Capacity Analysis of Interchange Ramp Terminals Final Report (1997) / Chapter Skim
Currently Skimming:
APPENDIX D Closely-Spaced Intersection Flow Models
APPENDIX D Closely-Spaced Intersection Flow Models
Pages 279-314
The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.
From page 279... ...
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.
|
From page 280... ...
_ 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.
|
From page 281... ...
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.
|
From page 282... ...
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)
|
From page 283... ...
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)
|
From page 284... ...
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.
|
From page 285... ...
Figure D-2. Characteristics of Traffic Flow for Two Capacity Conditions.
|
From page 286... ...
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.
|
From page 287... ...
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.
|
From page 288... ...
Wave Speeds at Traffic Signals During Undersaturated Conditions. The maximum queue backup for undersaturated conditions, [n'' is equal to A, = Wg*
|
From page 289... ...
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.
|
From page 290... ...
. Two wave speeds for the initial shock wave, W., should be computed: one based on arrival volume vie and one based on vg Should the volume arriving on red be eliminated by great progression, then the shock wave speed on red, We,,, would be zero (0.0)
|
From page 291... ...
D.5.! Transition Time The time a link ~ is in transition from undersaturated to oversaturated operating conditions is brief.
|
From page 292... ...
= number of vetches operating on Me him of length ~ at time t, vehicles; No = number of vehicles operating on the link at start of period, vehicles; vm = total arrival volume to head of link destined to movement m, vph; cm Nan,,` output capacity of link serving movement m, vph; and maximum number of vehicles that can store on link, vehicles kq ~ with a typical storage density of 143 ~kmpI, or storage spacing of 7.0 m/vein (23 flc/ vein)
|
From page 293... ...
The microscopic traffic simulation program NETSIM was used to develop these observations which represent the average value of ~ O replications of the conditions shown. The offset between the upstream arid downstream signals was varied while the total link throughput and the individual feeding flows were observed for both upstream movements.
|
From page 294... ...
In the following sections, two traffic models wall be presented that describe operating conditions dunng oversaturation. One simple mode!
|
From page 295... ...
1 d _ ,_ , 1 U '~' D ~ _ -- ~1 1r 1 I Queue Figure D-7. Traffic Flow Regions for Undersaturated and Oversaturated Conditions.
|
From page 296... ...
Because the two wave speeds are equal, We fractions are equal to the fractions of time the cycle (C) is effectively (g)
|
From page 297... ...
where: kq ks g r (D - 29) For example, if kq = 143 vpkmpl' k s = 51.3 vpkmpl' and s = 1900 vphpl, so that the nominal saturation speed is 3 7 Elmer, then for a green split at the downstream bottleneck intersection of 0.46, kq r 143 r = ~2 79 .
|
From page 298... ...
A range of split and offsets were examined using the NETSIM microscopic traffic simulation model. Three downstream green splits were tested so that the over a cycle of offsets to verify the model results.
|
From page 299... ...
total signal blockages that reduce the elective green time due to queue spilIbackinto the upstreamintersection.These issues are carefully evaluated in this traffic mode] to provide accurate prediction of the discharge flow rate, capacity and delay at the upstream intersection.
|
From page 300... ...
has extended this mode} to a wide garage of operating conditions, increased the modeling to three feeding movements, and added the effects of saturation flow variation with travel distance (as described in Appendix C) to the mode} structure.
|
From page 301... ...
In the PDX Model, however, links can be analyzed that may not be oversaturated by all phases combined, or may not be flooded by some combinations of phase sequence and/or offset, as noted earlier for Remarry starved links. C+TI C+To CP T3 T2 Tt To We w8 J U HI Queue g D ' Figure D-10.
|
From page 302... ...
Flow Chart of PDX Model. D -24 YES , OS oversatu ration: EFFG, = G
|
From page 303... ...
. Identify input Parameters The following parameters are identified as inputs to the program: Gu7n = Green time of upstream movements, see; Go = Downstream green time, see; C = Cycle time, sees, SL,EU = Start loss and end gain for each movement, see; = Offset between intersections, see; = Intersignal link length in meters, m, nmax = Number of vehicles that cart be stored in the intersignal link length; vein; vm = Arrival flow rate for upstream movement m, vph; tq = Blocking queue clearance time, see, if = Link travel time during saturation flow, see; and s = Unimpeded saturation flow rate, vpsg.
|
From page 304... ...
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.
|
From page 305... ...
, 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.
|
From page 306... ...
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.
|
From page 307... ...
An expenmental testbed was designed for this purpose. To verify the test results, the microscopic traffic simulation program' TRAF-NETSIM, was used to provide comparative results under the same operating conditions.
|
From page 308... ...
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.
|
From page 309... ...
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.
|
From page 310... ...
~ ~-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.
|
From page 311... ...
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.
|
From page 312... ...
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.
|
From page 313... ...
and Akcelik, R "Paired Intersections: Initial Development of Platooned A~xivaland Queue Interaction Models." Australian Road Research Board.
|
Key Terms
This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
More
information on Chapter Skim is available.