Furth's Traffic Engineering Notes on Pedestrian Timing (PDF)

Signalized Crosswalk TIming =========================== Traffic signals do not only serve people in vehicles; they also serve people on foot. This chapter covers crosswalk timing at signalized intersections and pedestrian delay. Most signalized crossings run concurrently with a parallel vehicle ph...

Signalized Crosswalk TIming =========================== Traffic signals do not only serve people in vehicles; they also serve people on foot. This chapter covers crosswalk timing at signalized intersections and pedestrian delay. Most signalized crossings run concurrently with a parallel vehicle phase. Consider a vehicle phase with 30 s green, 4 s yellow, and 2 s red clearance, as sketched in Figure 4-1; the cycle length is 90 s and the parallel crosswalk has a length *D* = 70 ft long. Also sketched in that figure are three different ways a concurrent pedestrian crossing could be timed. Those options will be discussed later; in summary, they are: - Option A: gives pedestrians the longest possible Walk interval that fits within the split of the concurrent vehicle phase; - Option B: adds two common restrictions that, as we'll see, force the Walk interval to be shorter (a full 6 seconds shorter); and - Option C: the minimum pedestrian timing required by the MUTCD. Figure 4-1: Example pedestrian timing options Pedestrian Indications and Functional Intervals ----------------------------------------------- Pedestrian signals have three indications, while pedestrian timing has four intervals. The indications are - **Walk** (with length *W*, indication is a white walking man), which means you may start to cross. The MUTCD recommends 7 s as the minimum Walk interval, though, by exception, it may be a short as 4 s. - **Flashing Don't Walk** (abbreviated FDW, with length *FDW*, flashing orange hand), which means don't begin, but if you've begun, continue crossing. Where there is a countdown display, it counts down the FDW with large orange digits. FDW may run during a concurrent vehicular phase's green or yellow, but not during its red clearance. - **Don't Walk** (solid orange hand), which is displayed during two intervals. - From when FDW ends until conflicting traffic is released is an interval called the **pedestrian phase end buffer** (abbreviated ff, with length *ff;* in the MUTCD, it's called "buffer time"). During this time, it is also safe to finish crossing. - The rest of the DW phase is the fourth interval. The combined length of FDW and the pedestrian phase end buffer should be enough for a pedestrian who began walking at the last moment of Walk to finish crossing. For the pedestrian phase end buffer, the MUTCD mandates at least 3 s (will become 2 s once the 2024 MUTCD is adopted). In practice, pedestrian phase end buffers vary from intersection to intersection. They are often made equal to the change interval (yellow + redClear) of the concurrent vehicle phase because it's convenient for controllers to end FDW when the yellow begins. ### Effective Pedestrian Intervals ***Effective Walk.*** Legally, pedestrians are supposed to begin to cross only during the Walk interval; however, in practice, most pedestrians will also begin to cross during the first few seconds of the FDW interval. (This is partly because the FDW interval is timed with slower pedestrians in mind, and so a person with average walking speed or faster can start crossing during the early part of the FDW and still clear the intersection safely.) By default, the *effective Walk interval* has length *W~eff~ = W + 4*. ***Effective Pedestrian Phase End Buffer.*** While the MUTCD mandates a minimum pedestrian phase end buffer, there is no limit on its maximum. Technically, it's safe to finish crossing during the phase end buffer no matter how long it is; however, pedestrians cannot finish crossing *in peace* while there is a DW display for more than about 3 seconds, because they know from experience that at many intersections, conflicting traffic is released after 3 seconds. In this writer's opinion, those first 3 seconds of the pedestrian phase end buffer should be considered the *effective pedestrian phase end buffer;* the rest of the phase end buffer does not effectively serve pedestrians. However, in industry practice, there is no such concept as "effective phase end buffer". To determine what's allowed by industry practice, treat the entire phase end buffer as effective phase end buffer. Pedestrian Start Time Needs --------------------------- Pedestrian timing should give pedestrians enough time to get started and then to finish crossing. In US practice, we have a primary and a secondary pedestrian timing standard. The primary standard calls for 7 s to get started, though 4 s is allowed. (In MA, we require 7 s.) The secondary standard calls for 2 s to get started. (To be precise, the MUTCD doesn't specify 2 s for slow crossers to begin, but rather assumes that peds will begin immediately at the onset of Walk from a starting point that can be up to 6 ft from the curb -- which, for a walking speed of 3.0 ft/s, is the same as departing the curb 2 s after the onset of Walk.) Commentary: It is this writer's opinion that reform is needed. 2 s is too little; at the same time, 7 s is too much, except where there are so many pedestrians that some have to stand waiting behind others. Elsewhere, 4 s -- what's used in European countries including Netherlands -- is the right amount needed. Pedestrian Clearance Needs -------------------------- Once a pedestrian steps off the curb, the time they need to clear the intersection is the crossing length divided by their walking speed. Pedestrian timing should provide enough time for people to clear in peace. Pedestrian signal timing has primary and secondary design speeds for pedestrians: Average walking speed is about 4.5 ft/s (about 3 mph). The default primary design speed, 3.5 ft/s, is the 6^th^ percentile walking speed. (Before 2009, the MUTCD's primary pedestrian design speed was 4.0 ft/s, and intersections that haven't been retimed in many years may still reflect that speed.) Where a large number of crossing pedestrians are seniors or young children, jurisdictions may consider using a lower primary design speed such as 3.0 ft/s. For general pedestrians, a person who begins walking at the last moment of the Walk interval should have enough time to cross in peace: *FDW + f~eff~ [\>] D/S~p1~ (4-1)* where *FDW* = length of the Flashing Don't Walk interval (s) *f~eff~* = length of the effective phase end buffer (s) (default 3 s) *D* = crosswalk length (ft) *S~p1~* = design speed for general pedestrians (default 3.5 ft/s) For this chapter's example crossing, *FDW + f~eff~ [\>] 70 /3.5 =* 20 s Crosswalk length *D* is measured from the curb to "the far side of the traveled way" (MUTCD, section 4E.06). If the street being crossed has parking lanes or shoulders, it is a matter of local judgment whether a far-side parking lane or shoulder is included in crosswalk length. In Massachusetts, crosswalk length is from curb to curb. The secondary clearance requirement is meant to accommodate slower pedestrians. Slower pedestrians, aware of their limitations, generally start to cross only at the onset of Walk. The MUTCD's requirement essentially allows them 2 seconds to begin crossing, resulting in this secondary clearance requirement: *W -- 2 + FDW + f~eff~ [\>] D/S~p2~ (4-2)* where *W* = length of the Walk interval (s) *S~p2~* = design speed for slower pedestrians (default 3.0 ft/s) Except for very long crossings, if the primary crossing standard (equation 4-1) is satisfied, the secondary requirement (equation 4-2) will be satisfied as well, and therefore design methods for setting *W* and *FDW* focus on meeting the primary standard. After *W* and *FDW* are chosen based on the primary standard, they can be checked against the secondary standard; if it is not met, *W* should be increased to meet it (leaving *FDW* unchanged). However, such adjustment is not usually needed except at crossings longer than 105 ft. Setting Walk and FDW Interval Lengths ------------------------------------- From crossings that are *not concurrent* with a vehicle phase (e.g., where a stand-alone shared use path crosses a road, or for an exclusive pedestrian phase), all of the pedestrian intervals (W, FDW, buffer) are typically set equal to their minimum values, following the primary crossing standard. (And modified, if needed, to meet the secondary standard.) However, most crossings are concurrent with a vehicular phase, whose timing needs are typically determined first, using methods described in the previous chapter. When setting the lengths of pedestrian intervals for a concurrent crossing , work backwards in time from the end of the phase. **First** set the pedestrian phase end buffer; **second,** set FDW to satisfy the primary clearance requirement; **third,** the remainder of the concurrent vehicular phase's split can be the Walk interval: *W = split -- phase end buffer -- FDW (but with a minimum of 7 s) (4-3)* (Later, we will discuss what to do if the result from equation 4-3 is less than 7 s.) **Fourth,** check whether the secondary clearance requirement calls for a still greater *W*, and if so, increase *W* accordingly. This fourth step can be skipped if the crossing is shorter than 100 ft. Three alternative pedestrian timings are used for illustration in Figure 4.1 Recall that the primary clearance need, calculated earlier, is 20 s (70 ft / 3.5 ft/s). Compare how much effective walk time pedestrians get: 20 s in Option A, 14 s in Option B, and 11 s in Option C. Clearly, Option A serves pedestrians best, because it gives them the most time to begin crossing, and therefore the least delay. This example demonstrates how three commonly followed policies work to make pedestrian service worse than it should be: - setting the pedestrian phase end buffer based on controller convenience (ending FDW at the onset of yellow) instead of making it a uniform 3, which is best for pedestrians; - not counting any of the phase end buffer against pedestrian clearance, which has the appearance of being pro-pedestrian ("it gives them more time to cross") but actually works against pedestrians because it tells them not to walk when it's safe to walk. - using a standard Walk interval length of 7 s even where a longer Walk interval would "fit" into the concurrent vehicular phase. ### Phase Length Governed by Vehicle Timing Needs vs. Pedestrian Timing Needs Until now, the discussion has assumed that the vehicular phase is long enough to fit a pedestrian phase. That will be the case whenever the result of equation 4-3 exceeds 7 s. In such a case, vehicular needs govern the phase length, and the pedestrian timing fits into it. But if equation 4-3 results in a Walk interval shorter than 7 s, it means the pedestrian crossing needs more time than the vehicular movement. For that case, the pedestrian movement governs the phase length, and the vehicular movement timing fits into it. The minimum split needed for vehicles is: *minSplit~veh~ = G~needed~ + Y + R~c~* while the minimum split needed for pedestrians is *minSplit~ped~ = W~min~ + FDW + ff* where *W~min~ =* 7 s, except at long crossings where the secondary clearance requirement may lead to the need for a longer Walk interval. If they run concurrently, they must have the same split, and so *Split = max (minSplit~veh~, minSplit~ped~)* where ***Vehicle timing needs govern if** **minSplit~veh~ [\>] minSplit~ped~**. Time vehicle phases based on their needs, and make the Walk interval just long enough so that the pedestrian phase split matches the needed vehicle split:* *W = minSplit~veh~ -- FDW -- phase end buffer (4-5)* ***Pedestrian timing needs** **govern if minSplit~veh~ \> minSplit~ped~**. Leave the Walk interval at its minimum length (7 s), and lengthen the concurrent vehicle phase's green to so that its split will match the split required by the pedestrian phase:* *G = minSplit~ped~ -- Y -- R~c~ (4-6)* The result of equation 4-6 is also called the pedestrian minimum green (ped-min-Green), and is important at intersections where the pedestrian phase is pushbutton-actuated. At an intersection of a major road with a minor road, the phase serving the major road through movement and its parallel pedestrian crossing is usually governed by vehicle timing needs, because the major road has a lot of traffic and the pedestrian crossing is short; at the same time, the phase serving the minor road and its parallel pedestrian crossing is usually governed by pedestrian timing needs, because vehicle demand is low while the pedestrian crossing is long. Caution: All of the equations of section 4-3 have been based on satisfying the primary clearance requirement, for general pedestrians. Once these timings have been chose, the secondary clearance requirement (equation 4-2), for slower pedestrians, should be checked. If not satisfied, increase *W*, which may mean lengthening the split, until it is. Pedestrian Delay and Lowest Pedestrian Speed Accommodated --------------------------------------------------------- How well does the timing of a pedestrian signal serve pedestrians? This section describes two performance measures: average pedestrian delay and lowest pedestrian speed accommodated, a measure of accessibility. This second measure is not yet widely known in the profession. ### Average Pedestrian Delay The period within which pedestrians begin to cross is the effective Walk interval, which, as stated earlier, is the Walk interval plus the first few seconds of FDW. The remainder of the signal cycle can be considered effective ped-red or *r~ped~* : *r~ped~ = C -- W~eff~ (4-8)* ***Average pedestrian delay*** is given by *d~ped~ = (r~ped~ /C) (r~ped~ /2) = r~ped~^2^/2C (4-10)* where the first term in parentheses is the fraction of pedestrians who are delayed and the second is the average delay to those who are delayed. Unlike with vehicles, queuing and discharge rate (which gave rise to the variable *t~q~*) are ignored because, except at very busy crossings, waiting pedestrians tend to stand side by side rather than queue one behind another, allowing them to all depart at the onset of Walk. A level of service for pedestrian crossings, on a scale A-F, can be assigned based on average delay using the table below, taken from the 2009 *HCM.* It also indicates how pedestrian non-compliance can be expected to rise as average delay becomes long. Table 4-1. Delay-Based Level of Service for Pedestrian Crossings. Source: *Highway Capacity Manual*, 2009 edition, Exhibit 18-9. **Average Ped Delay (s)** **Level of Service (LOS)** **Likelihood of Noncompliance** --------------------------- ---------------------------- --------------------------------- **0 to 10** A low **10 to 20** B **20 to 30** C moderate **30 to 40** D **40 to 60** E high **\> 60** F very high Non-compliance is more directly related to maximum delay than to average delay, and so where LOS is poor, it is helpful to report maximum delay, which equals *r~ped~*, as well as average delay to help people understand why poor compliance is likely. For example, if *C* = 100 s and *W~eff~* = 11, maximum delay, which equals *r~ped~*, is 89 s; it's easy to understand how waiting 89 s can seem unbearable, making it likely for people to cross against the signal if they can find a safe gap in traffic. Giving pedestrians an incentive to cross agains the signal is not good for safety, and so preventing long pedestrian delay is not only a matter of convenience or service, but a matter of safety as well. The main way to avoid long pedestrian delays is to avoid long signal cycles. Recognizing this, the City of Amsterdam's traffic signal policy is that cycle length must not exceed 100 s, and average pedestrian delay must not exceed 45 s. ### Lowest Pedestrian Speed Accommodated Wide, busy streets will become a barrier to pedestrians if traffic signals don't give them enough time to cross. Pedestrian signal timing can therefore be evaluated in terms of accessibility to slow pedestrians by determining the lowest pedestrian speed accommodated, *S~pLowest~*. By design, signals should be timed so that pedestrians walking at a speed of 3.0 ft/s can cross the street if they begin crossing within the first 2 seconds of Walk. But there are still some people who cannot walk this fast, and so if a pedestrian crossing can accommodate people with a still lower walking speed -- either because the crossing is short or the Walk interval is long -- that will improve accessibility. For this performance measure, we assume that slow pedestrians begin crossing on ly at the onset of Walk; however, we allow them 4 s to begin crossing, not just the 2 s provided by the secondary clearance requirement. The lowest speed accommodated is therefore [\$S\_{\\text{pLowest}} = \\frac{D}{W - 4 + FDW + \\ f\_{\\text{eff}}}\$]{.math.inline} *(4-11)* Comparing Alternative Pedestrian Timing Practices ------------------------------------------------- Performance measures for the three pedestrian timing options of Figure 4-1 are shown in Table 4-1. All three options take the timing of concurrent vehicle phase as given, and therefore do not affect service to vehicles; the question is how the pedestrian phase will be timed, and how well that will serve pedestrians. Recall that Option A maximizes the time given to pedestrians; Option B adds two technical restrictions, which are that FDW must end by the onset of Yellow and none of the pedestrian phase end buffer can count against pedestrian clearance time; and Option C is the "lazy" option which gives pedestrians only a minimum Walk interval. One can see that Option A has both the least pedestrian delay (27.2 s) and accommodates the lowest speed pedestrian accommodated (2.2 ft/s). The added restrictions in Option B increase pedestrian delay and reduce accessibility. Option C, the "lazy" option, has both the worst delay and the worst accessibility. Table 4-1. Evaluation of Figure 4-1's Pedestrian Timing Options Option A Option B Option C -------------------------------------- ---------- ---------- ---------- Maximum ped delay (s) 70.0 76.0 79.0 Average ped delay (s) 27.2 32.1 34.7 Delay-based level of service C D D Lowest ped speed accommodated (ft/s) 2.2 2.4 2.7 Note: *C* = 90 s and *D* = 70 ft. Leading pedestrian interval --------------------------- Where pedestrians move concurrently with a parallel vehicle phase, right-turning cars present a conflict. Normally, this is a permitted conflict, because turning cars go slowly and the obligation of yielding to pedestrians in such a situation is univerally understood. However, if the volume turning right is too high, the conflict can be stressful and even dangerous. Traffic signal timing can mitigate this conflict with *full protection* or *partial protection.* Full protection means giving pedestrians a phase that is distinct from the phase used by right turning cars -- either by having a distinct right turn phase (which requires a right turn lane), or by having an exclusive pedestrian phase. Boston's traffic signal policy calls for full protection where the number of vehicles turning right exceeds 5.5. vehicles per cycle, or where the intersection geometry allows high speed right turns. Partial protection means giving pedestrians a head start of several seconds, called a Leading Pedestrian Interval (LPI), whose objective is to enable pedestrians to establish their priority in the crosswalk before the first vehicle turning right can reach the conflict zone (where a right-turning car might collide with a pedestrian). Depending on how wide is the street being crossed, and how far back the stopline is, the head start needed for pedestrians to occupy the conflict zone could be as much as 6 s and as little as 1 s. Cities often use a standard value (e.g., 3 s in Washington, 4 s in New York, 7 s in Montreal). Where the concurrent vehicle movement has little traffic (as is typical of many minor streets), the phase length is typically governed by pedestrian timing needs anyway, and so the vehicle phase can readily afford to give up a few seconds of green time. However, where the signal timing is governed by vehicle needs, inserting an LPI creates additional lost time that will force the cycle to be longer, increasing delay for pedestrians as well as motorists. (These two sides often present themselves at the intersection of a major and minor street.) Boston's guidelines call for an LPI anywhere it will not force the cycle length to be longer; where it would force a longer cycle, they call for an LPI where the number of vehicles per cycle turning right exceeds 3.5. (And as stated earlier, 5.5 is the limit at which full protection is warranted.) Where pedestrian phases are pushbutton actuated, the LPI applies only when a pedestrian phase is called, of course. To ensure safety for blind pedestrians, LPIs should always be accompanied by an audible pedestrian signal. Blind pedestrians are trained to know when the Walk begins by listening for the rush of traffic, and with an LPI, that rush is *not* simultaneous with the onset of Walk. Other aspects of pedestrian crossings ------------------------------------- A leading pedestrian interval can mitigate the conflict between pedestrians and permitted turning conflicts. Later, we'll describe other techniques involving both signal timing and intersection layout to reduce the safety risk associated with turning conflicts. Crossings can be broken into two or more stages, with pedestrians waiting between stages at a crossing island, also called a pedestrian refuge island. Crossing islands must be at least 6 ft deep and equipped with pedestrian signals. However, unless the pedestrian phases leading to and from an island are well coordinated, this arrangement usually results in extremely long pedestrian delays. For example, several Boston-area two stage crossings we have studied have average delay around 100 s, and some three-stage crossings we have studied have average delay exceeding 120 and even 240 s. Therefore, multistage crossings should be used sparingly, and always with careful attention to coordinating the pedestrian phases so as to avoid intolerably long delays that will inevitably lead to poor pedestrian compliance. Where a road has a physical median, the crossing can still be designed for pedestrians to cross in a single pass. In such a case, the median is not a "refuge" and so there is no minimum depth requirement, and having pedestrian signals in the median is optional.