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CHAPTER 3 INTERPRETATION, APPRAISAL, APPLICATIONS 3.1 CAPACITY CHARACTERISTICS This section summarizes the models developed for capacity prediction. These models can ne used to predict capacity-related traffic characteristics for a range of conditions common to interchanges and closely-spaced signalized intersections. The specific characteristics considered include saturation flow rate, start-up lost time, end lost time, and lane utilization. The capacity of lane group represents the maximum number of vehicles that can be served by the group's traffic lanes during the time allocated to it within the signal cycle. A lane group flowing at capacity is typically characterized by the continuous discharge of queued traffic for the duration ofthe signal phase that controls it. To this extent, lane group capacity is dependent on the discharge characteristics of the departing traffic queue. These characteristics include the time lost at the start ofthe phase due to driver reaction time arid acceleration,the saturation flow rate, and the time lost at the end of the phase due to a necessary change interval. The following equation is commonly used to compute He capacity of a lane group: gs t35) 3,600 with where: g = [G + Y + RC - (Is ~ le)] r) CP c ' = capacity of the lane group, vpc; g= effective green time where platoon motion (flow) can occur, see, saturation flow rate for the lane group under prevailing conditions, vphg; G= green signal interval, see; Y= yellow interval, see; RC = red clearance interval, see, Is = start-up lost time, see, [e = clearance lost time, see; and CP = clear period during cycle/phase when subject flow is unblocked, sec. (36) Many of the variables defined in Equations 35 and 36 represent the basic set of capacity charactenstics. Models for estimating these characteristics (i.e., saturation flow rate, start-up lost time, and clearance lost time) for all traffic movements at interchange ramp terminals and closely- spaced intersections are described in the following sections. 3 - ~

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3.. Saturation Flow Rate Mocle' The saturation flow rate for a lane group can be predicted using the following equation: where: Nit X 50 Xf XfHV Xfg Xfp Xfbb XfRT XfLT fD fv s = saturation flow rate for the lane group under prevailing conditions, vphg; s0 = saturation flow rate per lane under ideal conditions, pcphgpl, fW = adjustment factor for lane width, All = adjustment factor for heavy vehicles; jig = adjustment factor for approach grade; fp = adjustment factor for parking; fib = adjustment factor for bus blockage; fRT= adjustment factor for right-turns in the lalle group; fit= adjustment factor for left-t~s in the lane group; fD = adjustment factor for distance to downstream queue at green onset; and if = adjustment factor for volume level (i.e., traffic pressure). (37) The first seven adjustment factors listed in this equation represent those described in the HCM 63, Chapter 99. The last two factors were developed for this research and are specifically applicable to interchanges and closely-spaced signalized intersections. A third adjustment factory was developed for this research that quantifies the effect of turn radius on the saturation flow rate of a left or r~ght-turn movement. This factor is introduced bY revising the adjustment factors for protected turn movements provided in Me HCM. right and lefc-turn adjustment factors are: fAT fRT fF JET f[T fR where: 1 1 + PRT: fR 1 - 1 ) LT( fR These revised : Protected, Shared Right-Turn Lane : Protected, Exclusive Right-Turn Lane : Protected, Shared Left-Turn Lane : Protected, Exclusive Left-Turn lane 3 - 2 (38) (39)

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fR = adjustment factor for the radius of the travel path (based on the radius of the applicable left or right-turn movement), PRT = portion of right-turns in the lane group, and PLT = portion of left-turns in the lane group. Adjustment factors for permissive-only and protected-permissive phasing can also be developed using Equations 38 and 39 as a basis. The ideal saturation flow rate so represents the saturation flow rate of a lane that is not affected by arty external environmentalfactors (e.g., grade), non-passenger-carvehicles (e.g., trucks), and constrained geometucs (e.g., less than 3.6-meter lane Widths, curved travel path). In this regard, the saturation flow rate would be equal to the ideal rate when all factor effects are optimum for efficient traffic flow and the corresponding adjustment factors are equal to I.0. Based on this deflation, it was determined that ideal conditions were represented by an infinite dist~ce-to-queue, non-spillback conditions, a tangent alignment (i.e., an infinite radius), and a traffic pressure representing that typically experienced during peak traffic periods. Under these conditions, 2,000 pcphgpl is recommended as the ideal saturation flow rate for all traffic movements at interchanges. One potential factor that was evaluated but not included in Equation 37 is that of phase duration. Some evidence was found Mat drivers adopted larger saturation flow rates for chases of short duration than for Dose of long duration. TO .' .- ~ ~. ~in. . ~ However, the relationship was not felt to be conclusive for both left-turn and through movements, thus, more research is believed to be needed before an adjustment for phase duration can be recommended for general applications. Distance-to-Queue Adjustment Factor. ~.. . ~. ~, The distance-to-queue adjustment factor fD accounts tor the adverse enect or downstream queues on the discharge rate of an upstream traffic movement. In general, the saturation flow rate is low for movements that have a downstream queue relatively near at the start ofthe phase; it is high for movements that are not faced with a downstream queue at the start of the phase. Thus, the distance-to-queue adjustment factor is based on the distance to the back of the downstream queue at the start of the subject phase. The variable "distance to queue" is measured from the subject (or upstream) movement stop fine to the "effective" back of queue. The effective back of queue represents the location of the back of queue if all vehicles on the downstream street segment (moving or stopped) at the start of the phase were joined into a stopped queue. If there are no moving vehicles at the start of the phase, then the effective and actual distance to queue are the same. If there are no vehicles on the downstream segment at the start of the phase, then the effective distance to queue would equal the distar~ceto the through movement stop line at the downstream intersection. The distance-to-queue is computed as: n D = L _ s lv (40) Nd 3 - 3

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with where: Lv = (1 PHF) LDC + PHPLHV (41) D = effective distance to the back of downstream queue (or stop line if no queue) at the start of the subject (or upstream) phase, m, ~ = distance between Me subject and downstream intersection stop lines (i.e., link length, m; nS = number of vehicles on the downstream sheet segment (moving or queued) at the start of the subject phase, vein; N.' = number of through lanes on the downstream segment, Cartes; [v = average large length occupied by a queued vehicle, m/vein, [pc = lane length occupied by a queued passenger car (= 7.0 m/pc), mlpc; L,HV = lane length occupied by a queued heavy vehicle (~ ~ 3 m/veh), m/veil, and PHV = portion of heavy vehicles in the traffic stream. The effect of distance-to-queue is also dependent on whether spilIback occurs during the subjectphase. Spillbackis characterized by the backward propagation of a downstream queue into the upstream intersection such that one or more of the upstream intersection movements are electively blocked from discharging during some or all of their respective signal phase. If spillback occurs dunug the phase, We saturation flow rate prior to the occurrence of the spillback is much ~ .~ ~ . ~ ~ ~ ~ .. e - ~. ~ ~ ~ . ~ ~ ~ - - ~ lower than it WOUlCl be ~i there were no spa. l hUS, the magnitude ot the adjustment to the saturation flow rate is dependent on whether spilIback occurs during the subjectphase. A procedure for determining if queue spillback occurs is provided Appendix C. The distance-to-queue adjushnent factor is tabulated in Table 21. It can also be computed using the following equation: f = D where: fD = adjustment factor for distance to downstream queue at green onset; and D = effective distance to the back of downstream queue (or stop line if no queue) at We start of the subject (or upstream) phase, m. no spillback 1 + 813 D 1 : with spillback + 21.8 D (42) 3 - 4

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Table 21. Adjustment factor for distance-to-queue (fD) . Distance to Back of Spillback Condition Queue at Start of Subject Phase, mNo SpillbackWith Spillback 150.6490.408 300.7870.579 600.8810.734 1200.9370.846 1800.9570 892 2400.9670.917 3000.9740.932 3600.9780.943 Turn Radius Adjustment Factor. Traffic movements Mat discharge along a curved Ravel path do so at rates lower than Rose of through movements. The effect of travel path radius is tabulated in Table 22. It Carl also be computed using the following equation: r - fR 1.71 R where: fR = adjusunent factor for the radius of the travel path; and R = radius of curvature of the left-turn travel path (at center of path), m. Table 22. Adjustment factor for turn radius IRE Radius of the Travel Movement Type Pd~ ale, m Left & Right-Turn Through 0.824 1.000 15 0.898 1.000 30 0.946 1.000 45 0.963 1.000 60 0.972 1.000 75 0.978 1.000 90 0.981 1.000 105 0.984 1.000 3 - 5 (43)

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This factor was calibrated for lefts n traffic movements; however, a comparison of this adjustment factor to that developed by others for right-sum movements indicates close agreement. Therefore, this factor is recommended for use with both left and right-turn movements. Traffic PressureAdjustmentFactor. Saturation flow rates are generally found to be higher during peak traffic demand periods than dunng off-peak periods. This trend is explained by the effect of "traffic pressure." In general, it is believed that traffic pressure reflects the presence of a large number of aggressive drivers (e.g., commuters) during high-volume traffic conditions. They demonstrate this aggressive behavior by accepting shorter headways dunng queue discharge than would less-aggressivedrivers. As these aggressive drivers are typically traveling during the morrung and evening peak traffic periods, they are found to represent a significant portion of the traffic demand associated with these periods. The effect of traffic pressure was found to vary by traffic movement. Specifically, the left- turn movements tended to be more affected by pressure as their saturation flow rates varied more widely then those of the through movements for similar conditions. It is possible that this difference between movements stems from the longer delays typically associated with left-turn movements. Based on the preceding definition, it is logical that the effect of traffic pressure is strongly correlated with the demand flow rate in the subject lane group. Thus, the effect of traffic pressure, as represented by traffic volume, is tabulated in Table 23 for each movement type. It can also be computed using Me following equation: fv = .07 - 0.00672 v`' 1.07 - 0.00486 vat : left-turn through or right-turn where: fV = adjustment factor for volume level (i.e., traffic pressure); and v'' = demand flow rate per lane (i.e., traffic pressure), vpcpl. (44) As noted previously, ideal conditions were defined to include a traffic pressure effect representative of peak traffic penods. In this regard, traffic pressures under ideal conditions were defined as 10 and 15 vpcpT for the leh-turn end through movements,respectively. These flow rates are conservativein their representationofhigher volume conditions es they exceed 80 to 90 percent of all traffic demands that were observed at the field study sites. One consequence of this approach to defining ideal conditions is that it is possible for the traffic pressure adjustment factor to have values above I.0 when the flow rate is extremely high. 3 - 6

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Table 23. Adjustment factor for volume level (ices, traffic pressure) ~v) . Traffic Volume, Movement Type vpcpl Left-Turn Through & Right-Turn 3.0 0.953 0.947 . 6.0 0.971 0.961 9.0 0.991 0.974 12.0 1.011 0.988 15.0 1.032 1.003 18.0 1.054 1.018 21.0 1.077 1.033 24.0 1.100 1.049 3.~.2 Start-up Lost Time The start-up lost time associated with a discharging traffic queue varies wad its saturation flow rate. More specifically, start-up lost time increases way saturation flow rate because it takes more time for We discharging queue to attain the higher speed associated with Me higher saturation flow rate. The recommended start-up lost times corresponding to a range of saturation flow rates are provided in Table 24. These values Carl also be computed using the following equation: 1 = -4.54 + 0.00368 s. > 0.0 s where: is = start-up lost time, see, arid s' = saturation flow rate per lane trader prevailing conditions (= shy), vphgpl. (45) The recommended start-up lost times are applicable to left, through, arid r~ght-turn movements. Table 24. Start-up lost time (!J Saturation Flow Rate, vphgpl | Start-up Lost Time, see __ 1,400 0.61 1,500 0.98 1,600 1.35 1,700 1.71 1,800 2.08 1,900 2.45 2,000 2.82 2,100 3.~S 3 - 7

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unavailable for traffic service. This time is intended to provide a small hme separation between the ~. . . . . . . - ~ 3.~.3 Clearance Lost Time The time lost at the end of the phase represents the portion of the chance interval that is franc movements associated wan successive signal phases and, Hereby, promote a safe change in right-of-way allocation. Clearance lost time at the end of the phase can be computed as: le = Y ~ RC - gY (46) where: le = clearance lost hme at end of phase, see; Y= yellowinterval,sec; RC = red clearance interval, see; and gy= effective green extension into the yellow interval, sec. For speeds in the range of 64 to 76 km/in and volume-to-capacity ratios of 0.~8 or less, the average green extension is 2.5 seconds. This average value is recommended for use in most capacity analysis. More appropriate values can be computed from Equation C-51 in Annendix C when the ~. . ~. ~, . _ ~~, ~. ~. ~ r speeds are outs~cte the garage or o~ to -lo hm/h or whence tor the analysts period exceeds 0.~. 3.~.4 Lane Utilization Dnvers do not distribute themselves evenly among the traffic lanes available to a lane group. As a consequence, the lane of highest demand has a higher volume-to-capacity ratio and the possibility of more delay than the other lanes In the group. The HCM (3) recognizes this phenomena and offers the use of a lane utilization factor Uto adjust the lane group volume such that it represents the flow rate in the lane of highest demand. The adjusted lane group volume can be computed as: v' = vg'U where: v ' = demand flow rate for the lane group, vpc; v = g unadjusted demand flow rate for the lane grouts voc: and U= lane utilization factor for the lane group. ~, . . . (47) There are two reasons for an uneven distubutionoftraffic volume among the available lanes. One reason is the inherent randomness in the number of vehicles in each lane. While drivers may prefer the lesser-used lanes because of He potential for reduced travel time, they are not always successfi~! in getting to them for a wide variety of reasons (e.g., Friable to ascertain which lane is truly lowest in volume, lane change prevented by vehicle in adjacent large, driver is not motivated to charge lanes, etc.~. Thus, it is almost a certainly that one lane of a multi-lane large group will have more vehicles in it than the other lanes, during arty given cycle. 3 - ~

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The second reason for an uneven distribution ofbaffic volume among the available lanes is driver desire to "preposition" for a turn maneuver at a downstream intersection. This activity commonly occurs on the arterial cross street at interchange ramp terminals and at any associated closely-spaced intersections. This propositioning causes drivers to concentrate in one lane at the upstream ramp terminal or intersectionin anticipation of a turn onto the freeway at the downstream ramp terminal. Random Behavior Model. The lane utilization factor for an intersection lane group that does not experience propositioning (e.g., at an isolated intersection) is dependent on the degree of randomness in the group's collective lane-choice decisions. In addition, it is also based on the group's traffic volume on a "per cycle" basis. In general, lane utilization is more uneven for groups with low demands or a high degree of randomness or both. The recommended lane utilization factors for random lane-choice decisions are provided in Table 25. These values can also be computed using the following equation: U = r 1 ~ 0.423 ( 2 . 1 ~ 0~433 N' where: Ur = lane utilization factor for random lane-choice decisions; v' = demand flow rate for the lane group, vpc, alla N= number of lanes in the lane group. JV- 1 2 v' (48) The recommendediane utilization factors are applicable to left, ~rough, and nght-turn lane groups. Table 25. Lane utilization factors for lane groups with random lane choice (Ur) Lane Group Flow Number of Lanes in the Lane Group Rate, vpc ~1 2 ~3 5.0 1.00 __1.32 1.67 10.0 1.00 1.22 1.45 15.0 1.00 1.17 1.36 20.0 1.00 1.15 - 1.31 25.0 1.00 1.13 1.28 30.0 1.00 ~1.12 1.25 35.0 1.00 1.11 1.23 40.0 1.00 1.10 ~1.22 - 4 2.08 1.74 .59 1.51 1.45 1.41 1.38 1.35 3 - 9

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PrepositioningModel. The lane utilization factor for interchanges and associated closely- spaced intersections can be stronglyinfluencedby drivers prepositioningfor downstream turns. The magnitude ofthe effect is largely a site-specific characteristic,depending on Me number of vehicles turning left or right at the downstream intersection (or ramp terminal). If this information is available (such as from a turn movement count where downstream destination is also recorded), the lane utilization factor can be computed as: Max (v' , v' ~ JO U = 1.05 dl dr `49y P v' where: Up = lane utilization factor for propositioning; I'm= number of vehicles in the subject lane group that watt be thing left at the downstream intersection, vpc; V 'fir = number of vehicles in the subject lane group Mat watt be turning right at the downstream intersection, vpc; and Marfv dab V dart = larger of v 'a'' and v 'or Lane Utilization Factor. The possibility of preposition~ng must be evaluated to determine whether to use Equation 48 or 49 to estimate the lane utilization factor U. This possibility can be determined from the following test: MaX(Y'd`' V err) > ~prepositioning Maxfv 'dl, v tarry < _ V' N : no preposltlonz'2g Based on the outcome of this test, the lane utilization factor is computed as: U= Up: propositioning Ur: no propositioning (50) (51) The distance to the downstream intersection could effect the propensity of drivers to preposition into their desired lane. In recognition ofthis effect, the test equation is recommend only for intersections located in interchange areas or near other closely-spaced intersections where the inter-signal distances are less than 300 meters. 3 - 10

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3.2 INTERCHANGE CAPACITY ESTIMATION METHODOLOGY 3.2.1 Signal Timing A two-level signalized interchange is essentially composed of two closely spaced intersections (except for a SPUN) connected by an internal arterial link. As shown in Figure 34, each intersection will have an arsenal input phase (a), and most will have a ramp input phase (b) together with an arsenal left turn phase (c). Elapsing cycle time is upward in the example phase sequences depicted in Figure 34. All diamond interchanges end two-quadrantparclos wall have all three phases per intersection in some configuration. Some four-quadrant parclos (Parclo BB) do not need the ramp phase (b) and others (Parclo AA) not the arterial left turn phase (c). Thus, for most interchange cases, three separate protected phases serve each ramp terminal. In 1973, Munjal (12) graphically examined the three critical conflicting phases at each intersection of a diamond interchange. This phase notation was adopted by the widely used diamond interchange computer program, PASSER Ill, developed by Texas Transportation Institute in ~ 977 (139. Almost all signal timing plans used at two-level interchangestoday can be described by using the a:b:c phase sequence in four combinations together truth a related signal offset between the two Various phase overlap intersections. Table 24 illustrates these phase sequence como~na~ons. combinations are also possible, depending on the Interchange type anct signal onset. Table 24. Basic Signal Phase Sequences at Interchanges Phase l Left-Side Right-Side | Signal Combination Intersection Intersection Sequence 1 | abc 2 abc acb Lead-Lag 3 acb abc Lag-Lead 4 acb acb Lag-Lag ~. red ~,, Figure 35 presents typical signal timing plans for some common interchange types for illustrative purposes. The four-phase strategyis depleted for diamondinterchanges. As can tee seen, n~rti~1 ~l~verl~f~ (arc in contrast to traditional diamond interchanges, provide some application variation but do not change the basic concepts. Two-quad pros have three phases per intersection;whereas, four-quad parclos have only two phases per side, deleting the ramp Phase b (Parclo BB) or arterial left turn Phase c (Parclo AA). The two-quad parclos may have Phase c in the inbound direction to the interchange (Parclo AA) or in Me outbound direction (Parclo BB). Moreover, the ramp phases (Phase b) may be ire advance of the cross street (Parclo AA), as in a conventional diamond, or beyond (Parclo BB). Parclos provide one distinguishing phasing difference to diamonds in that right-turn (sometimes free) signal overlaps are common. Single-point urban interchanges (SPUN) basically employ a conventional intersection phasing sequence, using 3 - I]

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INTERCHANGE Procedural Design Analysis performed using existing software packages Inferface HCS PASSER tl, ID TRANSY7-7F Offer srare 1 A~atysis Operational analysis as perforrnedby ff,e specific program Output Capacity Delay LOS Input Turning movemerd volumes for one interchange forth Type of analysis requested Int~nge types to analyze Geometric and Simon Condemns 1 C_ Analysis 1 Database conversion algoritfuT Analysis to be performed using proposed new single software package , _ _ Analysis Volume A~J~nt Module Satua0 - Flew Rate Module Effective Green Module Capacity Analysis Module Level of Service Module Output Future or existing fuming volumes for chosen interchanges LOS and performance measles for chosen intone Ranldng based on o~a~al performance measures and LOS Figure 39. Fltow diagram of optional procedural dlesign for INTERCHANGE. 3 - 32

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3.5 SIGNAL TIMING IMPROVEMENTS FOR CLOSELY SPACED INTERSECTIONS Developing optimal, or even good, signal timing plans for signalized interchanges that connect to a high-volume signalized crossing arterial is a complex task and current technology is limited. Unintentionally poor signal timings may produce oversaturation end avoidable congestion. Even if oversaturationis unavoidable due to excessive traffic volumes, improved operations can be provided along the arterial and interchange ramps by avoiding signal plans that we be inefficient for the given situation. All aspects of the operations should be examined. Short links, say less than ~ 50 m, are especially troublesome. Links that have a predominate input flow are subject to demand starvation, and much of the downstream green may be wasted if a poor signal plan is implemented. On the other hand, links having nearly balanced input flows, as can often happen around interchanges with high local access demands, are insensitive to some operational control measures. No unproductive conslra~nts should be placed on the overall system to try to treat such overloaded links for all other links would probably only get worse and no appreciable benefits would likely accrue. The following models are provided as guidelines toward improving traffic signal control during these problematic situations. Signal timing, traffic pattern, and queue storage length are principal factors of flow control during such high-volume conditions. Effects of these factors on flow were illustrated in Chapter Two. Within signal timing, signal offset is a robust and critical control vanable. In this section, signal offset, din, is defined as the elapsed time from the start of green of the major phase at the upstream intersection carrying the highest volume of input traffic onto the link id to the start of green ofthe arterial through phase at the downstream intersection. The upstream major phase will usually be the arsenal input phase, but not always in cases of high-volume turning traffic. The offset described below may become "negative" meaning an early start of the downstream green, but the offset used in the signal plan must be the equivalent"moduTo C" offset. Two offset controls will be described: (] ~ queue clearance offset and (2) storage offset. The larger ofthe two offsets should not be exceeded In most cases currently envisioned if peak flow efficiency is to be maintained. 3.5.! Queue Clearance Offset In special arterial traffic signal coordination cases where all the arsenal traffic is 100% through traffic (arsenal dominance), the ideal signal offset between the upstream signal and the downstream signal would be equal to the travel time over the link for the running speed of the ~c. As non-arsenal traffic (assumed to be non-coordinated) becomes a larger portion of the link flow, queuing dunng red increases and the downstream offset should be reduced to "clear the cross-street queue" before arrival of the major platoon. One offset selection model of this process is: r ~ where: ~3 ~- - r (93) u s 0,j = relative offset between major phases on link i-j, see, L = length of link id, meters, 3 -33

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u = running speed of arterial link flow, mps; r = effective red of downstream signal, see; or = downstream arrival volume on red, vph, and s = saturation flow of downstream phase, vphg. As the upstream turning volumes become a larger percentage of the total downstream volume, then or increases, the downstream queue grows, and the relative offset Bit should be reduced from the ideal progression offset to reduce spillback. Using the Highway Capacity Manual's (3) concept of detennining the proportion of arsenal traffic alTiving on the downstream green, P. then the queue clearance offset would be l = (1 - P) vC in u s where: Bid L u p v C = relative offset between major phases on link i-j, see; length of link id, meters; running speed of arsenal traffic flow, mps; proportion of arsenal traffic arriving on downstream green; total downstream arterial arrival volume on phase, vph; and cycle length, sec. (94) Onsets less than that given above would be expected produce some demand starvation. Any reduction in offset from Me ideal should not exceed the green time necessary to saturate the phase. During undersaturated conditions, offsets greater than this value will produce some queue spillback on the major (arterial) phase which may result in queue spillback into the intersection and oversaturation on the upstream link if the downstream link is too short (See Equation D-] I. 3.5.2 Maximum Storage Offset Another limit placed on signal offset adjustment that should be considered during high- volume conditions is related to the length ofthe link. To minimize the chances of demand starvation, the link offset should not be less than L 3600 NL e..= " u s! u 3.5 ~ ~ where: u N s 1 0,j = relative offset between major phases on link id, see, L = length of link id, meters; ~ .~, , naming speed of arterial traffic flow, mps, number of lanes on link id; saturation flow of downstream phase, vphg; and queue storage length per vehicle, about 7 m/vein. 3 - 34 (95)

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The final selection of offset should consider many factors, including the volume level, traffic pattern and degree of saturation of the downstream signal. However, to enhance the throughput efficiency dunng high-volume conditions, the link offset shows not be less than the larger of Equations 94 arid 95 given above. 3.6 ARTERIAL WEAVING SPEED ANALYSIS METHODOLOGY The procedure for computing the speeds of vehicles in the arsenal weaving section is outlined in the flow chart shown in Figure 37. This flow chart illustrates the sequence of computations required to compute the average running speed of artena] through and weaving vehicles in the weaving section. The arterial weaving section of interest is the one created by the combination of a signalized interchange off-ramp and an adjacent, closely-spaced signalized intersection. | Input Data Geometr~cs Traffic | M a ne Over S peed to r Arteria I Th roug h Ve h icles, Um a I | Weave Maneuver Distance, Drew | 1 , Probability of Being Blocked, Pu r Maneuver Speed for Weaving Vehicles, Um,w Figure 37. Flow chart to determine speeds in an arterial weaving section. The weaving maneuver considered is the off-ramp nght-turn movement that weaves across the arterial to make a leflc-turn at the downstream signalized intersection. The terminology "arterial weaving" is adopted in this methodologyto clearly indicate that the weaving occurs on streets whose traffic flow is periodicallyinterruptedby traffic signals, as compared to the more extensively studded weaving that occurs on uninterrupted flow facilities. 3 - 35

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3.6.1 Maneuver Speed for Arterial Through Vehicles Input data needed to compute the maneuver speed for arterial through vehicles includes the average arterial speed and flow rate entering the weaving section. This average speed represents the desired speed of the traffic stream when there is no weaving activity present. The arterial maneuver speed can be computed with the following equation: Um = 1.986 U0 7~7 e (-0 634 Vo/3600) (96) where: U,,2, a = average maneuver speed for arterial through vehicles, m/s; Ua = average arterial speed entering the weaving section, m/s; and Va = average arterial flow rate entering the weaving section, vph. The average maneuver speed is defined as the average running speed of arterial vehicles through the weaving section. It represents the ratio of travel distance to travel time within this section. The arterial and weaving maneuver speeds are computed in a similar manner; however, they do not tend to converge for low volume conditions. This trend is due to the fact that the weaving maneuver generally has to accelerate from a stopped (or slowed) condition whereas the arterial maneuver generally enters Me weaving section at speed. 3.6.2 Maneuver Speed for Weaving Vehicles The average maneuver speed for weaving vehicles is dependent on a variety of traffic conditions and events. Traffic conditions include the average arterial speed entering the weaving section, volume of weaving vehicles, and available weaving maneuver distance. The primary traffic event is the probability ofthe weaving vehicle not teeing blocked from entering the weaving section or delayed during its maneuver. The average arterial speed was discussed in the preceding section. The average weaving flow rate Vw represents the number of vehicles that completed off-ram~right-to-downstream-left-turn maneuver during the analysis period, it is a subset of the number of vehicles that enter the arterial via the off-ramp. The remaining variables require computation, equations for this purpose are described in the following paragraphs. The available weaving maneuver distance L4 w represents the average length of arterial available for a weaving vehicle to complete its weave maneuver. This distance can be estimated as: V r L a v L = ~ x (97) 1 - 51 Nt 3 - 36

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where: [q w = average length of queue joined by weaving vehicles, m. s' = saturation flow rate per lane under prevailing conditions (~ I,800), vphpI, N. = number of arterial through lanes in the subject direction, lanes, r = effective red time for the downstream intersection through movement; see, and average lane length occupied by a queued vehicle (See Equation C-45.), m/vein. The "probability of a weaving vehicle being unblocked" Pu represents the portion of time that the end of the off-ramp (i.e., the beginning of the weaving section) is not blocked by the passing ofthe arterial traffic stream or the spilIback of a downstream queue. This probability is dependent on the length of the weaving section. A "Ion"" weaving section is defined as a section that has sufficient length to allow a weaving driver to weave across the arterial one lane at a time. If this minimum length is not available, then the section is referred to as "short." The weave maneuver in a short section requires the simultaneous crossing of all arterial lanes (in Me subject direction) using more of a "crossing" than a "lane-changing" action. The equation for estimating Pu is: P u ~ ~N ~ ~Ir ~ ~ ~ ~2 0 where: Pu = probability of a weaving vehicle being unblocked, I~ = indicator variable (~.0 if Dm w ~ 90 by, - A, 0.0 otherwise); Dm w = average maneuver distance for weaving vehicles (= tw - [q w)' m, and [a = distar~ce between the off-ramp entry point and the stop line ofthe downstream intersection (i.e., the length of the weaving section), m. It should be noted that Pu is equal to 0.0 when the average queue length equals the length of the weaving section (i.e., when Dm w is effectively zero). Using the probability of a weaving vehicle being unblocked and the weaving volume, the average weaving maneuver speed can be computed as: Um w = 3 741 U0408 e ~l] 045~} -PU) VW/3600) where: U., w = average maneuver speed for weaving vehicles, mJs; and Vw = average weaving flow rate, vph. (99) Like the arterial maneuver speed, the weaving maneuver speed is defined as the average running speed of weaving vehicles through the weaving section. 3 - 37

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3.6.3 Example Application The following example is used to demonstrate the application of the arterial weaving speed analysis methodology. The arsenal weaving section has the following attributes: Geometric Data: Number of arsenal through lanes in the subject direction, N. = 2 lanes Length of the weaving section, to = 200 meters Traffic Data: Average arsenal speed entering Me weaving section, Ua = 12.5 m/s (45 km/in) Average arsenal flow rate entering the weaving section, Va = 1,000 vph Average weaving flow rate, Vw = 170 vph Saturation flow rate per large, s' = 1,800 vphgpl Elective red time for the downstream intersection, r = 50 seconds Average lane length occupied by a queued vehicle, [v = 7.0 m/vein Analysis: 1 . Using the average arterial speed and flow rate, the average maneuver speed for arterial through vehicles Um a can be computed as ~ 0.2 m/s. 2. Using the arterial flow rate, elective red time, saturation flow rate, and number of lanes, the average length of queue joined by weaving vehicles [q w can be computed as 135 meters. 3. The average length of queue, combined with the weaving section length, yields a maneuver distance Dm w of 65 meters. 4. Based on the maneuver distance of 65 meters, it can be concluded that the weaving section is too short for a driver to weave by changing lanes one at a time. The driver is more likely to cross all lanes at the same time (i e., IL = 0 0) 5. For short weaving sections, the probability of a weaving vehicle being unblocked Pu is computed as O.52. 6. The weaving flow rate and probability of blockage can be used to compute the average weaving maneuver speed Um w as 8.2 m/s. If the weaving section length were 3 00 meters long then it would be characterized as a "Ion"" section. In this case, weaving through the section would likely occur one lane at a time and the weaving speed would increase to 9.~ m/s. However,,the predicted arterialthrough movement speed Um a is unchanged (i.e., it equals ~ 0.2 m/s). 3 - 38

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3.7 RAMP WEAVING CAPACITY ANALYSIS METHODOLOGY The procedure to determine the interchange ramp weaving capacity across the connecting arsenal street for a specific progression factor arid arsenal through volume is shown in Figure 40. The flow chart illustrates the methodology to determine the ramp weaving capacity for crossing He arterial arid mar~euvenug into a downstream left turn bay given progressed flow along the arsenal. The procedures are as follows. Input Data: Geometrics Traffic ~ c Ramp Capacity for Random Flow along Arterial, Q R (Eq. 100) ~ c Adjustment for Sneakers Q'~ = QR + SR (Eq. 101) ~I Adjusted Ramp Capacity for given PF = Q PF (Eq. 102) Figure 40. Flow chart to determine ramp weaving capacity. 3 - 39

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3.7.1 Ramp Capacity During Random Flow Data necessary to compute ramp capacity for random flow are total arterial volume, number of lanes on the arsenal in the direction of merging operations, and the coefficients a, ,0. The data required to determine the ramp capacity for progressed flow include the number of lanes on the arterial, the required PF and v/c ratio e The number of lanes of the arterial are used to select the a arid ,B coefficients Tom Table 26 which are employed in the exponential regression equation for estimating ramp capacity during random flow conditions given below. V -ad, QR -Din 1-e ' where: OR = ramp crossing capacity, vph; V, = arterial through volume, vph; ~= coefficient of Me model = TC / 3600, and ,6 = coefficient of the model = Hs / 3600. Table 26. Coefficients of the exponential regression mode! Thru Lanes | 1 large 1 2 Caries | 3 larches . Coefficients a ~a ~ Exponential 0.00195 0.000657 0.00118 0.000574 0.00088 0.000565 R2 Value 0.9977 0.9995 0.9989 Conversion of I Tc l I Tc I ] Is | Tc | H Values (sec.) 7.02 2.36 4.26 2.06 3.17 2.03 Table 26 shows the coefficients a and ,8 of the exponential model computed for one, two and three thru lanes of arterials. The coefficients in the proposed exponential equation are accurate estimations of the TRAF-NETSIM imulated operations in terms of standard errors and their vanances. 3.7.2 Adjustment for Sneakers Additional ramp capacity may be obtained by ramp vehicles weaving across the arterial flow during the phase change intervals of the upstream signal. Simulation studies suggest that as many as three "sneakers"per phase change may cross during capacity conditions . Thus, the ramp crossing capacity adjusted for sneakers would be 3 - 40

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/ 3600 S n QR = QR ~ where: Q R QR so no = C - ramp weaving capacity adjusted for sneakers, vph; ramp weaving capacity for random flow, vph; and sneakers per phase change, vehicles, number of phases per cycle; and cycle length. 3.7.3 Adjustment for Progression (101) Ramp weaving capacity is affected by the quality of progression on the arterial street. The quality of progression is identified in the Highway Capacity Manual by progression factors. In order to obtain the ramp weaving capacity for different progression factors, weaving adjustment factors for progression, fpF are determined and multiplied by the ramp capacity which has been adjusted for sneakers. The adjustment procedure is QPF QR fPF where: QPF Q R fPF ramp weaving capacity adjusted for progression, vph; ramp weaving capacity for random flow, vph; and ramp weaving adjustment factor for progression. The adjushnent factors for progression range from 0. ~ to ~ .0 and are determined from fpF = 1 + 0~015 * e [0.0044*~-3.05*PF] where: fPF = ramp weaving capacity adjustment factor, PF = HCM progression factor, and V, = arterial volume per hour per lane (vphpl). (102) (103) Note that HCM PF values exceeding 1.0 should be replaced by their complimentary value to 1.0. That is, a PF of I.3 should be replaced by a value of 0.7 in the above equation. The progression factors are determined from Table 9. ~ 3 in the ~ 994 Highway Capacity Manual (39. 3 -41

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3.7.4 Example Application Geometric Data: Number of lanes on arterial Number of lanes on ramp Link length between ramp and downstream intersection Traffic Data: Arterial Through Volume Cycle Length Lost time per Phase Analysis: Ramp Capacity (for three lane arterial) ~ (for three large arterial) Sneaker Volume = 3 lanes = 1 lane = 1 83 meters (600 feet) = 1500 vph = 100 seconds = 4 seconds 0.000565 [From Table 26] [From Table 26] [3 vein/phase * 2 phase change intervals * 36 cycles - 216vph Assume the ramp capacity for a PF of 0.2 and v/c of 0.6 is to be determined. Ramp capacity for random flow Substituting values in the above equation yields QR QR = 701 vph Accounting for ramp vehicles weaving during the phase change interval Q R = QR + Sneaker Volume = 701 + 216 = 917vph For progressed flow along the arsenal having a PF of 0.2 and a v/c of 0 6, IF can be determined from Tahie 20 as ~ 074 Therefore Ramp Capacity for a PF of 0.2 and v/c of 0.6: QPF = Q R * fPF = 91 7 * 1. 074 = 984 vph 3 - 42