="fig" rid="F11">Figure 11</xref>. Stabilization in this experiment is defined as the latest point after all headway peaks at which all vehicles&#x2019; headways remain constant to within <inline-formula id="inf148">
<mml:math id="m149">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.005&#xa0;s for at least 15&#xa0;s. The average of the time headways at this point serves as <inline-formula id="inf149">
<mml:math id="m150">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3c4;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> for each <inline-formula id="inf150">
<mml:math id="m151">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> in the estimator <monospace>mean</monospace>.</p>
</list-item>
</list>
</p>
<p>With these estimator-based <inline-formula id="inf151">
<mml:math id="m152">
<mml:mrow>
<mml:mi>&#x3c4;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>-values, the original capacity <xref ref-type="disp-formula" rid="e1">Equation 1</xref> is adjusted by replacing the fixed headway term in the denominator with <inline-formula id="inf152">
<mml:math id="m153">
<mml:mrow>
<mml:mi>v</mml:mi>
<mml:msub>
<mml:mrow>
<mml:mo>&#x2211;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x22c5;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mover accent="true">
<mml:mrow>
<mml:mi>&#x3c4;</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">&#x302;</mml:mo>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>, where <inline-formula id="inf153">
<mml:math id="m154">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mover accent="true">
<mml:mrow>
<mml:mi>&#x3c4;</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">&#x302;</mml:mo>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> is the empirically derived time headway for AVs as a function of their share <inline-formula id="inf154">
<mml:math id="m155">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, while other vehicle types retain fixed values. The estimators <monospace>max</monospace> and <monospace>mean</monospace> provide these AV-specific headways based on the numerical experiments. <xref ref-type="fig" rid="F10">Figure 10b</xref> presents the results of the calculations that account for ToCs by utilizing these estimators. Both trends exhibit a notable decline in estimated lane capacity compared to the ToC-ignorant estimation depicted in <xref ref-type="fig" rid="F10">Figure 10a</xref>.</p>
</sec>
</sec>
<sec sec-type="results|discussion" id="s5">
<title>5 Results and discussion</title>
<p>
<xref ref-type="fig" rid="F12">Figure 12</xref> presents the overall results obtained from the simulation study outlined in <xref ref-type="sec" rid="s4-1">Section 4.1</xref>. First, we find that all maximum flows in the <monospace>AV00</monospace> share, ranging between <inline-formula id="inf155">
<mml:math id="m156">
<mml:mrow>
<mml:mn>3405</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>3611</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>veh/h</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>, fall within the expected capacity range from the calibration, i.e., <inline-formula id="inf156">
<mml:math id="m157">
<mml:mrow>
<mml:mn>3281</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>3647</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>veh/h</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>. We further analyze these results in detail for the four scenarios, following the order in which they were previously defined:<list list-type="simple">
<list-item>
<p>1. No ToCs: The results (green line) show that up to share <monospace>AV40</monospace>, maximum flows remain relatively stable, with a reduction of approximately <inline-formula id="inf157">
<mml:math id="m158">
<mml:mrow>
<mml:mn>100</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>veh/h</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula> compared to <monospace>AV00</monospace>. Beyond <monospace>AV50</monospace>, flow values begin to increase again. This trend can be linked to a homogenization effect in traffic flow as AV shares grow, which is influenced by the AV parametrization&#x2014;-specifically, the absence of <monospace>sigma</monospace> and a very small <monospace>speedDev</monospace> value of 0.01.</p>
</list-item>
<list-item>
<p>2. Unmanaged: In the case of entirely unmanaged ToCs (blue-colored bars), maximum flow decreases progressively from approximately <inline-formula id="inf158">
<mml:math id="m159">
<mml:mrow>
<mml:mn>3500</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>veh/h</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula> at <monospace>AV00</monospace> to around <inline-formula id="inf159">
<mml:math id="m160">
<mml:mrow>
<mml:mn>1450</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>veh/h</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula> at <monospace>AV85</monospace>. Regarding the different <inline-formula id="inf160">
<mml:math id="m161">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3c4;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mi>V</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> values, the results indicate high variations in maximum flow for <monospace>AV00</monospace> and <monospace>AV10</monospace>. These variations become less pronounced as the AV share increases, starting around <monospace>AV30</monospace>.</p>
</list-item>
<list-item>
<p>3. Managed: When ToCs are managed within the ODD zone (gray-colored bars), maximum flows exhibit a similar decreasing trend but remain notably higher than in the unmanaged scenario. Flows decline from <monospace>AV00</monospace> levels to approximately <inline-formula id="inf161">
<mml:math id="m162">
<mml:mrow>
<mml:mn>2950</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>veh/h</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula> at <monospace>AV85</monospace>. As in the unmanaged case, variations related to <inline-formula id="inf162">
<mml:math id="m163">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3c4;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mi>V</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> diminish with increasing AV shares, becoming noticeably less pronounced from <monospace>AV30</monospace> onward.</p>
</list-item>
<list-item>
<p>4. Unmanaged &#x201c;rightmost95&#x201d;: This scenario exhibits the lowest flow values across all AV shares (red-colored bars). A decline in maximum flow is already noticeable at <monospace>AV20</monospace> and continues consistently as the AV share increases, reaching a minimum of <inline-formula id="inf163">
<mml:math id="m164">
<mml:mrow>
<mml:mn>847</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>veh/h</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula> at <monospace>AV85</monospace>. In this scenario, capacity is inherently constrained because AVs are restricted to operating exclusively in the rightmost lane, leading to a disparate lane utilization with increasing AV share. Except for some LV and LGV vehicles traveling in the left lane, all HGVs and AVs remain on the right, thereby limiting capacity under unmanaged ToC conditions.</p>
</list-item>
</list>
</p>
<fig id="F12" position="float">
<label>FIGURE 12</label>
<caption>
<p>Maximum flow comparison across AV shares for the four scenarios: No ToCs (green line), Unmanaged ToCs (blue bars), Managed ToCs (gray bars), and Unmanaged &#x201c;rightmost95&#x201d; (red bars).</p>
</caption>
<graphic xlink:href="ffutr-06-1600739-g012.tif">
<alt-text content-type="machine-generated">Bar graph showing vehicle flow per hour (Flow q) across different mixes (AV00 to AV85). Multiple colored bars represent unmanaged and managed conditions with varying parameters (&#x3C4;MV). A green line indicates flow for &#x22;No ToCs&#x22;. Key included with color meanings.</alt-text>
</graphic>
</fig>
<p>Overall, the results in <xref ref-type="fig" rid="F12">Figure 12</xref> show that in the unmanaged scenario, maximum flow declines significantly with increasing AV share. At <monospace>AV85</monospace>, the max flow is approximately <inline-formula id="inf164">
<mml:math id="m165">
<mml:mrow>
<mml:mn>500</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>veh/h</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula> lower than in the managed case&#x2014;indicating that ToC management measures could help alleviate, but not fully prevent, capacity losses.</p>
<p>Furthermore, to compare these simulation results with the theoretical lane capacities estimated in <xref ref-type="sec" rid="s4-2">Section 4.2</xref> and <xref ref-type="fig" rid="F10">Figure 10c</xref>, we derive the relative percentage reductions in capacity across the increasing AV share. <xref ref-type="fig" rid="F13">Figure 13</xref> summarizes these reductions for the unmanaged scenario, differentiating between the estimators <monospace>max</monospace> and <monospace>mean</monospace>, while <monospace>constant</monospace> is included as a reference that ignores ToC effects. For each estimator, we report the root mean squared error (RMSE) and the coefficient of determination (<italic>R</italic>
<sup>2</sup>) to quantify the goodness of fit to the simulated capacity reductions&#x2014;where lower RMSE and <italic>R</italic>
<sup>2</sup> values closer to one indicate better agreement with the simulation data. The simulated results reveal a capacity loss of up to nearly 60% at <monospace>AV85</monospace>. We also make the following observations:<list list-type="simple">
<list-item>
<p>
<inline-formula id="inf165">
<mml:math id="m166">
<mml:mrow>
<mml:mo>&#x2022;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> While the <inline-formula id="inf166">
<mml:math id="m167">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3c4;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mi>V</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> dependency is relatively small in the simulation results, it becomes increasingly important in the estimator outcomes.</p>
</list-item>
<list-item>
<p>
<inline-formula id="inf167">
<mml:math id="m168">
<mml:mrow>
<mml:mo>&#x2022;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> The notably poor performance of the constant estimator, including negative <italic>R</italic>
<sup>2</sup> values in some cases, is expected since it does not capture capacity changes induced by ToCs.</p>
</list-item>
<list-item>
<p>
<inline-formula id="inf168">
<mml:math id="m169">
<mml:mrow>
<mml:mo>&#x2022;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> Both estimators, <monospace>max</monospace> and <monospace>mean</monospace>, although accounting for ToCs, notably underestimate the capacity reductions in the mid-range AV share (AV20&#x2013;80). This can be attributed to the simplicity of the numerical experiments we conducted to derive the estimator values. In particular, intensified vehicle interactions due to driver imperfections (parameter <monospace>sigma</monospace> <inline-formula id="inf169">
<mml:math id="m170">
<mml:mrow>
<mml:mi>&#x3c3;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>) and speed factor variances are disregarded in these experiments. Additionally, the numerical experiments employ single-lane vehicle strings and uniform acceleration and deceleration parameters, omitting lane-changing interactions and parameter variability that are present in the two-lane simulation scenario (<italic>cf.</italic> <xref ref-type="fig" rid="F5">Figure 5</xref>).</p>
</list-item>
<list-item>
<p>
<inline-formula id="inf170">
<mml:math id="m171">
<mml:mrow>
<mml:mo>&#x2022;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> Compared to the ToC-ignorant estimator <monospace>constant</monospace>, the other estimators perform notably better in predicting ToC-related capacity reductions, particularly <monospace>max</monospace>, which achieves the best RMSE and <italic>R</italic>
<sup>2</sup> scores. At AV85 share, <monospace>max</monospace> matches best with the simulation results, as vehicle interaction effects with non-AVs have almost completely vanished (still 15% HGVs present), leading to minimal driving behavior variability that coincides with the numerical experiment setup, where all vehicles share the same parameterization.</p>
</list-item>
</list>
</p>
<fig id="F13" position="float">
<label>FIGURE 13</label>
<caption>
<p>ToC-related relative percentage reductions of the capacity with varied mean <inline-formula id="inf171">
<mml:math id="m172">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3c4;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mi>V</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>-values for the unmanaged scenario. For reference, the estimator &#x201c;constant&#x201d; (gray-colored), which does not account for ToCs, is included. The RMSE and <italic>R</italic>
<sup>2</sup> metrics indicate estimation accuracy.</p>
</caption>
<graphic xlink:href="ffutr-06-1600739-g013.tif">
<alt-text content-type="machine-generated">Line graph showing relative capacity reductions (%) across mixed autonomous vehicle deployment levels (AV00 to AV85). The lines represent different management and estimation strategies with varying \( \tau_{MV} \) values (0.8, 1.0, 1.2). The legend details line styles and colors for simulation, max, mean, and constant estimates. Estimator performance metrics are provided with RMSE and \( R^2 \) values for each \( \tau_{MV} \). Performance metrics are tabulated for each estimation method and \( \tau_{MV} \) scenario.</alt-text>
</graphic>
</fig>
<p>In summation, the capacity reductions observed in the simulation might align only unsatisfactorily with theoretical estimates, as deviations occur in the mid-range AV shares due to the simplified assumptions of the estimators. This partial mismatch is also reflected in the RMSE and <italic>R</italic>
<sup>2</sup> values, for which no established benchmarks exist in this context. Therefore, our assessment of estimator performance focuses on relative differences and qualitative trends within the observed results. However, the estimator <monospace>max</monospace> performs best in comparison to the simulation results, substantiating our suspicion that the maxima in time headway increments dominate ToC-related capacity effects. Nevertheless, the overall findings from <xref ref-type="fig" rid="F12">Figures 12</xref>, <xref ref-type="fig" rid="F13">13</xref> highlight the potential ToC effects on capacity reductions across various scenarios and parameter dependencies, in line with the stated expectations.</p>
</sec>
<sec sec-type="conclusion" id="s6">
<title>6 Conclusion</title>
<p>To investigate ToC-related capacity reductions, we conducted comprehensive simulation experiments with a calibrated two-lane highway scenario, as well as numerical experiments to estimate the large-scale impact of time headway increments during consecutive control transitions. Our main findings can be summarized as follows: (i) capacity reductions of up to <inline-formula id="inf172">
<mml:math id="m173">
<mml:mrow>
<mml:mn>2000</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>veh/h</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>, corresponding to approximately <inline-formula id="inf173">
<mml:math id="m174">
<mml:mrow>
<mml:mn>60</mml:mn>
<mml:mi>%</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> loss, were observed in shares with near-full Level 3 automation but no traffic management coordination; (ii) ToC effects became notably impactful starting from a Level 3 share of <inline-formula id="inf174">
<mml:math id="m175">
<mml:mrow>
<mml:mn>10</mml:mn>
<mml:mi>%</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> to <inline-formula id="inf175">
<mml:math id="m176">
<mml:mrow>
<mml:mn>20</mml:mn>
<mml:mi>%</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>; (iii) a coordination of ToCs could mitigate losses by roughly <inline-formula id="inf176">
<mml:math id="m177">
<mml:mrow>
<mml:mn>1000</mml:mn>
<mml:mtext>&#x2003;</mml:mtext>
<mml:mtext>veh/h</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula> or <inline-formula id="inf177">
<mml:math id="m178">
<mml:mrow>
<mml:mn>30</mml:mn>
<mml:mi>%</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>; (iv) binding Level 3 operation to the rightmost lane resulted in the most severe reduction, with up to <inline-formula id="inf178">
<mml:math id="m179">
<mml:mrow>
<mml:mn>2660</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>veh/h</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula> or <inline-formula id="inf179">
<mml:math id="m180">
<mml:mrow>
<mml:mn>75</mml:mn>
<mml:mi>%</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> loss; and (v) maxima in time headway increments during ToCs emerge as the dominant factor contributing to these capacity effects.</p>
<p>Several relevant limitations should be acknowledged, as they may affect the applicability and interpretation of our findings. Recent research on data from Level 4 AVs reveals reduced time headways when MVs follow AVs (<xref ref-type="bibr" rid="B15">Jiao et al., 2024</xref>). Such effects, which might also apply to Level 3 systems, are not considered in this study. An additional aspect that has not yet been discussed is the impact of human response times for non-emergency ToCs. Throughout this investigation, the response time distribution was kept the same, at <inline-formula id="inf180">
<mml:math id="m181">
<mml:mrow>
<mml:mi>&#x3bc;</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>7</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>s</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula> in all simulations, in line with our previous studies. More recent data from real-world tests presented by <xref ref-type="bibr" rid="B24">Pipkorn et al. (2023)</xref> indicate response times closer to 5 s, from which the authors infer that a lead time of <inline-formula id="inf181">
<mml:math id="m182">
<mml:mrow>
<mml:mn>10</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>s</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>, as specified in the R157, should be feasible for human drivers to take over in time. In our simulations, a few random sample reruns with these lower response times indicated approximately 10&#x2013;<inline-formula id="inf182">
<mml:math id="m183">
<mml:mrow>
<mml:mn>20</mml:mn>
<mml:mi>%</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> higher capacities compared to the results presented here. A further limiting factor might be SUMO&#x2019;s ACC model, which is parametrized for full string stability and deployed here as a proxy for Level 3 automated vehicles, although experimental studies and theoretical work have demonstrated string instabilities in ACC-equipped platoons, as we also discussed in <xref ref-type="bibr" rid="B2">Alms and Wagner (2024)</xref>. All these limitations could potentially affect traffic capacity, though their precise contribution cannot be reliably quantified at this stage.</p>
<p>Future work should therefore include the development of a more accurate Level 3 model in SUMO, for example, an ACC-based ALKS system, as well as a systematic investigation of how model assumptions and human response variability together affect traffic capacity. Another important direction is to further examine the effects of MRMs, which are relevant for failed Level 3 transitions and Level 4 automation, on overall traffic, especially if they are not managed properly.</p>
<p>Lastly, we would like to reflect on the broader capacity implications of AVs. Our overall vehicle parametrization inherently results in slightly reduced theoretical capacities&#x2014;even without ToCs&#x2014;due to the implementation of lower time headways for MVs and higher ones for AVs, which contrasts with assumptions commonly made in other studies. While experimental research has demonstrated counterbalancing effects at high AV shares, which our own simulations also imply, this effect is diminished in the context of Level 3 systems. Unlike Level 4 or CACC-equipped vehicles, Level 3 automation, in its current form, does not typically support the low time headways often assumed to contribute to capacity gains. However, practical capacity impacts at relevant market penetration rates between 10% and 20% are likely still many years away, leaving room for further technical and regulatory development of Level 3 systems. Yet, in combination with the ToC-related capacity constraints demonstrated in this study, we take a more cautious view and do not share the seemingly widespread optimism regarding beneficial capacity effects of AVs in the mid-term.</p>
</sec>
</body>
<back>
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<title>Data availability statement</title>
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<title>Author contributions</title>
<p>RA: Conceptualization, Data curation, Formal Analysis, Investigation, Methodology, Software, Validation, Visualization, Writing &#x2013; original draft, Writing &#x2013; review and editing. PW: Conceptualization, Methodology, Supervision, Writing &#x2013; review and editing.</p>
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<ref-list>
<title>References</title>
<ref id="B1">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Alms</surname>
<given-names>R.</given-names>
</name>
<name>
<surname>Noulis</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Mintsis</surname>
<given-names>E.</given-names>
</name>
<name>
<surname>L&#xfc;cken</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Wagner</surname>
<given-names>P.</given-names>
</name>
</person-group> (<year>2022</year>). <article-title>Reinforcement learning-based traffic control: mitigating the adverse impacts of control transitions</article-title>. <source>IEEE Open J. Intelligent Transp. Syst.</source> <volume>3</volume>, <fpage>187</fpage>&#x2013;<lpage>198</lpage>. <pub-id pub-id-type="doi">10.1109/OJITS.2022.3158688</pub-id>
</citation>
</ref>
<ref id="B2">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Alms</surname>
<given-names>R.</given-names>
</name>
<name>
<surname>Wagner</surname>
<given-names>P.</given-names>
</name>
</person-group> (<year>2024</year>). <article-title>Control transitions in level 3 automation: safety implications in mixed-autonomy traffic</article-title>. <source>Safety</source> <volume>10</volume>, <fpage>1</fpage>. <pub-id pub-id-type="doi">10.3390/safety10010001</pub-id>
</citation>
</ref>
<ref id="B3">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Alvarez Lopez</surname>
<given-names>P.</given-names>
</name>
<name>
<surname>Banse</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Barthauer</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Behrisch</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Cou&#xe9;raud</surname>
<given-names>B.</given-names>
</name>
<name>
<surname>Erdmann</surname>
<given-names>J.</given-names>
</name>
<etal/>
</person-group> (<year>2025</year>). <article-title>Simulation of urban mobility (SUMO)</article-title>. <pub-id pub-id-type="doi">10.5281/zenodo.14796685</pub-id>
</citation>
</ref>
<ref id="B4">
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Alvarez Lopez</surname>
<given-names>P.</given-names>
</name>
<name>
<surname>Behrisch</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Bieker-Walz</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Erdmann</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Fl&#xf6;tter&#xf6;d</surname>
<given-names>Y.-P.</given-names>
</name>
<name>
<surname>Hilbrich</surname>
<given-names>R.</given-names>
</name>
<etal/>
</person-group> (<year>2018</year>). &#x201c;<article-title>Microscopic traffic simulation using SUMO</article-title>,&#x201d; in <source>
<italic>The 21st IEEE International Conference on Intelligent Transportation systems</italic> (IEEE)</source>, <fpage>2575</fpage>&#x2013;<lpage>2582</lpage>.</citation>
</ref>
<ref id="B5">
<citation citation-type="journal">
<collab>BASt</collab> (<year>2021</year>). <article-title>
<italic>Road Traffic Census Report 2021 - Ergebnisbericht der Stra&#xdf;enverkehrsz&#xe4;hlung 2021</italic>. Tech. rep</article-title>. <source>Fed. Highw. Res. Inst. (BASt)</source>.</citation>
</ref>
<ref id="B6">
<citation citation-type="book">
<collab>BASt</collab> (<year>2025</year>). <source>Stra&#xdf;enverkehrsz&#xe4;hlung &#x2013; verkehrsdatenbank</source>.</citation>
</ref>
<ref id="B7">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Bolovinou</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Anagnostopoulou</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Roungas</surname>
<given-names>V.</given-names>
</name>
<name>
<surname>Amditis</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Gonz&#xe1;lez</surname>
<given-names>R. B.</given-names>
</name>
<name>
<surname>Coello</surname>
<given-names>L. T.</given-names>
</name>
<etal/>
</person-group> (<year>2023</year>). <article-title>HI-DRIVE Deliverable D3.1/Use cases definition and description</article-title>. <source>Tech. Rep. Eur. Comm.</source>
</citation>
</ref>
<ref id="B8">
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Brilon</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Geistefeldt</surname>
<given-names>J.</given-names>
</name>
</person-group> (<year>2010</year>). <source>
<italic>&#xdc;berpr&#xfc;fung der Bemessungswerte des HBS f&#xfc;r Autobahnabschnitte au&#xdf;erhalb der Knotenpunkte</italic>, vol. 1033 of <italic>Forschung Stra&#xdf;enbau und Stra&#xdf;enverkehrstechnik</italic>
</source>. <publisher-loc>Bremerhaven, Germany</publisher-loc>: <publisher-name>Wirtschaftsverl. NW Verl. f&#xfc;r neue Wissenschaft</publisher-name>.</citation>
</ref>
<ref id="B9">
<citation citation-type="book">
<collab>British Standards Institution</collab> (<year>2020</year>). <source>PAS 1883:2020 - operational design domain (ODD) taxonomy for automated driving systems (ADS) &#x2013; specification</source>. <publisher-loc>London, UK</publisher-loc>: <publisher-name>British Standards Institution</publisher-name>.</citation>
</ref>
<ref id="B10">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Calvert</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>van Arem</surname>
<given-names>B.</given-names>
</name>
</person-group> (<year>2020</year>). <article-title>A generic multi-level framework for microscopic traffic simulation with automated vehicles in mixed traffic</article-title>. <source>Transp. Res. Part C Emerg. Technol.</source> <volume>110</volume>, <fpage>291</fpage>&#x2013;<lpage>311</lpage>. <pub-id pub-id-type="doi">10.1016/j.trc.2019.11.019</pub-id>
</citation>
</ref>
<ref id="B11">
<citation citation-type="book">
<collab>Digitale Plattform Stadtverkehr Berlin</collab> (<year>2024</year>). <source>Verkehrsdetektion berlin</source>.</citation>
</ref>
<ref id="B12">
<citation citation-type="book">
<collab>FGSV</collab> (<year>2015</year>). <source>Handbuch f&#xfc;r die Bemessung von Stra&#xdf;enverkehrsanlagen: HBS 2015. No. FGSV 299 B in FGSV W1 - Wissensdokumente</source> (<publisher-loc>Cologne, Germany</publisher-loc>: <publisher-name>FGSV-Verl</publisher-name>). <edition>2015 Edn</edition>.</citation>
</ref>
<ref id="B13">
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Friedrich</surname>
<given-names>B.</given-names>
</name>
</person-group> (<year>2016</year>). <source>The effect of autonomous vehicles on traffic</source>. <publisher-loc>Berlin, Heidelberg</publisher-loc>: <publisher-name>Springer Berlin Heidelberg</publisher-name>, <fpage>317</fpage>&#x2013;<lpage>334</lpage>. <pub-id pub-id-type="doi">10.1007/978-3-662-48847-8_16</pub-id>
</citation>
</ref>
<ref id="B14">
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Geistefeldt</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Giuliani</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Busch</surname>
<given-names>F.</given-names>
</name>
<name>
<surname>Schendzielorz</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Haug</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Vortisch</surname>
<given-names>P.</given-names>
</name>
<etal/>
</person-group> (<year>2017</year>). &#x201c;<article-title>HBS-conform simulation of freeway traffic flow</article-title>,&#x201d; in <source>vol. 279 of Berichte der Bundesanstalt f&#xfc;r Stra&#xdf;en- und Verkehrswesen, Reihe V: Verkehrstechnik</source> (<publisher-loc>Germany</publisher-loc>: <publisher-name>Federal Highway Research Institute</publisher-name>).</citation>
</ref>
<ref id="B15">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Jiao</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>G.</given-names>
</name>
<name>
<surname>Calvert</surname>
<given-names>S. C.</given-names>
</name>
<name>
<surname>van Cranenburgh</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>van Lint</surname>
<given-names>H.</given-names>
</name>
</person-group> (<year>2024</year>). <article-title>Beyond behavioural change: investigating alternative explanations for shorter time headways when human drivers follow automated vehicles</article-title>. <source>Transp. Res. Part C Emerg. Technol.</source> <volume>164</volume>, <fpage>104673</fpage>. <pub-id pub-id-type="doi">10.1016/j.trc.2024.104673</pub-id>
</citation>
</ref>
<ref id="B16">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Kohanpour</surname>
<given-names>E.</given-names>
</name>
<name>
<surname>Davoodi</surname>
<given-names>S. R.</given-names>
</name>
<name>
<surname>Shaaban</surname>
<given-names>K.</given-names>
</name>
</person-group> (<year>2025</year>). <article-title>Trends in autonomous vehicle performance: a comprehensive study of disengagements and mileage</article-title>. <source>Future Transp.</source> <volume>5</volume>, <fpage>38</fpage>. <pub-id pub-id-type="doi">10.3390/futuretransp5020038</pub-id>
</citation>
</ref>
<ref id="B17">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Liu</surname>
<given-names>Q.</given-names>
</name>
<name>
<surname>Gao</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Cai</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Lv</surname>
<given-names>C.</given-names>
</name>
</person-group> (<year>2024</year>). <article-title>Learning from trajectories: how heterogeneous CACC platoons affect the traffic flow in highway merging area</article-title>. <source>IEEE Trans. Veh. Technol.</source> <volume>73</volume>, <fpage>16212</fpage>&#x2013;<lpage>16224</lpage>. <pub-id pub-id-type="doi">10.1109/TVT.2024.3419143</pub-id>
</citation>
</ref>
<ref id="B18">
<citation citation-type="confproc">
<person-group person-group-type="author">
<name>
<surname>L&#xfc;cken</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Mintsis</surname>
<given-names>E.</given-names>
</name>
<name>
<surname>Porfyri</surname>
<given-names>K.</given-names>
</name>
<name>
<surname>Alms</surname>
<given-names>R.</given-names>
</name>
<name>
<surname>Fl&#xf6;tter&#xf6;d</surname>
<given-names>Y.-P.</given-names>
</name>
<name>
<surname>Koutras</surname>
<given-names>D.</given-names>
</name>
</person-group> (<year>2019</year>). &#x201c;<article-title>From automated to manual - modeling control transitions with SUMO</article-title>,&#x201d;in <conf-name>SUMO user conference 2019</conf-name>. Editors <person-group person-group-type="editor">
<name>
<surname>Weber</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Bieker-Walz</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Hilbrich</surname>
<given-names>R.</given-names>
</name>
<name>
<surname>Behrisch</surname>
<given-names>M.</given-names>
</name>
</person-group> (<publisher-loc>Stockport, United Kingdom</publisher-loc>: <publisher-name>EPiC Series in Computing</publisher-name>), <volume>62</volume>, <fpage>124</fpage>&#x2013;<lpage>144</lpage>. <pub-id pub-id-type="doi">10.29007/sfgk</pub-id>
</citation>
</ref>
<ref id="B19">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Maerivoet</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Akkermans</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Carlier</surname>
<given-names>K.</given-names>
</name>
<name>
<surname>Fl&#xf6;tter&#xf6;d</surname>
<given-names>Y.-P.</given-names>
</name>
<name>
<surname>L&#xfc;cken</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Alms</surname>
<given-names>R.</given-names>
</name>
<etal/>
</person-group> (<year>2019</year>). <article-title>TransAID Deliverable 4.2 - preliminary simulation and assessment of enhanced traffic management measures</article-title>. <source>Tech. Rep. Eur. Comm.</source>
</citation>
</ref>
<ref id="B20">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>McDonald</surname>
<given-names>A. D.</given-names>
</name>
<name>
<surname>Alambeigi</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Engstr&#xf6;m</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Markkula</surname>
<given-names>G.</given-names>
</name>
<name>
<surname>Vogelpohl</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Dunne</surname>
<given-names>J.</given-names>
</name>
<etal/>
</person-group> (<year>2019</year>). <article-title>Toward computational simulations of behavior during automated driving takeovers: a review of the empirical and modeling literature</article-title>. <source>Hum. Factors</source> <volume>61</volume>, <fpage>642</fpage>&#x2013;<lpage>688</lpage>. <pub-id pub-id-type="doi">10.1177/0018720819829572</pub-id>
</citation>
</ref>
<ref id="B21">
<citation citation-type="journal">
<collab>Mercedes-Benz Group</collab> (<year>2024</year>). <article-title>Mercedes-Benz is approved for 95 km/h Level 3 autonomous driving in Germany</article-title>. <source>Tech. Rep. Mercedes Benz Group</source>.</citation>
</ref>
<ref id="B22">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Mintsis</surname>
<given-names>E.</given-names>
</name>
<name>
<surname>Koutras</surname>
<given-names>D.</given-names>
</name>
<name>
<surname>Porfyri</surname>
<given-names>K.</given-names>
</name>
<name>
<surname>Mitsakis</surname>
<given-names>E.</given-names>
</name>
<name>
<surname>L&#xfc;cken</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Erdmann</surname>
<given-names>J.</given-names>
</name>
<etal/>
</person-group> (<year>2019</year>). <article-title>TransAID Deliverable 3.1 - modelling, simulation and assessment of vehicle automations and automated vehicles&#x2019; driver behaviour in mixed traffic</article-title>. <source>Tech. Rep. Eur. Comm.</source>
</citation>
</ref>
<ref id="B23">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Park</surname>
<given-names>J. E.</given-names>
</name>
<name>
<surname>Byun</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Kim</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Ahn</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Shin</surname>
<given-names>D. K.</given-names>
</name>
</person-group> (<year>2021</year>). <article-title>The impact of automated vehicles on traffic flow and road capacity on urban road networks</article-title>. <source>J. Adv. Transp.</source> <volume>2021</volume>, <fpage>1</fpage>&#x2013;<lpage>10</lpage>. <pub-id pub-id-type="doi">10.1155/2021/8404951</pub-id>
</citation>
</ref>
<ref id="B24">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Pipkorn</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Tivesten</surname>
<given-names>E.</given-names>
</name>
<name>
<surname>Flannagan</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Dozza</surname>
<given-names>M.</given-names>
</name>
</person-group> (<year>2023</year>). <article-title>Driver response to take-over requests in real traffic</article-title>. <source>IEEE Trans. Human Mach. Syst.</source> <volume>53</volume>, <fpage>823</fpage>&#x2013;<lpage>833</lpage>. <pub-id pub-id-type="doi">10.1109/THMS.2023.3304003</pub-id>
</citation>
</ref>
<ref id="B25">
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Rummel</surname>
<given-names>J.</given-names>
</name>
</person-group> (<year>2017</year>). <source>Replication of the hbs autobahn with sumo</source>. <comment>Berichte aus dem DLR-Institut f&#xfc;r Verkehrssystemtechnik</comment>, <publisher-loc>Berlin, Germany</publisher-loc>: <publisher-name>Institute of Transportation Systems, German Aerospace Center</publisher-name> <fpage>171</fpage>&#x2013;<lpage>178</lpage>.</citation>
</ref>
<ref id="B26">
<citation citation-type="journal">
<collab>SAE International</collab> (<year>2021</year>). <article-title>SAE international recommended practice: taxonomy and definitions for terms related to driving automation systems for on-road motor vehicles</article-title>. <source>SAE Int.</source> <pub-id pub-id-type="doi">10.4271/J3016_202104</pub-id>
</citation>
</ref>
<ref id="B27">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Sauvaget</surname>
<given-names>J.-L.</given-names>
</name>
<name>
<surname>Dakil</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Griffon</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Anagnostopoulou</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Bolovinou</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Sintonen</surname>
<given-names>H.</given-names>
</name>
<etal/>
</person-group> (<year>2023</year>). <article-title>HI-DRIVE deliverable D5.1/descriptions of &#x201c;operations&#x201d;</article-title>. <source>Tech. Rep. Eur. Comm.</source>
</citation>
</ref>
<ref id="B28">
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Schrader</surname>
<given-names>M.</given-names>
</name>
</person-group> (<year>2024</year>). <source>Calibrating traffic microsimulation for optimization of intelligent transportation systems using roadside radar</source>. <publisher-loc>Tuscaloosa, AL</publisher-loc>: <publisher-name>The University of Alabama</publisher-name>. <comment>Ph.d. thesis</comment>.</citation>
</ref>
<ref id="B29">
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Schulte-Tigges</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Matheis</surname>
<given-names>D.</given-names>
</name>
<name>
<surname>Reke</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Walter</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Kaszner</surname>
<given-names>D.</given-names>
</name>
</person-group> (<year>2023</year>). &#x201c;<article-title>Demonstrating a V2X enabled system for transition of control and minimum risk manoeuvre when leaving the operational design domain</article-title>,&#x201d; in <source>HCI in mobility, transport, and automotive systems</source>. Editor <person-group person-group-type="editor">
<name>
<surname>Kr&#xf6;mker</surname>
<given-names>H.</given-names>
</name>
</person-group> (<publisher-loc>Cham</publisher-loc>: <publisher-name>Springer Nature Switzerland</publisher-name>), <fpage>200</fpage>&#x2013;<lpage>210</lpage>. <pub-id pub-id-type="doi">10.1007/978-3-031-35678-0_12</pub-id>
</citation>
</ref>
<ref id="B30">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Shuttleworth</surname>
<given-names>J.</given-names>
</name>
</person-group> (<year>2019</year>). <article-title>SAE updates J3016 automated-driving graphic</article-title>. <source>Mobil. Eng.</source>
</citation>
</ref>
<ref id="B31">
<citation citation-type="journal">
<collab>TransAID</collab> (<year>2021</year>). <article-title>Transition areas for infrastructure-assisted driving (TransAID)</article-title>. <source>H2020 Res. Proj. 723390, Eur. Comm.</source>
</citation>
</ref>
<ref id="B32">
<citation citation-type="journal">
<collab>UNECE</collab> (<year>2023</year>). <article-title>Addendum 156 &#x2013; UN regulation No. 157 - amendment 4 - uniform provisions concerning the approval of vehicles with regard to automated lane keeping systems</article-title>. <source>Tech. Rep.</source> <comment>United Nations Economic commission for Europe</comment>.</citation>
</ref>
<ref id="B33">
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Van Aerde</surname>
<given-names>M.</given-names>
</name>
</person-group> (<year>1995</year>). &#x201c;<article-title>A single regime speed-flow-density relationship for freeways and arterials</article-title>,&#x201d; in <source>74th annual meeting of the transportation research board</source>. <comment>Preprint paper no. 950802</comment>.</citation>
</ref>
<ref id="B34">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Van Lint</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Calvert</surname>
<given-names>S. C.</given-names>
</name>
</person-group> (<year>2018</year>). <article-title>A generic multi-level framework for microscopic traffic simulation&#x2014;theory and an example case in modelling driver distraction</article-title>. <source>Transp. Res. Part B Methodol.</source> <volume>117</volume>, <fpage>63</fpage>&#x2013;<lpage>86</lpage>. <pub-id pub-id-type="doi">10.1016/j.trb.2018.08.009</pub-id>
</citation>
</ref>
<ref id="B35">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Wagner</surname>
<given-names>P.</given-names>
</name>
</person-group> (<year>2012</year>). <article-title>Analyzing fluctuations in car-following</article-title>. <source>Transp. Res. Part B Methodol.</source> <volume>46</volume>, <fpage>1384</fpage>&#x2013;<lpage>1392</lpage>. <pub-id pub-id-type="doi">10.1016/j.trb.2012.06.007</pub-id>
</citation>
</ref>
<ref id="B36">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Wang</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Ren</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Xu</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Zheng</surname>
<given-names>N.</given-names>
</name>
<name>
<surname>Peng</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Tong</surname>
<given-names>H.</given-names>
</name>
</person-group> (<year>2024</year>). <article-title>Exploring the impact of conditionally automated driving vehicles transferring control to human drivers on the stability of heterogeneous traffic flow</article-title>. <source>IEEE Trans. Intel. Veh.</source>, <fpage>1</fpage>&#x2013;<lpage>17</lpage>. <pub-id pub-id-type="doi">10.1109/TIV.2024.3419789</pub-id>
</citation>
</ref>
<ref id="B37">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Wang</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Xu</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Peng</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Tong</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Ren</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>and</surname>
<given-names>Y. J.</given-names>
</name>
</person-group> (<year>2025a</year>). <article-title>Predicting the duration of reduced driver performance during the automated driving takeover process</article-title>. <source>J. Intel. Transp. Syst.</source> <volume>29</volume>, <fpage>218</fpage>&#x2013;<lpage>233</lpage>. <pub-id pub-id-type="doi">10.1080/15472450.2024.2307029</pub-id>
</citation>
</ref>
<ref id="B38">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Wang</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Xu</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Shao</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Zheng</surname>
<given-names>N.</given-names>
</name>
<name>
<surname>Peng</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Tong</surname>
<given-names>H.</given-names>
</name>
<etal/>
</person-group> (<year>2025b</year>). <article-title>Identifying factors affecting driver takeover time and crash risk during the automated driving takeover process</article-title>. <source>J. Transp. Saf. Secur.</source> <volume>0</volume>, <fpage>1</fpage>&#x2013;<lpage>26</lpage>. <pub-id pub-id-type="doi">10.1080/19439962.2025.2450695</pub-id>
</citation>
</ref>
<ref id="B39">
<citation citation-type="confproc">
<person-group person-group-type="author">
<name>
<surname>Ward</surname>
<given-names>T.</given-names>
</name>
</person-group> (<year>2024</year>). &#x201c;<article-title>Areas of improvement for autonomous vehicles: a machine learning analysis of disengagement reports</article-title>,&#x201d; in <conf-name>2024 International Conference on Electrics and Computer (INTCEC)</conf-name>. <comment>ArXiv:2408.00051</comment>.</citation>
</ref>
<ref id="B40">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Xiao</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>van Arem</surname>
<given-names>B.</given-names>
</name>
</person-group> (<year>2017</year>). <article-title>Realistic car-following models for microscopic simulation of adaptive and cooperative adaptive cruise control vehicles</article-title>. <source>Transp. Res. Rec.</source> <volume>2623</volume>, <fpage>1</fpage>&#x2013;<lpage>9</lpage>. <pub-id pub-id-type="doi">10.3141/2623-01</pub-id>
</citation>
</ref>
</ref-list>
</back>
</article>