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class="vector-toc-list"> <li id="toc-Different_measures" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Different_measures"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Different measures</span> </div> </a> <ul id="toc-Different_measures-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Railway_examples" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Railway_examples"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Railway examples</span> </div> </a> <ul id="toc-Railway_examples-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_examples" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Other_examples"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Other examples</span> </div> </a> <ul id="toc-Other_examples-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Low-headway_systems" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Low-headway_systems"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Low-headway systems</span> </div> </a> <ul id="toc-Low-headway_systems-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Headway_and_route_capacity" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Headway_and_route_capacity"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Headway and route capacity</span> </div> </a> <button aria-controls="toc-Headway_and_route_capacity-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Headway and route capacity subsection</span> </button> <ul id="toc-Headway_and_route_capacity-sublist" class="vector-toc-list"> <li id="toc-Minimum_safe_headway" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Minimum_safe_headway"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Minimum safe headway</span> </div> </a> <ul id="toc-Minimum_safe_headway-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Capacity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Capacity"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Capacity</span> </div> </a> <ul id="toc-Capacity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Examples" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Examples"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Examples</span> </div> </a> <ul id="toc-Examples-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Headways_and_ridership" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Headways_and_ridership"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Headways and ridership</span> </div> </a> <ul id="toc-Headways_and_ridership-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>References</span> </div> </a> <button aria-controls="toc-References-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle References subsection</span> </button> <ul id="toc-References-sublist" class="vector-toc-list"> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Notes"> <div 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.hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">This article is about the transportation term. For other uses, see <a href="/wiki/Headway_(disambiguation)" class="mw-disambig" title="Headway (disambiguation)">Headway (disambiguation)</a>.</div> <p><b>Headway</b> is the distance or duration between vehicles in a transit system measured in space or time. The <i>minimum headway</i> is the shortest such distance or time achievable by a system without a reduction in the speed of vehicles. The precise definition varies depending on the application, but it is most commonly measured as the distance from the tip (front end) of one vehicle to the tip of the next one behind it. It can be expressed as the distance between vehicles, or as time it will take for the trailing vehicle to cover that distance. A "shorter" headway signifies closer spacing between the vehicles. <a href="/wiki/Airplane" title="Airplane">Airplanes</a> operate with headways measured in hours or days, <a href="/wiki/Freight_train" title="Freight train">freight trains</a> and <a href="/wiki/Commuter_rail" title="Commuter rail">commuter rail</a> systems might have headways measured in parts of an hour, <a href="/wiki/Rapid_transit" title="Rapid transit">metro</a> and <a href="/wiki/Light_rail" title="Light rail">light rail</a> systems operate with headways on the order of 90 seconds to 20 minutes, and vehicles on a <a href="/wiki/Freeway" class="mw-redirect" title="Freeway">freeway</a> can have as little as 2 seconds headway between them. </p><p>Headway is a key input in calculating the overall <a href="/wiki/Route_capacity" title="Route capacity">route capacity</a> of any transit system. A system that requires large headways has more empty space than passenger capacity, which lowers the total number of passengers or cargo quantity being transported for a given length of line (railroad or highway, for instance). In this case, the capacity has to be improved through the use of larger vehicles. On the other end of the scale, a system with short headways, like cars on a freeway, can offer relatively large capacities even though the vehicles carry few passengers. </p><p>The term is most often applied to <a href="/wiki/Rail_transport" title="Rail transport">rail transport</a> and <a href="/wiki/Bus_transport" class="mw-redirect" title="Bus transport">bus transport</a>, where low headways are often needed to move large numbers of people in mass transit railways and <a href="/wiki/Bus_rapid_transit" title="Bus rapid transit">bus rapid transit</a> systems. A lower headway requires more infrastructure, making lower headways expensive to achieve. Modern large cities require passenger rail systems with tremendous capacity, and low headways allow passenger demand to be met in all but the busiest cities. Newer signalling systems and <a href="/wiki/Moving_block_signalling" class="mw-redirect" title="Moving block signalling">moving block</a> controls have significantly reduced headways in modern systems compared to the same lines only a few years ago. In principle, automated <a href="/wiki/Personal_rapid_transit" title="Personal rapid transit">personal rapid transit</a> systems and <a href="/wiki/Platoon_(automobile)" title="Platoon (automobile)">automobile platoons</a> could reduce headways to as little as fractions of a second. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Description">Description</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Headway&action=edit&section=1" title="Edit section: Description"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Different_measures">Different measures</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Headway&action=edit&section=2" title="Edit section: Different measures"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>There are a number of different ways to measure and express the same concept, the distance between vehicles. The differences are largely due to historical development in different countries or fields. </p><p>The term developed from railway use, where the distance between the trains was very great compared to the length of the train itself. Measuring headway from the front of one train to the front of the next was simple and consistent with timetable scheduling of trains, but constraining tip-to-tip headway does not always ensure safety. In the case of a metro system, train lengths are uniformly short and the headway allowed for stopping is much longer, so tip-to-tip headway may be used with a minor safety factor. Where vehicle size varies and may be longer than their stopping distances or spacing, as with freight trains and highway applications, tip-to-tail measurements are more common. </p><p>The units of measure also vary. The most common terminology is to use the time of passing from one vehicle to the next, which closely mirrors the way the headways were measured in the past. A timer is started when one train passes a point, and then measures time until the next one passes, giving the tip-to-tip time. This same measure can also be expressed in terms of vehicles-per-hour, which is used on the <a href="/wiki/Moscow_Metro" title="Moscow Metro">Moscow Metro</a> for instance.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Distance measurements are somewhat common in non-train applications, like vehicles on a road, but time measurements are common here as well. </p> <div class="mw-heading mw-heading3"><h3 id="Railway_examples">Railway examples</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Headway&action=edit&section=3" title="Edit section: Railway examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:3_aspect_headway.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/19/3_aspect_headway.jpg/550px-3_aspect_headway.jpg" decoding="async" width="550" height="130" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/19/3_aspect_headway.jpg/825px-3_aspect_headway.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/19/3_aspect_headway.jpg/1100px-3_aspect_headway.jpg 2x" data-file-width="3882" data-file-height="916" /></a><figcaption>An example of headway on a railway system with multiple block section. Train B can only enter a section with a green or yellow "aspect" (light), and must reduce speed when passing a yellow signal to the point where they can stop within the sighting distance.</figcaption></figure> <p>Train movements in most rail systems are tightly controlled by <a href="/wiki/Railway_signalling" title="Railway signalling">railway signalling</a> systems. In many railways drivers are given instructions on speeds, and routes through the rail network. <a href="/wiki/Train" title="Train">Trains</a> can only accelerate and decelerate relatively slowly, so stopping from anything but low speeds requires several hundred metres or even more. The track distance required to stop is often much longer than the range of the driver's vision. If the track ahead is obstructed, for example a train is at stop there, then the train behind it will probably see it far too late to avoid a collision. </p><p>Signalling systems serve to provide drivers with information on the state of the track ahead, so that a collision may be avoided. A side effect of this important safety function is that the headway of any rail system is effectively determined by the structure of the signalling system, and particularly the spacing between signals and the amount of information that can be provided in the signal. Rail system headways can be calculated from the signalling system. In practice there are a variety of different methods of keeping trains apart, some which are manual such as train order working or systems involving telegraphs, and others which rely entirely on signalling infrastructure to regulate train movements. Manual systems of working trains are common in area with low numbers of train movements, and headways are more often discussed in the context of non-manual systems. </p><p>For <a href="/wiki/Automatic_block_signalling" class="mw-redirect" title="Automatic block signalling">automatic block signalling</a> (ABS), the headway is measured in minutes, and calculated from the time from the passage of a train to when the signalling system returns to full clear (proceed). It is not normally measured tip to tip. An ABS system divides the track into block sections, into which only one train can enter at a time. Commonly trains are kept two to three block sections apart, depending on how the signalling system is designed, and so the length of the block section will often determine the headway. </p><p>To have visual contact as a method to avoid collision (such as during <a href="/wiki/Shunting_(rail)" title="Shunting (rail)">shunting</a>) is done only at low speeds, like 40 km/h. A key safety factor of train operations is to space the trains out by at least this distance, the "brick-wall stop" criterion.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> In order to signal the trains in time to allow them to stop, the railways placed workmen on the lines who timed the passing of a train, and then signalled any following trains if a certain elapsed time had not passed. This is why train headways are normally measured as tip-to-tip times, because the clock was reset as the engine passed the workman. </p><p>As remote signalling systems were invented, the workmen were replaced with signal towers at set locations along the track. This broke the track into a series of block sections between the towers. Trains were not allowed to enter a section until the signal said it was clear. This had the side-effect of limiting the maximum speed of the trains to the speed where they could stop in the distance of one block section. This was an important consideration for the <a href="/wiki/Advanced_Passenger_Train" title="Advanced Passenger Train">Advanced Passenger Train</a> in the <a href="/wiki/United_Kingdom" title="United Kingdom">United Kingdom</a>, where the lengths of block sections limited speeds and demanded a new braking system be developed.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>There is no perfect block-section size for the block-control approach. Longer sections, using as few signals as possible, are advantageous because signals are expensive and are points of failure, and they allow higher speeds because the trains have more room to stop. On the other hand, they also increase the headway, and thus reduce the overall capacity of the line. These needs have to be balanced on a case-by-case basis.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Other_examples">Other examples</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Headway&action=edit&section=4" title="Edit section: Other examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the case of automobile traffic, the key consideration in braking performance is the user's reaction time.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Unlike the train case, the stopping distance is generally much shorter than the spotting distance. That means that the driver will be matching their speed to the vehicle in front before they reach it, eliminating the "brick-wall" effect. </p><p>Widely used numbers are that a car traveling at 60 mph will require about 225 feet to stop, a distance it will cover just under 6 seconds. Nevertheless, highway travel often occurs with considerable safety with tip-to-tail headways on the order of 2 seconds. That's because the user's reaction time is about 1.5 seconds so 2 seconds allows for a slight overlap that makes up for any difference in braking performance between the two cars. </p><p>Various <a href="/wiki/Personal_rapid_transit" title="Personal rapid transit">personal rapid transit</a> systems in the 1970s considerably reduced the headways compared to earlier rail systems. Under computer control, reaction times can be reduced to fractions of a second. Whether traditional headway regulations should apply to PRT and car train technology is debatable. In the case of the <a href="/wiki/Cabinentaxi" title="Cabinentaxi">Cabinentaxi</a> system developed in <a href="/wiki/Germany" title="Germany">Germany</a>, headways were set to 1.9 seconds because the developers were forced to adhere to the brick-wall criterion. In experiments, they demonstrated headways on the order of half of a second.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>In 2017, in the UK, 66% of cars and Light Commercial Vehicles, and 60% of motorcycles left the recommended two-second gap between themselves and other vehicles.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Notice plainlinks metadata ambox ambox-notice" role="presentation" style="width:100%;margin:0;"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/1/1d/Information_icon4.svg/40px-Information_icon4.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/1/1d/Information_icon4.svg/60px-Information_icon4.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/1/1d/Information_icon4.svg/80px-Information_icon4.svg.png 2x" data-file-width="620" data-file-height="620" /></span></span></div></td><td class="mbox-text" style="text-align: left;"><div class="mbox-text-span">Graphs are unavailable due to technical issues. There is more info on <a href="https://phabricator.wikimedia.org/T334940" class="extiw" title="phab:T334940">Phabricator</a> and on <a href="https://www.mediawiki.org/wiki/Extension:Graph/Plans" class="extiw" title="mw:Extension:Graph/Plans">MediaWiki.org</a>.</div></td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Low-headway_systems">Low-headway systems</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Headway&action=edit&section=5" title="Edit section: Low-headway systems"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Headway spacing is selected by various safety criteria, but the basic concept remains the same – leave enough time for the vehicle to safely stop behind the vehicle in front of it. The "safely stop" criterion has a non-obvious solution, however; if a vehicle follows immediately behind the one in front, the vehicle in front simply cannot stop quickly enough to damage the vehicle behind it. An example would be a conventional train, where the vehicles are held together and have only a few millimetres of "play" in the couplings. Even when the locomotive applies emergency braking, the cars following do not suffer any damage because they quickly close the gap in the couplings before the speed difference can build up. </p><p>There have been many experiments with automated driving systems that follow this logic and greatly decrease headways to tenths or hundredths of a second in order to improve safety. Today, modern <a href="/wiki/Communication-based_train_control" class="mw-redirect" title="Communication-based train control">CBTC</a> railway signalling systems are able to significantly reduce headway between trains in the operation. Using automated "car follower" <a href="/wiki/Cruise_control" title="Cruise control">cruise control</a> systems, vehicles can be formed into <a href="/wiki/Platoon_(automobile)" title="Platoon (automobile)">platoons</a> (or flocks) that approximate the capacity of conventional trains. These systems were first employed as part of personal rapid transit research, but later using conventional cars with autopilot-like systems. </p><p><a href="/wiki/Paris_M%C3%A9tro_Line_14" title="Paris Métro Line 14">Paris Métro Line 14</a> runs with headways as low as 85 seconds,<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> while several lines of the <a href="/wiki/Moscow_Metro" title="Moscow Metro">Moscow Metro</a> have peak hour headways of 90 seconds.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Headway_and_route_capacity">Headway and route capacity</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Headway&action=edit&section=6" title="Edit section: Headway and route capacity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Route capacity is defined by three figures; the <a href="/wiki/Number_of_passengers" class="mw-redirect" title="Number of passengers">number of passengers</a> (or weight of cargo) per vehicle, the maximum safe speed of the vehicles, and the <a href="/wiki/Route_capacity" title="Route capacity">number of vehicles per unit time</a>. Since the headway factors into two of the three inputs, it is a primary consideration in capacity calculations.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> The headway, in turn, is defined by the braking performance, or some external factor based on it, like block sizes. Following the methods in Anderson:<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Minimum_safe_headway">Minimum safe headway</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Headway&action=edit&section=7" title="Edit section: Minimum safe headway"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The minimum safe headway measured tip-to-tail is defined by the braking performance: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{min}=t_{r}+{\frac {kV}{2}}\left({\frac {1}{a_{f}}}-{\frac {1}{a_{l}}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>k</mi> <mi>V</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{min}=t_{r}+{\frac {kV}{2}}\left({\frac {1}{a_{f}}}-{\frac {1}{a_{l}}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e8dbf22703c1c5b0f5a504bfa2314f3ea7fe33e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:28.812ex; height:6.176ex;" alt="{\displaystyle T_{min}=t_{r}+{\frac {kV}{2}}\left({\frac {1}{a_{f}}}-{\frac {1}{a_{l}}}\right)}"></span> </p><p>where: </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{min}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{min}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/682ab46f5599b6d94ae2308d4d0cb88390c3fd8d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.586ex; height:2.509ex;" alt="{\displaystyle T_{min}}"></span> is the minimum safe headway, in seconds</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span> is the speed of the vehicles</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t_{r}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t_{r}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a50aad1c6e0103f6f74a56aff0561f45714161a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.813ex; height:2.343ex;" alt="{\displaystyle t_{r}}"></span> is the reaction time, the maximum time it takes for a following vehicle to detect a malfunction in the leader, and to fully apply the emergency brakes.</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{f}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{f}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3eb2b84dda825421629764ce4f9f9805a9f56412" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.366ex; height:2.343ex;" alt="{\displaystyle a_{f}}"></span> is the minimum braking deceleration of the follower.</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{l}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{l}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e570d1973809ac155bf82828f02c2e4e0e8e809e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.952ex; height:2.009ex;" alt="{\displaystyle a_{l}}"></span> is the maximum braking deceleration of the leader. For brick-wall considerations, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{l}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{l}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e570d1973809ac155bf82828f02c2e4e0e8e809e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.952ex; height:2.009ex;" alt="{\displaystyle a_{l}}"></span> is infinite and this consideration is eliminated.</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}"></span> is an arbitrary safety factor, greater than or equal to 1.</li></ul> <p>The tip-to-tip headway is simply the tip-to-tail headway plus the length of the vehicle, expressed in time: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{tot}={\frac {L}{V}}+t_{r}+{\frac {kV}{2}}\left({\frac {1}{a_{f}}}-{\frac {1}{a_{l}}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mi>o</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>L</mi> <mi>V</mi> </mfrac> </mrow> <mo>+</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>k</mi> <mi>V</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{tot}={\frac {L}{V}}+t_{r}+{\frac {kV}{2}}\left({\frac {1}{a_{f}}}-{\frac {1}{a_{l}}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6df6edb484bcfec5090a2b2a4891742ea0caa3af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:33.265ex; height:6.176ex;" alt="{\displaystyle T_{tot}={\frac {L}{V}}+t_{r}+{\frac {kV}{2}}\left({\frac {1}{a_{f}}}-{\frac {1}{a_{l}}}\right)}"></span> </p><p>where: </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{tot}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mi>o</mi> <mi>t</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{tot}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7d3bc72f1fdac4f2c4abfebf49536322ef95806f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.575ex; height:2.509ex;" alt="{\displaystyle T_{tot}}"></span> time for vehicle and headway to pass a point</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103168b86f781fe6e9a4a87b8ea1cebe0ad4ede8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle L}"></span> is the vehicle length</li></ul> <div class="mw-heading mw-heading3"><h3 id="Capacity">Capacity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Headway&action=edit&section=8" title="Edit section: Capacity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The vehicular capacity of a single lane of vehicles is simply the inverse of the tip-to-tip headway. This is most often expressed in vehicles-per-hour: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{veh}={\frac {3600}{T_{min}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> <mi>e</mi> <mi>h</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3600</mn> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{veh}={\frac {3600}{T_{min}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/528049aff608d277da45b5d449f81feb1d9a42d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:12.722ex; height:5.509ex;" alt="{\displaystyle n_{veh}={\frac {3600}{T_{min}}}}"></span> </p><p>where: </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{veh}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> <mi>e</mi> <mi>h</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{veh}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/707ecbcb372f17c0fbc45f1a7e6f69702cb01c05" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.137ex; height:2.009ex;" alt="{\displaystyle n_{veh}}"></span> is the number of vehicles per hour</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{min}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{min}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/682ab46f5599b6d94ae2308d4d0cb88390c3fd8d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.586ex; height:2.509ex;" alt="{\displaystyle T_{min}}"></span> is the minimum safe headway, in seconds</li></ul> <p>The passenger capacity of the lane is simply the product of vehicle capacity and the passenger capacity of the vehicles: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{pas}=P{\frac {3600}{T_{min}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>a</mi> <mi>s</mi> </mrow> </msub> <mo>=</mo> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3600</mn> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{pas}=P{\frac {3600}{T_{min}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dac2fcfcbc49eb42fdc5b33f770246786633ac81" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:14.424ex; height:5.509ex;" alt="{\displaystyle n_{pas}=P{\frac {3600}{T_{min}}}}"></span> </p><p>where: </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{pas}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>a</mi> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{pas}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/46acc8c948b379bbbaa8d98a4828bd82742bf9f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.095ex; height:2.343ex;" alt="{\displaystyle n_{pas}}"></span> is the number of passengers per hour</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span> is the maximum passenger capacity per vehicle</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{min}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{min}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/682ab46f5599b6d94ae2308d4d0cb88390c3fd8d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.586ex; height:2.509ex;" alt="{\displaystyle T_{min}}"></span> is the minimum safe headway, in seconds</li></ul> <div class="mw-heading mw-heading3"><h3 id="Examples">Examples</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Headway&action=edit&section=9" title="Edit section: Examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Consider these examples: </p><p>1) freeway traffic, per lane: 100 km/h (~28 m/s) speeds, 4 passengers per vehicle, 4 meter vehicle length, 2.5 m/s^2 braking (1/4 <i>g</i>), 2 second reaction time, brick-wall stop, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}"></span> of 1.5; </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{tot}={\frac {4}{28}}+2+{\frac {1.5\times 28}{2}}\left({\frac {1}{2.5}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mi>o</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>4</mn> <mn>28</mn> </mfrac> </mrow> <mo>+</mo> <mn>2</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1.5</mn> <mo>×</mo> <mn>28</mn> </mrow> <mn>2</mn> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2.5</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{tot}={\frac {4}{28}}+2+{\frac {1.5\times 28}{2}}\left({\frac {1}{2.5}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72f6a79006a59c86cb0a1c0734ed61235d190c8c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:33.267ex; height:6.176ex;" alt="{\displaystyle T_{tot}={\frac {4}{28}}+2+{\frac {1.5\times 28}{2}}\left({\frac {1}{2.5}}\right)}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{pas}={P}\times {\frac {3600}{T_{tot}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>a</mi> <mi>s</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3600</mn> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mi>o</mi> <mi>t</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{pas}={P}\times {\frac {3600}{T_{tot}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/baf69cff2b70a13b4e1a04a1bf6a94262e415e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:17.265ex; height:5.509ex;" alt="{\displaystyle n_{pas}={P}\times {\frac {3600}{T_{tot}}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{tot}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mi>o</mi> <mi>t</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{tot}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7d3bc72f1fdac4f2c4abfebf49536322ef95806f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.575ex; height:2.509ex;" alt="{\displaystyle T_{tot}}"></span> = 10.5 seconds ; <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{pas}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>a</mi> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{pas}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/46acc8c948b379bbbaa8d98a4828bd82742bf9f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.095ex; height:2.343ex;" alt="{\displaystyle n_{pas}}"></span> = 7,200 passengers per hour if 4 people per car and 2 seconds headway is assumed, or 342 passengers per hour if 1 person per car and 10,5 seconds headway is assumed.</dd></dl> <p>The headway used in reality is much less than 10.5 seconds, since the brick-wall principle is not used on freeways. In reality, 1.5 persons per car and 2 seconds headway can be assumed, giving 1800 cars or 2700 passengers per lane and hour. </p><p>For comparison, the <a href="/wiki/Marin_County,_California" title="Marin County, California">Marin County, California</a> (near <a href="/wiki/San_Francisco" title="San Francisco">San Francisco</a>) states that peak flow on the three-lane <a href="/wiki/U.S._Route_101_in_California" title="U.S. Route 101 in California">Highway 101</a> is about 7,200 <i>vehicles</i> per hour.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> This is about the same number of passengers per lane. </p><p>Notwithstanding these formulas it is widely known that reducing headway increases risk of collision in standard private automobile settings and is often referred to as <a href="/wiki/Tailgating" title="Tailgating">tailgating</a>. </p><p>2) metro system, per line: 40 km/h (~11 m/s) speeds, 1000 passengers, 100 meter vehicle length, 0.5 m/s^2 braking, 2 second reaction time, brick-wall stop, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}"></span> of 1.5; </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{tot}={\frac {100}{11}}+2+{\frac {1.5\times 11}{2}}\left({\frac {1}{0.5}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mi>o</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>100</mn> <mn>11</mn> </mfrac> </mrow> <mo>+</mo> <mn>2</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1.5</mn> <mo>×</mo> <mn>11</mn> </mrow> <mn>2</mn> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>0.5</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{tot}={\frac {100}{11}}+2+{\frac {1.5\times 11}{2}}\left({\frac {1}{0.5}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/10221edc9964c6292e85e381a13164b63ad4fc61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:34.429ex; height:6.176ex;" alt="{\displaystyle T_{tot}={\frac {100}{11}}+2+{\frac {1.5\times 11}{2}}\left({\frac {1}{0.5}}\right)}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{pas}={1000}\times {\frac {3600}{T_{tot}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>a</mi> <mi>s</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1000</mn> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3600</mn> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mi>o</mi> <mi>t</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{pas}={1000}\times {\frac {3600}{T_{tot}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4122c89ffa6a30d48dacf56a857d607ef72dd949" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:20.169ex; height:5.509ex;" alt="{\displaystyle n_{pas}={1000}\times {\frac {3600}{T_{tot}}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{tot}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mi>o</mi> <mi>t</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{tot}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7d3bc72f1fdac4f2c4abfebf49536322ef95806f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.575ex; height:2.509ex;" alt="{\displaystyle T_{tot}}"></span> = 28 seconds ; <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{pas}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>a</mi> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{pas}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/46acc8c948b379bbbaa8d98a4828bd82742bf9f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.095ex; height:2.343ex;" alt="{\displaystyle n_{pas}}"></span> = 130,000 passengers per hour</dd></dl> <p>Note that most signalling systems used on metros place an artificial limit on headway that is not dependent on braking performance. Also the time needed for station stops limits the headway. Using a typical figure of 2 minutes (120 seconds): </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{pas}={1000}\times {\frac {3600}{120}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>a</mi> <mi>s</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1000</mn> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3600</mn> <mn>120</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{pas}={1000}\times {\frac {3600}{120}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/70146849456c85bdd0dbeb842e58a93477b0a7e1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:20.169ex; height:5.176ex;" alt="{\displaystyle n_{pas}={1000}\times {\frac {3600}{120}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{pas}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>a</mi> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{pas}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/46acc8c948b379bbbaa8d98a4828bd82742bf9f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.095ex; height:2.343ex;" alt="{\displaystyle n_{pas}}"></span> = 30,000 passengers per hour</dd></dl> <p>Since the headway of a metro is constrained by signalling considerations, not vehicle performance, reductions in headway through improved signalling have a direct impact on passenger capacity. For this reason, the <a href="/wiki/London_Underground" title="London Underground">London Underground</a> system has spent a considerable amount of money on upgrading the SSR Network,<sup id="cite_ref-SSR_14-0" class="reference"><a href="#cite_note-SSR-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Jubilee_line" title="Jubilee line">Jubilee</a> and <a href="/wiki/Central_line_(London_Underground)" title="Central line (London Underground)">Central</a> lines with new <a href="/wiki/Communication-based_train_control" class="mw-redirect" title="Communication-based train control">CBTC</a> signalling to reduce the headway from about 3 minutes to 1, while preparing for the <a href="/wiki/2012_Olympics" class="mw-redirect" title="2012 Olympics">2012 Olympics</a>.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p><p>3) automated <a href="/wiki/Personal_rapid_transit" title="Personal rapid transit">personal rapid transit</a> system, 30 km/h (~8 m/s) speeds, 3 passengers, 3 meter vehicle length, 2.5 m/s^2 braking (1/4 <i>g</i>), 0.01 second reaction time, brake-failure on lead vehicle for 1 m/s slowing, bot 2.5, m/s if lead vehicle breaks. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}"></span> of 1.1; </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{tot}={\frac {3}{8}}+0.01+{\frac {1.1\times 8}{2}}\left({\frac {1}{2.5}}-{\frac {1}{2.5}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mi>o</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>8</mn> </mfrac> </mrow> <mo>+</mo> <mn>0.01</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1.1</mn> <mo>×</mo> <mn>8</mn> </mrow> <mn>2</mn> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2.5</mn> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2.5</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{tot}={\frac {3}{8}}+0.01+{\frac {1.1\times 8}{2}}\left({\frac {1}{2.5}}-{\frac {1}{2.5}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81fd4e5d95002b8416876c972bf9ac417e6adb1a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:40.562ex; height:6.176ex;" alt="{\displaystyle T_{tot}={\frac {3}{8}}+0.01+{\frac {1.1\times 8}{2}}\left({\frac {1}{2.5}}-{\frac {1}{2.5}}\right)}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{pas}={3}\times {\frac {3600}{0.385}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>a</mi> <mi>s</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3600</mn> <mn>0.385</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{pas}={3}\times {\frac {3600}{0.385}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5b6f1163d0771989caefbd952d089950b738d94b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:17.329ex; height:5.176ex;" alt="{\displaystyle n_{pas}={3}\times {\frac {3600}{0.385}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{tot}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mi>o</mi> <mi>t</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{tot}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7d3bc72f1fdac4f2c4abfebf49536322ef95806f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.575ex; height:2.509ex;" alt="{\displaystyle T_{tot}}"></span> = 3 seconds ; <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{pas}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>a</mi> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{pas}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/46acc8c948b379bbbaa8d98a4828bd82742bf9f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.095ex; height:2.343ex;" alt="{\displaystyle n_{pas}}"></span> = 28,000 passengers per hour</dd></dl> <p>This number is similar to the ones proposed by the <a href="/wiki/Cabinentaxi" title="Cabinentaxi">Cabinentaxi</a> system, although they predicted that actual use would be much lower.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> Although PRTs have less passenger seating and speeds, their shorter headways dramatically improve passenger capacity. However, these systems are often constrained by brick-wall considerations for legal reasons, which limits their performance to a car-like 2 seconds. In this case: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{pas}={3}\times {\frac {3600}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>a</mi> <mi>s</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3600</mn> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{pas}={3}\times {\frac {3600}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6bef5885d6a0f209678465a74ee510e0c1970f36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:16.682ex; height:5.176ex;" alt="{\displaystyle n_{pas}={3}\times {\frac {3600}{2}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{pas}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>a</mi> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{pas}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/46acc8c948b379bbbaa8d98a4828bd82742bf9f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.095ex; height:2.343ex;" alt="{\displaystyle n_{pas}}"></span> = 5,400 passengers per hour</dd></dl> <div class="mw-heading mw-heading2"><h2 id="Headways_and_ridership">Headways and ridership</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Headway&action=edit&section=10" title="Edit section: Headways and ridership"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Headways have an enormous impact on <a href="/wiki/Ridership" class="mw-redirect" title="Ridership">ridership</a> levels above a certain critical waiting time. Following Boyle, the effect of changes in headway are directly proportional to changes in ridership by a simple conversion factor of 1.5. That is, if a headway is reduced from 12 to 10 minutes, the average rider wait time will decrease by 1 minute, the overall trip time by the same one minute, so the ridership increase will be on the order of 1 x 1.5 + 1 or about 2.5%.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> Also see Ceder for an extensive discussion.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Headway&action=edit&section=11" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Notes">Notes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Headway&action=edit&section=12" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width reflist-columns-2"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">The Metro normally states their best headway as 142 trains per hour, but their <a rel="nofollow" class="external text" href="http://engl.mosmetro.ru/pages/page_0.php?id_page=2">english page</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090821095919/http://engl.mosmetro.ru/pages/page_0.php?id_page=2">Archived</a> 21 August 2009 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> uses the more familiar units.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">Parkinson and Fisher, pg 17</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">For a links to a variety of sources on the brick-wall stop in public transit planning, see Richard Gronning, <a rel="nofollow" class="external text" href="http://faculty.washington.edu/jbs/itrans/brickwall-stops.doc">"Brick-Wall Stops and PRT"</a>, June 2009</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text">Leonard Hugh Williams, "Advanced Passenger Train: A Promise Unfulfilled", Ian Allan, 1985, <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-7110-1474-4" title="Special:BookSources/0-7110-1474-4">0-7110-1474-4</a></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">Parkinson and Fisher, pg 18–19</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVan_WinsumBrouwer1997" class="citation journal cs1">Van Winsum, W.; Brouwer, W. (1997). "Time Headway in Car following and Operational Performance during Unexpected Braking". <i>Perceptual and Motor Skills</i>. <b>84</b> (3 supplement): 1247–1257. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2466%2Fpms.1997.84.3c.1247">10.2466/pms.1997.84.3c.1247</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/9229443">9229443</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:6944186">6944186</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Perceptual+and+Motor+Skills&rft.atitle=Time+Headway+in+Car+following+and+Operational+Performance+during+Unexpected+Braking&rft.volume=84&rft.issue=3+supplement&rft.pages=1247-1257&rft.date=1997&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A6944186%23id-name%3DS2CID&rft_id=info%3Apmid%2F9229443&rft_id=info%3Adoi%2F10.2466%2Fpms.1997.84.3c.1247&rft.aulast=Van+Winsum&rft.aufirst=W.&rft.au=Brouwer%2C+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeadway" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text">Carnegie, Appendix 1</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/743878/vehicle-speed-compliance-statistics-2017.pdf">"Vehicle Speed Compliance Statistics, Great Britain: 2017"</a> <span class="cs1-format">(PDF)</span>. <i>gov.uk</i><span class="reference-accessdate">. Retrieved <span class="nowrap">14 September</span> 2023</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=gov.uk&rft.atitle=Vehicle+Speed+Compliance+Statistics%2C+Great+Britain%3A+2017&rft_id=https%3A%2F%2Fassets.publishing.service.gov.uk%2Fgovernment%2Fuploads%2Fsystem%2Fuploads%2Fattachment_data%2Ffile%2F743878%2Fvehicle-speed-compliance-statistics-2017.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeadway" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.urban-transport-magazine.com/en/paris-metro-line-14-extended-and-to-become-the-longest-fastest-and-most-performant-line/">"Paris Metro Line 14 extended, transforming it into the longest, fastest and best performing line"</a>. 23 December 2020.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Paris+Metro+Line+14+extended%2C+transforming+it+into+the+longest%2C+fastest+and+best+performing+line&rft.date=2020-12-23&rft_id=https%3A%2F%2Fwww.urban-transport-magazine.com%2Fen%2Fparis-metro-line-14-extended-and-to-become-the-longest-fastest-and-most-performant-line%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeadway" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.railjournal.com/in_depth/moscow-metro-benefits-from-modernisation/">"Moscow metro benefits from modernisation"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Moscow+metro+benefits+from+modernisation&rft_id=https%3A%2F%2Fwww.railjournal.com%2Fin_depth%2Fmoscow-metro-benefits-from-modernisation%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeadway" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://ops.fhwa.dot.gov/trafficanalysistools/tat_vol3/sect5.htm">"Traffic Analysis Toolbox"</a>, US Department of Transit, FHWA-HRT-04-040</span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text">Anderson, pg. 47–48</span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.co.marin.ca.us/depts/pw/main/HWY101.pdf">"How a Freeway Breaks Down"</a>, Marin County Public Works</span> </li> <li id="cite_note-SSR-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-SSR_14-0">^</a></b></span> <span class="reference-text">Bombardier to Deliver Major London Underground Signalling.<a rel="nofollow" class="external autonumber" href="http://www.bombardier.com/en/transportation/media-centre/press-releases/details?docID=0901260d80181411">[1]</a> Press release, Bombardier Transportation Media Center, 2011. Accessed June 2011</span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text">railway-technology.com, <a rel="nofollow" class="external text" href="https://www.railway-technology.com/projects/london-olympics/">"London Olympics Transport Upgrade"</a></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://faculty.washington.edu/jbs/itrans/big/Cabintaxi%20PRT-GRT%20Study.pdf">"Communications on research ained at improving transport conditions in cities, towns and other built-up areas"</a>, <i>Forschung Stadtverkehr</i>, Issue 25 (1979)</span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text">Boyle, pg. 13</span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text">Ceder, pg. 537–542</span> </li> </ol></div> <div class="mw-heading mw-heading3"><h3 id="Bibliography">Bibliography</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Headway&action=edit&section=13" title="Edit section: Bibliography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin" style=""> <ul><li>John Edward Anderson, "Transit Systems Theory", Lexington Books, 1978</li> <li>John Edward Anderson, <a rel="nofollow" class="external text" href="http://faculty.washington.edu/jbs/itrans/cap2.htm">"The Capacity of a Personal Rapid Transit System"</a>, 13 May 1997</li> <li>Daniel Boyle, "Fixed Route Transit Ridership Forecasting and Service Planning Methods", <i>Synthesis of Transit Practice</i>, Volume 66 (2006), Transportation Research Board, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-309-09772-X" title="Special:BookSources/0-309-09772-X">0-309-09772-X</a></li> <li>Jon Carnegie, Alan Voorhees and Paul Hoffman, <a rel="nofollow" class="external text" href="http://faculty.washington.edu/jbs/itrans/big/PRTfinalreport.pdf">"Viability of Personal Rapid Transit In New Jersey"</a>, February 2007</li> <li>Avishai Ceder, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=QucV7bDg9N4C">"Public transit planning and operation: theory, modelling and practice"</a>, Butterworth-Heinemann, 2007, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-7506-6166-6" title="Special:BookSources/0-7506-6166-6">0-7506-6166-6</a></li> <li>Tom Parkinson and Ian Fisher, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=NbYqQSQcE2MC">"Rail Transit Capacity"</a>, Transportation Research Board, 1996, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-309-05718-3" title="Special:BookSources/0-309-05718-3">0-309-05718-3</a></li></ul> </div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist 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href="/wiki/Regional_rail" title="Regional rail">Regional rail</a></li> <li><a href="/wiki/Street_running_train" title="Street running train">Street running</a></li> <li><a href="/wiki/Suspension_railway" title="Suspension railway">Suspension railway</a></li> <li><a href="/wiki/Tram" title="Tram">Tram</a> <ul><li><a href="/wiki/Cable_car_(railway)" title="Cable car (railway)">Cable car</a></li> <li><a href="/wiki/Horsecar" title="Horsecar">Horsecar</a></li> <li><a href="/wiki/Light_rail" title="Light rail">Light rail</a></li> <li><a href="/wiki/Tram-train" title="Tram-train">Tram-train</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Vehicle_for_hire" title="Vehicle for hire">Vehicles<br /> for hire</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Auto_rickshaw" title="Auto rickshaw">Auto rickshaw taxi</a></li> <li><a href="/wiki/Boda_boda" title="Boda boda">Boda boda</a></li> <li><a href="/wiki/Combination_bus" title="Combination bus">Combination bus</a></li> <li><a href="/wiki/Cycle_rickshaw" title="Cycle rickshaw">Cycle rickshaw</a></li> <li><a href="/wiki/Demand-responsive_transport" title="Demand-responsive transport">Demand-responsive transport</a> <ul><li><a href="/wiki/Microtransit" title="Microtransit">Microtransit</a></li> <li><a href="/wiki/Paratransit" title="Paratransit">Paratransit</a></li></ul></li> <li><a href="/wiki/Dollar_van" class="mw-redirect" title="Dollar van">Dollar van</a></li> <li><a href="/wiki/Dolmu%C5%9F" title="Dolmuş">Dolmuş</a></li> <li><a href="/wiki/Hackney_carriage" title="Hackney carriage">Hackney carriage</a></li> <li><a href="/wiki/Jeepney" title="Jeepney">Jeepney</a></li> <li><a href="/wiki/Limousine" title="Limousine">Limousine</a></li> <li><a href="/wiki/Motorcycle_taxi" title="Motorcycle taxi">Motorcycle taxi</a></li> <li><a href="/wiki/Marshrutka" title="Marshrutka">Marshrutka</a></li> <li><a href="/wiki/Nanny_van" title="Nanny van">Nanny van</a></li> <li><a href="/wiki/Personal_rapid_transit" title="Personal rapid transit">Personal rapid transit</a></li> <li><a href="/wiki/Pesero" title="Pesero">Pesero</a></li> <li><a href="/wiki/Public_light_bus" title="Public light bus">Public light bus</a></li> <li><a href="/wiki/Pulled_rickshaw" title="Pulled rickshaw">Pulled rickshaw</a></li> <li><a href="/wiki/Share_taxi" title="Share taxi">Share taxi</a></li> <li><a href="/wiki/Songthaew" title="Songthaew">Songthaew</a></li> <li><a href="/wiki/Taxi" title="Taxi">Taxi</a></li> <li><a href="/wiki/Auto_rickshaw" title="Auto rickshaw">Tuk tuk</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Carpool" title="Carpool">Carpooling</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Car_jockey" title="Car jockey">Car jockey</a></li> <li><a href="/wiki/Flexible_carpooling" class="mw-redirect" title="Flexible carpooling">Flexible carpooling</a></li> <li><a href="/wiki/Ridesharing_company" title="Ridesharing company">Real-time ridesharing</a></li> <li><a href="/wiki/Slugging" title="Slugging">Slugging</a></li> <li><a href="/wiki/Vanpool" title="Vanpool">Vanpool</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Maritime_transport" title="Maritime transport">Ship</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cable_ferry" title="Cable ferry">Cable ferry</a></li> <li><a href="/wiki/Ferry" title="Ferry">Ferry</a></li> <li><a href="/wiki/Gondola" title="Gondola">Gondola</a></li> <li><a href="/wiki/Hovercraft" title="Hovercraft">Hovercraft</a></li> <li><a href="/wiki/Hydrofoil" title="Hydrofoil">Hydrofoil</a></li> <li><a href="/wiki/Ocean_liner" title="Ocean liner">Ocean liner</a></li> <li><a href="/wiki/Vaporetto" title="Vaporetto">Vaporetto</a></li> <li><a href="/wiki/Water_taxi" title="Water taxi">Water taxi</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Cable_transport" title="Cable transport">Cable</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Aerial_tramway" title="Aerial tramway">Aerial tramway</a></li> <li><a href="/wiki/Cable_ferry" title="Cable ferry">Cable ferry</a></li> <li><a href="/wiki/Cable_railway" title="Cable railway">Cable railway</a></li> <li><a href="/wiki/Elevator" title="Elevator">Elevator</a></li> <li><a href="/wiki/Funicular" title="Funicular">Funicular</a></li> <li><a href="/wiki/Gondola_lift" title="Gondola lift">Gondola lift</a> <ul><li><a href="/wiki/Bicable_gondola_lift" class="mw-redirect" title="Bicable gondola lift">bicable</a></li> <li><a href="/wiki/Tricable_gondola_lift" title="Tricable gondola lift">tricable</a></li></ul></li> <li><a href="/wiki/Inclined_elevator" title="Inclined elevator">Inclined elevator</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other<br />transport</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Airline" title="Airline">Airline</a></li> <li><a href="/wiki/Airliner" title="Airliner">Airliner</a></li> <li><a href="/wiki/Carsharing" title="Carsharing">Carsharing</a> <ul><li><a href="/wiki/Bicycle-sharing_system" title="Bicycle-sharing system">Bicycle-sharing</a></li> <li><a href="/wiki/Scooter-sharing_system" title="Scooter-sharing system">Scooter-sharing</a></li></ul></li> <li><a href="/wiki/Elevator" title="Elevator">Elevator</a></li> <li><a href="/wiki/Escalator" title="Escalator">Escalator</a></li> <li><a href="/wiki/Horse-drawn_vehicle" title="Horse-drawn vehicle">Horse-drawn vehicle</a></li> <li><a href="/wiki/Hyperloop" title="Hyperloop">Hyperloop</a></li> <li><a href="/wiki/Inclined_elevator" title="Inclined elevator">Inclined elevator</a></li> <li><a href="/wiki/Moving_walkway" title="Moving walkway">Moving walkway</a></li> <li><a href="/wiki/Personal_transporter" title="Personal transporter">Personal transporter</a></li> <li><a href="/wiki/Robotaxi" title="Robotaxi">Robotaxi</a></li> <li><a href="/wiki/Shweeb" title="Shweeb">Shweeb</a></li> <li><a href="/wiki/Slope_car" title="Slope car">Slope car</a></li> <li><a href="/wiki/Trackless_train" title="Trackless train">Trackless train</a></li> <li><a href="/wiki/Vactrain" title="Vactrain">Vactrain</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Locations</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Airport" title="Airport">Airport</a></li> <li><a href="/wiki/Bus_bulb" title="Bus bulb">Bus bulb</a></li> <li><a href="/wiki/Bus_garage" title="Bus garage">Bus garage</a></li> <li><a href="/wiki/Bus_lane" title="Bus lane">Bus lane</a></li> <li><a href="/wiki/Bus_stand" title="Bus stand">Bus stand</a></li> <li><a href="/wiki/Bus_station" title="Bus station">Bus station</a></li> <li><a href="/wiki/Bus_stop" title="Bus stop">Bus stop</a></li> <li><a href="/wiki/Bus_turnout" title="Bus turnout">Bus turnout (bus bay)</a></li> <li><a href="/wiki/Dry_dock" title="Dry dock">Dry dock</a></li> <li><a href="/wiki/Passenger_terminal_(maritime)" class="mw-redirect" title="Passenger terminal (maritime)">Ferry terminal</a></li> <li><a href="/wiki/Hangar" title="Hangar">Hangar</a></li> <li><a href="/wiki/Harbor" title="Harbor">Harbor</a></li> <li><a href="/wiki/Interchange_station" title="Interchange station">Interchange station</a></li> <li><a href="/wiki/Kassel_kerb" title="Kassel kerb">Kassel kerb</a></li> <li><a href="/wiki/Layover" title="Layover">Layover</a></li> <li><a href="/wiki/Metro_station" title="Metro station">Metro station</a></li> <li><a href="/wiki/Park_and_ride" title="Park and ride">Park and ride</a></li> <li><a href="/wiki/Port" title="Port">Port</a></li> <li><a href="/wiki/Queue_jump" title="Queue jump">Queue jump</a></li> <li><a href="/wiki/Taxi_stand" title="Taxi stand">Taxicab stand</a></li> <li><a href="/wiki/Train_station" title="Train station">Train station</a></li> <li><a href="/wiki/Tram_stop" title="Tram stop">Tram stop</a></li> <li><a href="/wiki/Transit_mall" title="Transit mall">Transit mall</a></li> <li><a href="/wiki/Transport_hub" title="Transport hub">Transport hub</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Ticket_(admission)" title="Ticket (admission)">Ticketing</a><br />and <a href="/wiki/Fare" title="Fare">fares</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Automated_fare_collection" title="Automated fare collection">Automated fare collection</a></li> <li><a href="/wiki/Bus_advertising" title="Bus advertising">Bus advertising</a></li> <li><a href="/wiki/Contract_of_carriage" title="Contract of carriage">Contract of carriage</a></li> <li><a href="/wiki/Dead_mileage" title="Dead mileage">Dead mileage</a></li> <li><a href="/wiki/Exit_fare" title="Exit fare">Exit fare</a></li> <li><a href="/wiki/Fare_avoidance" title="Fare avoidance">Fare avoidance</a></li> <li><a href="/wiki/Fare_capping" title="Fare capping">Fare capping</a></li> <li><a href="/wiki/Fare_evasion" title="Fare evasion">Fare evasion</a></li> <li><a href="/wiki/Free_public_transport" title="Free public transport">Free public transport</a></li> <li><a href="/wiki/Free_travel_pass" title="Free travel pass">Free travel pass</a></li> <li><a href="/wiki/Integrated_ticketing" title="Integrated ticketing">Integrated ticketing</a></li> <li><a href="/wiki/Manual_fare_collection" title="Manual fare collection">Manual fare collection</a></li> <li><a href="/wiki/Money_train" title="Money train">Money train</a></li> <li><a href="/wiki/Paid_area" title="Paid area">Paid area</a></li> <li><a href="/wiki/Penalty_fare" title="Penalty fare">Penalty fare</a></li> <li><a href="/wiki/Proof-of-payment" title="Proof-of-payment">Proof-of-payment</a></li> <li><a href="/wiki/Reduced_fare_program" title="Reduced fare program">Reduced fare program</a></li> <li><a href="/wiki/Transfer_(public_transit)" title="Transfer (public transit)">Transfer</a></li> <li><a href="/wiki/Transit_pass" title="Transit pass">Transit pass</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Routing</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Circle_route" title="Circle route">Circle route</a></li> <li><a href="/wiki/Cross-city_route" title="Cross-city route">Cross-city route</a></li> <li><a href="/wiki/Network_length_(transport)" title="Network length (transport)">Network length</a></li> <li><a href="/wiki/Non-revenue_track" title="Non-revenue track">Non-revenue track</a></li> <li><a href="/wiki/Radial_route" title="Radial route">Radial route</a></li> <li><a href="/wiki/Transport_network_analysis" title="Transport network analysis">Transport network</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Facilities</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Checked_baggage" title="Checked baggage">Checked baggage</a></li> <li><a href="/wiki/List_of_first_class_commuter_transport_services" class="mw-redirect" title="List of first class commuter transport services">First class</a></li> <li><a href="/wiki/Sleeping_car" title="Sleeping car">Sleeper</a></li> <li><a href="/wiki/Standing_passenger" title="Standing passenger">Standing passenger</a></li> <li><a href="/wiki/Travel_class" title="Travel class">Travel class</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Scheduling</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bus_bunching" title="Bus bunching">Bus bunching</a></li> <li><a href="/wiki/Clock-face_scheduling" title="Clock-face scheduling">Clock-face scheduling</a></li> <li><a class="mw-selflink selflink">Headway</a></li> <li><a href="/wiki/Night_service_(public_transport)" title="Night service (public transport)">Night (owl) service</a></li> <li><a href="/wiki/On-time_performance" title="On-time performance">On-time performance</a></li> <li><a href="/wiki/Public_transport_timetable" title="Public transport timetable">Public transport timetable</a></li> <li><a href="/wiki/Short_turn" title="Short turn">Short turn</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Politics</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Airport_security" title="Airport security">Airport security</a></li> <li><a href="/wiki/Complete_streets" title="Complete streets">Complete streets</a></li> <li><a href="/wiki/Green_transport_hierarchy" title="Green transport hierarchy">Green transport hierarchy</a></li> <li><a href="/wiki/Farebox_recovery_ratio" title="Farebox recovery ratio">Farebox recovery ratio</a> <ul><li><a href="/wiki/Rail_subsidies" title="Rail subsidies">Rail subsidies</a></li></ul></li> <li><a href="/wiki/Public_transport_security" title="Public transport security">Security</a></li> <li><a href="/wiki/Street_hierarchy" title="Street hierarchy">Street hierarchy</a></li> <li><a href="/wiki/Transit_district" title="Transit district">Transit district</a></li> <li><a href="/wiki/Transit_police" title="Transit police">Transit police</a></li> <li><a href="/wiki/Transportation_authority" title="Transportation authority">Transportation authority</a></li> <li><a href="/wiki/Transportation_demand_management" title="Transportation demand management">Transportation demand management</a></li> <li><a href="/wiki/Transportation_planning" title="Transportation planning">Transportation planning</a> <ul><li><a href="/wiki/Transit-oriented_development" title="Transit-oriented development">Transit-oriented development (TOD)</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Technology<br /> and signage</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Destination_sign" title="Destination sign">Destination sign</a></li> <li><a href="/wiki/Passenger_information_system" title="Passenger information system">Passenger information system</a></li> <li><a href="/wiki/Platform_display" title="Platform display">Platform display</a></li> <li><a href="/wiki/Platform_screen_doors" title="Platform screen doors">Platform screen doors</a></li> <li><a href="/wiki/List_of_public_transport_smart_cards" title="List of public transport smart cards">Smart cards</a> <ul><li><a href="/wiki/CIPURSE" title="CIPURSE">CIPURSE</a></li> <li><a href="/wiki/Calypso_(electronic_ticketing_system)" title="Calypso (electronic ticketing system)">Calypso</a></li></ul></li> <li><a href="/wiki/Ticket_machine" title="Ticket machine">Ticket machine</a></li> <li><a href="/wiki/Public_transport_timetable" title="Public transport timetable">Timetable</a></li> <li><a href="/wiki/Transit_map" title="Transit map">Transit map</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other topics</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Boarding_(transport)" title="Boarding (transport)">Boarding</a></li> <li><a href="/wiki/Bus_rapid_transit_creep" title="Bus rapid transit creep">Bus rapid transit creep</a></li> <li><a href="/wiki/Crush_load" title="Crush load">Crush load</a></li> <li><a href="/wiki/Dwell_time_(transportation)" title="Dwell time (transportation)">Dwell time</a></li> <li><a href="/wiki/Hail_and_ride" title="Hail and ride">Hail and ride</a></li> <li><a href="/wiki/Land_transport" title="Land transport">Land transport</a></li> <li><a href="/wiki/Outline_of_transport" title="Outline of transport">Outline of transport</a></li> <li><a href="/wiki/Passenger_load_factor" title="Passenger load factor">Passenger load factor</a></li> <li><a href="/wiki/Public_good_(economics)" title="Public good (economics)">Public good</a></li> <li><a href="/wiki/Request_stop" title="Request stop">Request stop</a></li> <li><a href="/wiki/Service_(economics)" title="Service (economics)">Service</a></li> <li><a href="/wiki/Sustainable_transport" title="Sustainable transport">Sustainable transport</a></li> <li><a href="/wiki/Timing_point" title="Timing point">Timing point</a></li> <li><a href="/wiki/Transport_economics" title="Transport economics">Transport economics</a></li> <li><a href="/wiki/Micromobility" title="Micromobility">Micromobility</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><b><span class="nowrap"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Nuvola_apps_ksysv_square.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Nuvola_apps_ksysv_square.svg/16px-Nuvola_apps_ksysv_square.svg.png" decoding="async" width="16" height="16" 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