Click for next page ( 280


The National Academies | 500 Fifth St. N.W. | Washington, D.C. 20001
Copyright © National Academy of Sciences. All rights reserved.
Terms of Use and Privacy Statement



Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.

OCR for page 279
APPENDIX D CLOSELY-SPACED INTERSECTION FLOW MODELS D.1 OVERVIEW The following appendix presents research that addresses traffic operations on the arterial street connections (links) between He traffic signals at signalized interchange ramp terminals, and also on the connecting links to adjacent intersections downstream from the interchange. Various Arc models are applied to Be complex traffic operational conditions. The fundamental problems of queue spilIback arid flow blockage are addressed. Guidelines for identifying "closely-spaced" intersections are provided. A detailed computer-based aigorithm,basedon the Prosser-Dunn model, for assessing the impacts of queue spilIback was developed arid applied to a wide range of traffic conditions, including oversaturation. D.2 LINK FLOW CONDITIONS Traffic flow on a signalized cross arterial link traveling through an interchange is very complex due to several factors. The downstream traffic signal routinely interrupts the flow forming queues behind the signal which must be subsequently dissipated Junng the next cycle. The amount of queue formation depends on the amount of upstream mining traffic, the quality of signal progression, and the resulting total traffic demand that arrives on the movement. Traffic operations on the link ultimately depend on whether the link's arrival demand volume for any movement exceeds the link's capacity to service it. If the link becomes oversaturated, due to demand exceeding output capacity, then the link urine initially experience severe queue spilIback and soon watt become flooded with cars. The degree of resulting traffic flow and congestion depends almost entirely on the ability of the link to discharge vehicles downstream, otherwise total stoppage (grid lock) mI} occur. During heavily congested conditions, signal coordination primarily determines which feeding movements get to proceed, but usually not the Overall quantity of flow on the link. Assuming that traffic conditions on a link are urldersaturated, then flows on the link may be assumed to cycle through a series of states shown in Figure D-} where the arrival flows from the upstream movements proceed downstream and some are routinely stopped, accumulated in queue behind the downstream signal displaying red, and then subsequently serviced on the following green. Whereas arrival flows to the interchange ramps and some minor cross streets may be random at some average arrival flow rate, most arrival demands to the head of a link are, in reality, the output flow profile from an upstream signal modified by some platoon dispersion, depending on the distance "raveled downstream. Platoons are usually not dispersed Critic they travel about two (2.0) minutes, so platooned flow along the crossing arterial is common for urban interchange operations. D - ~

OCR for page 279
L u TV ~ q.= Flow, q (vph) _ Vm (qm+ql+qr) Saturation q -S Arrival Flow qm = V "d" qm= V No Flow qm= 0 Green Red Green Time in Cycle Figure D-1. Traffic Flow Conditions on a Link. D - 2

OCR for page 279
D.2.l HCM Arrival Flow Profile Anival flow to a downstream closely-spaced arterial signal is inherently dependent on upstream traffic and signal conditions which may not be well known. Modeling assumptions may have to be made to provide tractable solutions. For Highway Capacity Manual fly level of analysis, one assumption usually made is Hat He anival flow to an arterial signal is composed of two component flows: one arriving during the downstream green and one during He red, or Va = Vg (g/CJ + Vr (r/C) where: v = a Vg = vr g/C = r/C = = average arrival volume during cycle, vph, anival volume on green, vph; arrival volume on red, vph; green ratio; and red ratio. D.2.2 PASSER I! Arrival Flow Profile (D-~) The next higher level of arrival flow profile found in traffic signal timing software is in the PASSER I} - 90 software developed by IT] for arterial signal timing optimization (29. PASSER I! assumes a two-flow model somewhat like the HCM except that one flow, the larger arrival flow, is defined as being the flow of the larger arriving platoon, in time, space, and rate of flow, and all other flows are combined into a single secondary flow region. This flow model is va = vp (s/CJ + vnp (C p)/C (D-2) where: v = a Vp = ~= no average arrival volume during cycle, vph, maximum arrival volume in largest platoon, vph, and average arrival volume during remainder of cycle, vph. Flow profiles depend on the progression arid are calculated based on the resulting time-space diagram for the arterial. Delay is calculated as being the area of the queue polygon resulting from the piece-w~se integration of the input-output flow profiles over a representative cycle. D.2.3 PASSER Ill Arrival Flow Profile PASSER Ill is a computer model developed by TT! that is widely used to evaluate arid optimized traffic operations at signalized diamond interchanges (3~. Its arrival flow model provides the next higher level of sensitivity to variation in predictable arrival patterns. PASSER Ill models D-3

OCR for page 279
three flow regions of the cycle, having two flows for each of the three upstream protected phases (i.e., A, B. C). The resulting downstream flow profiles are va VAP (Ap/C) + VAa fA a/C) + VBp (Bp/C) + Vga (Ba/C) + vcp (Ca/C) + VCa (Ca/C) (D-3) where: average arrival volume during cycle, vph; platoon flow downstream from Phase A, vph; average arrival flow to/fiom Phase A, vph; platoon flow downstream from Phase B. vph; average arrival flow to/from Phase B. vph; platoon flow downstream from Phase C, vph; and average arrival flow to/from Phase C, vph. For diarnondinterchanges,arrival flows comingirom an upstream Phase C signal are normally zero because this phase is the outbound left turn phase to the on-ramp. D.2.4 TRANSYT 7F Arrival Flow Profile An even higher-level arrival flow model is employed in TRANSYT 7F, another signal timing optimization and analysis program supported by Federal Highway Administration (4). A discretized output flow profile is developed for each upstream input flow which, when adjusted for platoon dispersion, becomes a component to the arrival flow profile of interest. The individual arrival flow profiles are summed to generate the total arrival flow profile. As in the above programs, the upstream phasing sequence must be defined together with all elements ofthe time-space diagram, signal progression, and platoon dispersion The discretizationtime slice in TRANSYT 7F can be as small as I/60 of a cycle. Thus, there can be up to sixty discrete arriva] flows calculated for a movement, which are the sums of all upstream feeding flows for that time slice (T+K), or v&(T+K&) = ~vm(T+K=) (D-4) where T is the travel time between the intersections. This high level of detail can only be achieved by automating the analytics to make the volume estimation process practically feasible. D.2.5 Arr~val Flow Mode! Recommended The selection of arrival flow modeling sets the standard for the level of precision for all ~e level of service modeling to follow. It is presumed that the average flows that would occur during the cycle, peek period, and wi~in the hour of interest can be estimated with suff~cient accuracy. For external approaches or isolated approaches that do not have a signal within two minutes travel time to the subject approach, the assumption of random arrival flows (Poisson) is sufficient. For traditional coordinated arterial signal systems having modest turning traffic (say 20%) and generous D -4

OCR for page 279
intersection spacings, a two-flow model (flow during red, flow during green) as employed in Chapter 1 1 (Arterials) of the HCM is probably sufficient in most cases. An obvious improvement would be to transition to a two-flow model like used in PASSER II (flow during platoon, flow not in platoon). For interchanges operating with high turning traffic and within a system of closely- spaced intersections, arrival modeling should be at least as detailed as used in PASSER III wherein six arrival flows are possible, two (platoon and non platoon) for each of three feeding movements during the cycle. While coordination in interchange systems is probably not as effective (due to higher turning traffic and more balanced flows) as in arterial systems having predominate through traffic, at least the features of platoons arriving at interchanges could be readily identified so that queuing and delays could be reduced somewhat over solutions assuming random flow. D.3 MACROSCOPIC FLOW MODELING Models of traffic flow routinely used to describe continuous flow traffic facilities, like freeways, can also be used to describe the dyna~nicsof flow attraff~c signals (5). These models can be used to describe the nature of operational problems experienced. Traffic signal operation routinely creates brief interruptions to continuous flow, forming bottlenecks where the arrival demand exceeds output capacity during the red interval. Shock waves form behind the signal due to the queuing and spillback that occurs (6). D.3.! Flow Models When traffic flow can be assumed to be in a steady-state condition, even for a fairly brief period of time (t) and space (x) such as for random arrival flow or platoon flow at saturation, then the average flow rate during this period, v (vpt) can be thought of as being produced by a traffic stream having an average density k (vpx) traveling at an average speed u (xpt)' or v =ku where: v = average traffic flow rate' vpt, k = average traffic stream density, vpx; and z' = average traffic speed, xpt. (D-5) In undersaturated,signalized arterial operations,the flow rate on a short section of roadway just upstream of a traffic signal is usually in one of three states: v = v, v = 0, or v = s. That is, the flow is characterized as being either the arrival flow, stopped in queue, or the queue has been transformed into a platoon with saturation flow, s. These three flow states were identified in Figure D-1 . Whether these changes from one state to another occur almost instantaneously(creating shock waves) or transition over a brief period of time (forming characteristic waves) is more of a theoretical issue and presumed herein to be of minimal importance. For convenience, rapid response to signal change is assumed so that conventional shock wave analysis can be employed. D - 5

OCR for page 279
Basic macroscopic traffic flow modeling for steady-state conditions presumes (hoary car- follow~ng laws and empirical observations) that the speed of operation is a function of the average density of the section of road (immediately ahead) and the current speed (5) such that ~U~-m i- = 1 u k f q and solving Equation D-6 for u =f(k) and substituting into v = k u, ~ = kf~J yields v = k Uf t1 _ ~ k yI~1~1/~1-m) q for the section x of interest, where: v = traffic flow in section x at t, vpt; k = traffic density, vpx; Uf = free speed, xpt; kq = jammed queue density, vpx; and I, m = shape coefficients. (D-6) (D-7) The traffic flow graphs (for Case I) shown in Figure D-2 were drawn for the following assumed arterial operating conditions: Uf = 64 km/in (40 mph); kq = 143 vpkmpI, (7m/veh, 230 vpmpI, 23 It /veh), s = 1800 vphp} at a saturation flow speed of 37 km/in (23 mph). Under these assumptions,] = 2.645 and m = 0.666. The three flow vanables (v, k and u) are all interrelated and can be calculated given one of them together with the section parameters arid coefficients. D.3.2 Saturation Flow Saturation flow can be assumed to be the "capacitor" flow region of the flow curves, suggesting that the saturation flow may increase as the platoon speeds up, or flows faster if the platoon can travel faster for a given vehicular spacing (density). Research shows that saturation flow increases with increases roadway quality and operating speed. Over several editions of the HCM, freeway capacity has increased from about ~ 800 vphpT at 50 km/in to 2000 vphp! at 70 kmAl, and is now approaching 2300 vphp! at 90 larch. This NCHRP research combined with the results of NCHRP 3-40 (~) suggests similar bends for sianalizedintersections end interchanges when flowing - - - ~ ~ ~ - -7 ~ ~ ~ - ~ ~ ~ o ~ ~ . . ~ . ~ ~ ~ a, 1 at equal loadings and pressure. Figure ~-;z also Sates now the ~low-censlty curves would expand with increasing quality of operations. Case I] assumes a saturation flow of 2,000 vphp} at 40 km/in (25 mph). The loci to the family of curves would represent the expected saturation flow at the signal when We platoon is flowing at its maximum flow for increasing quality of operating conditions. D - 6

OCR for page 279
Flow vs Density 2000 1800 1600 1400 - ~ 1200 - 1000 0 800 - E~ - 600 400 200 O 2000 - . 18~ , _ , '. \ Saturation Flow stopped Quelle \' Case I ~ \ "+ Case II :'.. 1 1 1 11~ 2S SO 7S 10012S lSO Density (vpkm) Speed vs Flow 1600 1400 1200 1000 800 600 400 200 o ~ ~ . ~ ' ~ ,"~ """ ;;~/ Samration Flow \ / \ ' .'/ \ '% ~HI ~ ~II ~ it" ~ ERIC ~ lk ~'` ~ 1 1 1 1 1 1 ~1 ~ 0 10 20 30 40 50 60 70 80 90 Speed (kmph) S=1800 vph S=2000 vph Uf= 64 kInph Uf= 88 kmph . Figure D-2. Characteristics of Traffic Flow for Two Capacity Conditions. D-7

OCR for page 279
D.3.3 Shock Wave Speed When arterial arrival flow passing through a green signal is suddenly stopped by the onset of red, the output flow suddenly drops from ~ = v to v = 0. When this charge in output flow of the section occurs, the storage begins to queue behind the signal at a storage density k,, the queuing Clam density'' of about 7.0 meters per vehicle (23 feet/vehicle). The speed at which the storing queue propagates (spills back) upstream can be estimated from shock wave theory 66) as W l~v v (D-8) q where: Wr = shock wave spillback speed due to red onset, xpt, v = arrival volume (dunng red), vpt; and k = traffic stream density, vpx. The speed at which the shock wave propagates upstream increases with increasing arrival volume. For an approach having average flow conditions described as Case ~ in Figure D-2, and a green ratio of 30% which yields a phase capacity of 540 vphpl, then for arrival volumes of 20, 60 and 100 % of signal capacity, the shock wave speed progressing upstream during red would be estimated by Equation D-8 to be 0.22, 0.67, and 1.12 mps, respectively. However, if the signal became oversaturated or poorly timed such Mat the start of red ended platoon motion while at saturation flow v = s, then the shock wave speed would rise to 5.35 mps. However, as long as the signal is undersaturated, the maximum queue length per cycle would remain the same. - 7 .A '' ~ D.3.4 Platoon Wave Speed When the signal turns green following an extended red time and subsequent queue buildup, the platoon responds and begins to move forward, reaching saturation flow conditions in a few seconds after green onset. For HCM-level of analysis, the platoon is assumed to reach saturation flow almost immediately once the queue-platoon transformation begins at any point in the queue. Under these simplifying assumptions, the platoon's green wave speed would be given by W = where: Wg k - h _ Ant = REV S g Ak k - k q s platoon start-up green wave, apt; saturation flow during green, vptpl; platoon density during saturation flow, vpxpl; and queue storage density, vpxpl. D - 8 (D-9)

OCR for page 279
The queue's transformation into a moving platoon would propagate upstream following green onset at 5.35 mps (12 mph). If the output saturation flow is unimpeded on the downstream link, then the green wave speed is fairly constant over all arrival volume conditions, simplifying the analysis. The main problem would be to determine how far upstream queue spilIback has progressed each cycle before it begins clearing. D.3.5 Clearing Wave Speed Once the platoon begins to move forward on green, flow in the platoon is assumed to be saturation until the platoon clears the stopline. The arrival volume, v, is entering the upstream end ofthe platoon; whereas, saturation flow, s, presumably is occurring downstream to the stopline, or downstream boundary. During this cleanng penod, the back of the platoon is traveling downstream from its maximum backup at the platoon clearing wave speed of W = Av = s - v C Ak ks - k (D-10) Continuing with the data of Figure D-2 where kq = 143 vpkmpI, s = I 800 vphpI, us = 37 km/il, then ks = 48.6 vpkmp] from k = v/u. An examination of the above wave speeds follows. Figure D-3 presents the resulting wave speeds for the above conditions for volume-to- capacityratiosofO.2to I.O for aselectedg/C ratio of 0.3 end a LOO-second cycle. The speed ofthe shock wave, W., is very slow (about ~ nips) and only increases slightly with increasing v/c ratios of the signal. The platoon start-up wave, Wg, is noted to be a constant of 5.35 mps, and the platoon clearing wave is high (about ~ 6 mps) and only decreases slightly with increasing arrival volumes. Thus, because the wave speeds are fairly insensitive to arrival volumes at traffic signals, analyses based on the wave speeds are relatively stable as long as traffic flow on the link is undersaturated. D.3.6 Queue SpilIback The duration and extent of queue spilIback determines whether an upstream intersection wall be severely affected by downstream operations. In essence, the characterization of adjacent intersections being too "closely spaced" can be defined for undersaturated conditions where X<= 1 . Using the above shock wave theory, the maximum length of queue spilIback can be determined in time arid space by algebraic solution of the Wr and Wg wave intercepts for a given red time. r The elapsed time following green onset before Wg catches Wr is ~7 W T = r r (D-1 1) g W- W where Tg is the elapsed time since the onset of (effective) green. D-9

OCR for page 279
we we 2s 1 = 2.645 20 - . m = 0.666 E ~-- - IS C ~ 10 3 s- O- ~1 0 0.2 0.4 0.6 - Wr o.g l 1.2 Phase Volume-t - Capacity Ratio, X Figure D-3. Wave Speeds at Traffic Signals During Undersaturated Conditions. The maximum queue backup for undersaturated conditions, [n'' is equal to A, = Wg*T,, or W W L = g r r m W ~ W g r subject to the restriction that the downstream phase is not oversaturated. (D-12) Figure D-4 presents the queue spilIback for an approach having random flow-(uniformly distributed over the cycle) for v/c ratios up to ~ .0, or saturation. The traffic and control conditions are as above (s = ~ 800 vphpI, C = ~ 00 see, g/C = 0.31. The capacity of the approach is 540 vphp! (c = 0.3 * ~ 800~. The maximum queue spilIback distance upstream from the stopline would be S2 meters and 99 meters for v/c ratios of 0.6 and ~ .0, respectively, using Equation D-12. These results indicate that storage links less than ~ 00 m may often experience spilIback problems on entry flows where good progression is not provided, even when the downstream flow is undersaturated. D- 10

OCR for page 279
100 90 So - as - - An 70 60 SO 40 30 20 10 o . ~1 C = 100 see g/C = 0.3 Random Flow _ ~ / I 1 1 0 0.2 0.4 0.6 0.8 1 1.2 Phase Volume - Capacity Ratio, X Figure Dot. Affects of Volume on Queue SpilIback for Undersaturated Coalitions. D.3.7 Two-Flow Arrival Models The ~ 994 Highway Capacity Manual (HCM) and its proposed arterial enhancements (l, 79 assume that the arrival volume along an arsenal is composed of two arrival flows: a flow arriving on He red, ~,~ and a flow arriving on the green, vg, as noted in Equation Dot. The HCM's two-flow arrival mode} cart also be applied to the above queue spilIback equations with little change in form. Defining the arrival volume on green, vg, to be v = R^v g -'P where harp is the platoon ratio, and the arrival volume on red, or, to be v = r (D-13) C - g R p v r D- 11 (D-14)

OCR for page 279
The offset ~ between the intersections u-a7 is considered from the start of the green period of movement ~ at the upstream intersection until the start of the through green at the downstream intersection. Hence, Go starts a time ~ after To, equal to the offset with respect to the upstream intersection. The end of the downstream bottleneck phase, EM, is EM= To + B+ Go where ~ = offset in seconds from u to al. Step 3. Calculate To and T2 (D-41) The beginning of the clear period, T., at the upstream intersection starts when the blocking queue clears the upstream movement of interest after the start of through movement green time at the downstream intersection. Note that it has been assumed that a blocking queue exists. This may be determined later to not be true if volumes are not high enough for the length of link involved. If true, then T~=To +0 + tq (D-42) In order to evaluate whether the intersignal link length wait be completely blocked under different traffic conditions, some related factors have to be evaluated. One of them is the volume-to- -capaci~ ratio (X~) at the downstreamintersection. Another one is the critical link length (Lo) which determines the occurrence of queue spillback. The critical link length is calculated as follows: L~ = G~*Wr*Wg*6C- G~)/~(lYr+ W~)~6C/X~- G~)J where: Wr = Wq = Shock-wave speed (mps); and Platoon starting wave speed (mps). (D-43) When Xa. is greater than 1 .0, the downstream link will be oversaturated by vehicles coming from He upstream intersection. If the link length ~ is greater than critical link length [c, it is assumed that a proportion of the storage vehicles w~11 not be cleared from the link due to the limited capacity at the downstream intersection. Hence, some residual queue will remain on the link when the green ends. When the link length is shorter than the critical link length, all vehicles stored on the link will be cleared. If X~ is less than ~ .0, queue spillback may also occur due to an inappropriate signal timing plan for the downstream green time and offset. This problem can be solved by using He same assumption as the one for oversaturation and by checking the results after the loop calculation in the computer program. If some blockage is found to occur, then saturation flow adjusunents are made to account for either impelled or blocked flow using Equation C-46 in the prevlous appenc 1X. D -26

OCR for page 279
The time at the upstream intersection, denoted as T2, when vehicles discharged from the upstream intersection ~} first begin queuing at the downstream intersection stop line on red, is calculated as follows: T2 = To + ~ + Go - If T2 2 To (Daft) Step 4. Calculate Input Flow Rates during the Cycle The potential flow rates from the upstream intersection during the cycle are calculated in this step. Each upstream movement's capacity is computed based on the elective green period of that movement (SMm + SL to EMm + KU) and the saturation flow rate s. The duration oftime, t9 that every other movement experiences saturation flow is given by Is = Vi (C - g; ~ / (Si - Vj ~ (D - S) Thus, from time SMm ~ AL to tS the flow is saturation and from tS to the end of movement green time (EMm + BL), the movement flows at its arrival flow rate, v. In the event Is is greater then the end of green of the movement, the flow continues at saturation flow for the entire period of green for that movement. The flow at all other times in the cycle (e.g., dunug yellow and red clearance time) is assumed to be zero. Step 5. FindEnd of Clear Period, T3 The next step in the process is to find T3, Me end of the clear period at the upstream intersection. The time T3 is defined as We time when the intersignal length would be once again completely filled with vehicles, thus blocking the upstream intersection. The related duration of time t3 iS needed to accumulate enough vehicles to fill the link ~ after time T2. The number of seconds required to completely fill the intersignal length depends on the output flow of vehicles from the upstream intersection after T2. The potential output flow for every second in the cycle is known from We previous steps. The summation of the output flows (vehicles per second) from the upstream intersection over time (seconds), gives the number of vehicles that may enter link ~ until the link completely fills to its storage capacity, An,, over We duration t3, or n~t3,l) = nO ~ ~`qum < nma~ o < t3 < C (D-46) The assessment of no is critical to the algorithm. no = 0 when T. < T2. However, if the link can store more vehicles than the downstream phase can serve (its capacity) (because the link may be long and/or the phase relatively short)then T 0 (instead of zero, or some other value) at time T= To. When T2 < T ,, vehicles already on the link cannot clear the next downstream phase. Thus, the most vehicles that can enter the link during the next cycle cannot D-27

OCR for page 279
exceed the downstream phase capacity, cm. If it is ultimately found that all the upstream flows can use the link for a time period T3 longer than To + C, then the link does not totally fill wing the cycle and the upstream signal is unblocked, but it may still have some reduced output flow. When queue blockage occurs, the end of the clear period for entry into the upstream intersection would be T3 = T2 + t3 T2 < T3 ' TO ~ C (D-47) In the PDX program, a simple DO-Ioop calculates t3. The loop increments the number of seconds after t2 and for each second adds the number of vehicles entering the link. No departing vehicles need to be considered here. When the link either fills completely or reaches Me next cycle (T~ + C) , We incrementation process stops. We number of time steps used gives We number of seconds elapsed after t2, which is t3. The saturation flow-queue interactionmodel described in Appendix C has been implemented in the PDX program. As each upstream phase begins to be analyzed dunug the cycle, the downstream queue length is calculated. The available travel distance to the back of the queue is then determ~ned,know~ngL. The adjusted saturation flow is determinedirom Equation C-8 for the upstream movement of interest. Preliminary analyses based on initial pointers and Equation D-43 estimate whether queue spilIback is likely. Should the completed t~me-step analysis not support the initial assumption, then the alternate equation is selected and the process repeated. Sfep 6. Identify Clear Period The clear period is defined as the time in the cycle from the end of queue blocking to the start of blocking in the next cycle at the upstream intersection. The clear period, CP, is the duration from T. to T3 when upstream input flow can occur, or CP = T3 T. (D-4g) The values of To and T3 have not been calculated module C. Thus, they can have values greater than the cycle length. While calculating the clear period, the values of SMm and EMm should be adjusted for start loss and end gun, respectively, at some convenient point in the program. Sfep 7. Compute the Modif edF Effective Green Period The modified effective green period (get) during which the upstream movement can discharge vehicles is the time overlap of the unblocked effective green (au) of the movement arid Me clear period. The clear period is calculated in the previous step. Table D- ~ ~ shows the modified effective green periods (aged) for Movement ~ for different positions of to and t3 with respect to the upstream signal time as calculated in the PDX program. Thus, the real effective green (g = geld is g = g rip CP D -28 (D-49)

OCR for page 279
Table D-~. Modified Effective Green Periods for Movement Value of I, ~Value of t3 ~gerf SMOG ~ t' t, ~t3-t, | EM it; t3 ~| EM' - I, | EM, I,; mod(t3, ~ -)t, | EM - SM, EM, C; mod(t3, C)< EM, ~t3 - SMOG I, C; mod(t3, C) EM, ~EM, - SM, ~t3<2C; mod(t3,C)q,M, ~ mod(t3,C)-mod(t,,C) I, > C; ~t3 mod(t3, C) ~EM, ~ EM, - mod(t,, C) SMOG2C;mod(t,,C)>mod(t3, -) 2C; mod(t,, C) OCR for page 279
Testbed Design. In order to test the above program's applicability,an experimental teethed was designed. An arbitrary paired intersection system was set up with all the traffic and signal timing variables affecting saturation flow being defined. This test system was analyzed using the Prosser-Dunne FORTRAN program for a range of conditions and the movement's capacities were computed. A design scheme of the study paired intersection was shown in Figure D-9. Required inputs such as traffic volumes, signal timing parameters such as green times, offsets, cycle lengths, and spacing between intersection were carefully prepared. Only a pretimed signal system was considered for this research. The spacing between the two intersections was considered to be 100, 200, and 300 meters, respectively. These spacings were assumed to be representative of most closely-spaced intersections within an interchange environment. Other parameters in the teethed are summarized in Table D-12. Table D-12. Testing Parameters for the Program and Simulation V/C Ratios 0.8, 0.9, 1.0, 1.1, 1.2, 1.S | Cycle length | 100 seconds Upstream Phase Splits ~ ?: | Downstream Phase Splits | 50-50, 60~O, 70-30 Offsets at ~ seconds Intervals (0 to C) | Spacing 7 100, 200, 300 meters l Total Cases Studied 900 1 ~ .. _. Total number of NETSIM simulations ~ Results and Verification. The computer program was run by using the above operating conditions to get Me data base. Each of the above cases was simulated 10 times using TRAF- NETSIM to obtain average simulation results. A total of 9000 NETSIM runs were performed during the testing process. The study results were categorized and evaluated according to different operating conditions and are summarized in the following sections. The throughput-offset relationship was examined in order to study the outputs from the PDX pro gram. The effects of different volume-to-capacity ratios and intersignal spacings were studied. A very close relationship between PDX program and NETSIM simulation was observed dunng the comparison process. The results are shown in Figures D-12 Trough D-15. In each figure, results from the PDX Model and TRAF-NETSIM are shown in the same dimension for comparison purposes. Figure D-16 is the regression plot between NETSIM arid PDX Model. The coefficient of regression between the two models was observed to be 0.85. Furler research studies are underway to improve the PDX Model. D - 30

OCR for page 279
. ~- 600 - ~ t _r ~ SOO - _ ~ l~h~ugh-S'm ~ t I 1=~ _ X Tdel~im g300; - X ~oug~Model ~ ~ __ _ ~ Righ~Model s 200 - ~ ~-M - l _ ~ Td a l-l Cod cl 100 O- l l l l 0 20 40 60 80 100 Offset (see) Figure D-12. Throughput-Offset Relationship between NETSIM and PDX Models for a spacing of 100 meters; v/c of 0.S and Saturation Flow of 1900 vphgpl. 2000 1600 -1200 800 400 o _ . _ ~-X ~ ~ X X X X ~ _ _^ _ _ ~ i it_ 0 20 40 60 Offset (see) 80 100 -Is Ritht-Sim ~ LcR-S~ - X Total~im X Throug~Motel let-Model I L~t-Model -- Total-Model Figure D-13. Throughput-Offset Relationship between NETSIM and PDX Models for a spacing of 100 meters; v/c of 1.5 and Saturation Flow of 1900 vphgpl. D -31

OCR for page 279
2000 1600 ~ ~=Through-Sim 1200 ~ LeB-Sim _ X Total-Sim S ~ Through-Modet g 800; _' \* \ Right-Mod~t ' ~ ~i\. ~ ~-Total-Model ~ 400~ 0 20 40 60 80 100 Offset (see) Figure D-140 Throughput-Ofiset Relationship between NETSIM and PDX Models for a spacing of 200 meters; v/c of {.5 and Saturation Flow of 1900 vphgpl. 1' 2000 =~1600 ~_ , 47 ~+ ~|=T~ 41200- Lcft-Sim ~X Total-Sim S _ ~-- : ~ lbrou0Model g 800- '~ ~ \ ~ Ritht-Modet ~ ~5 ~I -M-I ~I ~ ~ ~ am_ . ~Total-Model 40075~ ~ 0 20 40 60 80 100 Offset (see) Figure D-15. Throughput-Offset Relationship between NE:TSIM and PAX Models for a spacing of 300 meters; v/c of 1.5 and Saturation Flow of 1900 vphgpl. D-32

OCR for page 279
1200 ~ t . ~ .-.' I {~L6cc~ i- 1 X t -~ :~r y=eg85~ 1 C Low at' ' ~, R2~0.8^ 1 0 200 400 600 Boo 1000 1200 NETSIM Throughput (vph) Figure D-16. Linear Regression between NETSIM and PDX Model Throughputs. D.7.4. Discussion of the PDX Mode! This computer program has been extensively calibrated against simulation results obtained from TRAF-NETSIM simulation program. The purpose of the calibration effort was to pinpoint the best fit parameter values used in this computer program to produce reasonable results. Traffic engineering judgement was also exercised during this process. Overall, the computer traffic program demonstrated good flexibility and accuracy in processing different types of traffic conditions based on the comparison results observed by the research team. It should be noted that in the original Prosser-Dunne Model, traffic operating conditions were always assumed to be oversaturated, therefore, blocking would always occur because of insufficient service capacity at the downstreamintersection. It was found, however, that blocking or queue spilIback may also occur during undersaturated conditions given the limited storage spacing and bad offsets. Project study results have shown the most important factors that affect the estimation of queue spilIback or blocking occurrence are downstream signal intersection's green time, the intersignal spacing (i.e., link length) and the volume-to-capacity ratio. Besides these factors, a critical spacing that defines the boundary condition of the occurrence of queue spiliback was identified as a function of the downstream intersection's green time and volume to capacity ratio and other parameters. This new methodology helps define different types of problems based D-33

OCR for page 279
on the varying nature of different operating conditions and renders the corresponding treatments. After applying these enhancements to the original Prosser-Dunne Model, a wide variety of real- worId operating conditions can now be categorized and evaluated systematically by their specific types of problems, such as queue spiliback due to inadequate storage spacing and/or oversaturation. Several key parameters used in the PDX computer program were calibrated extensively ureter different operating conditions. Sufficient attention has been given to the effects of the selected values of the saturation flow density on the subsequent calculation of other variables. Because of its direct impacts on the estimate of saturation flow speed and interacting traffic wave speed, any change to the saturation flow density would result in different mode] outputs. So far, the parameter values used in the model have been calibrated to produce reasonable outputs compared with the simulation results from TRAF-NETSIM. Other calibrated parameters include the phase lost time and the unimpeded saturation flow rate. A vehicle unit length of 7.0 meters (23 feet) at jam density was used as the result of our nationwide data collection and analysis effort. Another major Improvement made to the computer traffic mode] was the introduction of the Queue Estimation Model. As an important part of traffic signal operation, especially during saturation periods, the behavior and characteristics of queuing traffic and its evaluation methodology have been studied by various researchers recently. The study approach used by the research team during the mode! development end calibrationwas to obtain queue traffic information dynamically throughout the cycle. A queue calculation submodule was provided to achieve this purpose. Similarto Me capacity analysis methodology,the queue submodule performs second-by- second calculations to estimate the changing queue status at the downstream intersection. The useful information provided by this program can be subsequently analyzed or used in over traffic engineering models when studying the traffic operating conditions of a paired intersection. The effects of available downstream travel distance to the back of queue was also provided in the PDX Model. As presentedin Equation C-8, Me saturation flow rate on green may be reduced by insufficient clear distance at start of green that permits platoon vehicles from accelerating to nominal saturation flow speeds. Thus, the clear period may have impeded saturation flow, but not blocked flow. D.7.5 Existing Software Enhancements Implementation of Queue-Interaction Models into internationally recognized computer programs is highly recommended. Some work toward this objective is known to be already underway (10,11,129. D-34

OCR for page 279
REFERENCES 1. "Highway Capacity Manual." Special Report 209, Transportation Research Board, Washington, D.C., Third Edition, (1994). 2. Chang, E.C. and Messer, C.~. "PASSER Il-90 Users Manual." Texas Transportation Institute, College Station, Texas, (19901. Fambro, D. B., Chau&ary, N.A. and Messer, C.~. "PASSER IlI-90 User's Manual." Texas Transportation Institute, College Station Texas, (1991~. 4. Wallace, C.E. and Courage, K.G. "TRANSYT-7F User's Mar~ual." University of Florida, Gainesville, (1988~. May, A.D. Traffic Flow Fundamentals. Prentice-Hall, Englewood Cliffs, New Jersey, (1990) p.306. 6. Lighthill, M.~. and Whitham, G.B. "On Kinematic Waves: Part Il. A Theory of Traffic Flow On Long Crowded Roads." Proceeding of the Royal Society, A2239, No. INS, (1955~. . Fambro, D.B., Rouphail, N.M., SIoup. P.R., Daniel, I.R., Id, I., Anwar, M., and R.~. Engelbrecht. "Highway Capacity Revisions for Chapters 9 and ~ 1." Report No. FHWA- RD-96-088, Federal Highway Administration, Washington, D.C. (1996~. 8. Leiberman, E.B, McShane, M.R., and Messer, C.~. Traffic Signal Control For Saturated Conditions. KLD Associates, Inc. NCHRP Project 3-38~3) Report, Vol 2., (1992) p. 15. 9. Prosser, N. and Dunne, M. "A Procedure for Estimating Movement Capacities at Signalised Paired Intersections." 2nd International Symposium on Highway Capacity, Sydney, Australia, (1994~. 10. Rouphail, N.M. and Akcelik, R. "Paired Intersections: Initial Development of Platooned A~xivaland Queue Interaction Models." Australian Road Research Board. Working Paper WD TE91/010, Vermont South, Australia (19911. . Akcelik, R., Besley, M., and Shepherd, R. "SIDRA (Windows) Input Redesign for Paired Intersection Modelling." DiscussionNoteto WD 96/008. Australian Road Research Board, Vermont South, Australia (1996~. 12. Chaudhary, N.A. and Messer, C.~. "PASSERIV-96, Version2. l, User/ReferenceManu~." Texas Transportation Institute, College Station, Texas. (1996~. D-35

OCR for page 279