A Dynamic Offset Tuning Procedure Using Travel Time Data1 Gary E. Shoup2 and Darcy Bullock3
KEYWORDS Travel time, Real-Time traffic control, coordinated actuated arterial, early return to green, offset, adaptive signal system ABSTRACT Vehicle reidentification equipment and algorithms are approaching the point where collection of real-time arterial link travel time data will soon be possible. Such equipment and algorithms will provide a new way for traffic control systems to automatically measure their performance and adapt in real-time to the actual traffic demands on the system. Using the concept of link travel time data, this paper describes a procedure to set offsets offline for a coordinated actuated arterial signal system. The offset setting procedure is developed in CORSIM and based on recording individual vehicle travel times between coordinated actuated intersections. Establishing offsets in this manner mitigates the “early return to green” problem associated with coordinated actuated systems and accounts for downstream queues which may negatively impact progression. The offline procedure presented, provides the foundation for an online algorithm that could adjust offsets based on real-time travel data. INTRODUCTION The state of the practice in new traffic signal system installations is dual ring actuated controllers that are coordinated using force off times that provide an equitable distribution of green time when all phases are saturated (max out). In the absence of sufficient demand to extend phases all the way to their force off points, the extra green time is reallocated to the coordinated phases, typically the through movement. Since all intersections along a corridor do not have the same degree of saturation on all phases, the amount of extra green time allocated to the coordinated phases varies by intersection. This varying amount of extra green time is what is called the "early return to green” problem and is illustrated in Figure 1a and Figure 1b (1, 2, 3). In Figure 1a, each phase is extended until the phase force off is encountered. In Figure 1b, phases 3, 4, 1, 7, 8, and 5 terminate early because of insufficient demand. As a result, the green time in Figure 1b for phases 2 & 6 starts significantly earlier then Figure 1a. To illustrate the impact this “early return” to green has on a coordinated actuated arterial, consider the hypothetical green bands shown in Figure 2a and Figure 2b. In Figure 2a, all controllers are extending all phases to their force off points and are essentially operating as a fixed time system. In Figure 2b, the non-coordinated arterial phases are not saturated 1
1999 TRB Annual Meeting Preprint 991086. Graduate Research Assistant, School of Civil Engineering, Purdue University, West Lafayette, IN 47907; Phone: (765) 495-6881; Fax: (765) 496-1105;
[email protected] 3 Corresponding Author, Associate Professor, School of Civil Engineering, Purdue University, West Lafayette, IN 47907; Phone: (765) 494-2226; Fax: (765) 496-1105;
[email protected] 2
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and each of the signals reallocates some of the extra green time to the through movement. This variation in the green times for the non-coordinated phases changes how the signal system offsets perform. Consequently, the offset of the start of the through green is not located at the optimal location. Although the actuated controller offsets could be adjusted to account for this special case, there has never been an online methodology developed that would allow the offsets to be dynamically adjusted to alleviate this “early return to green” problem. Such an adjustment procedure is desperately needed, because force off and offset times for a system, are designed based upon a few design hour volumes. However, real arterial volumes fluctuate significantly throughout the day and are rarely the same as their design volumes. Traffic responsive operation is not a reasonable procedure for adjusting offsets in response to fluctuating side street volumes because of the combinatorial explosion of side street volume patterns, each of which would require a unique offset plan. The remainder of this paper describes an offline, offset tuning procedure that uses observed vehicle travel times between intersections to fine-tune offsets. Tuning offsets in this manner mitigates the “early return to green” problem caused by varying green times for the non-coordinated phases, as well as accounts for downstream queues that adversely impact progression. This offline tuning procedure provides the foundation for creating an online algorithm for dynamically adjusting offsets. LITERATURE REVIEW Several researchers have identified the problem of the “early return to green” over the past decade (3, 4, 5). However, while the “early return to green” problem with a coordinated actuated controller has been identified, only limited amounts of research have been conducted on how to mitigate the problem. One prior research effort suggested that the “early return to green” problem could be mitigated by using the average green times allocated to the non-coordinated phases in computing offsets with TRANSYT-7F. By calculating the average green times for the non-coordinated phases, the cycle coordination point was adjusted to change the offset in relation to other controllers operating within a coordinated actuated arterial. This offline procedure provided encouraging results when applied to several NETSIM models based upon actual arterial conditions (6, 7). Another study recommended addressing the “early return to green” by first establishing offsets for a coordinated actuated arterial with a pretimed signal optimization package such as PASSER-II. Then, after the signal timings are implemented in the field for an actual arterial, it was suggested that field observations be conducted to determine the expected green times for the non-coordinated phases at each intersection. The expected green times could then be entered into a pretimed signal optimization package as constraints for the maximum green times corresponding to each of the non-actuated phases. Once the new times are entered, a second optimization run for the offsets could be performed (4). Unfortunately, no quantitative data based upon this “early return to green” strategy was published.
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A similar study based upon field collection procedures suggested recording the actual times in the background cycle for when the coordinated phase begins and ends at each of the signalized intersections of an arterial. With such data collected, a time-space diagram based on the average times for the coordinated phase was used to improve an arterial bandwidth. Actual field data was collected for a specific arterial in California and significant improvements in the arterials bandwidth were reported (5). All of the above strategies suggested that to reduce the impact of the “early return to green”, the offsets should be adjusted by accounting for the average green splits of a signal’s non-actuated phases. Our research implicitly embodies this concept but also improves upon earlier algorithms by incorporating the measurement of real-time travel data which would allow implementation in an online system. TRAVEL TIME DETECTION Vehicle reidentification equipment and algorithms are quickly approaching the point where field implementation of them will allow the collection of real-time travel data. Recent advancements in automatic vehicle identification have yielded procedures to reidentify vehicles with inductive loops, video image processing, and toll tags (8, 9, 10). Currently, a research project is being conducted in cooperation with the Partners for Advanced Transit and Highway (PATH) in California to develop a travel time measurement algorithm based on actual inductive loop data collected on Highway 24 at San Francisco East Bay (10). Additionally, a separate project on I-880, south of Oakland, California is being used to develop a vehicle matching algorithm that utilizes existing loop detectors (8). Vehicle reidentification algorithms based on inductive loops and video image processing appear very promising. Most applications to date have envisioned using reidentification algorithms to obtain general MOE data and forecast origin-destination matrixes. We believe these emerging vehicle reidentification algorithms can also be used by arterial signal systems to dynamically adapt offsets. TRAVEL TIME RELATION TO OFFSETS By knowing a vehicle’s travel time between two signalized intersections, the offset between two signalized intersections can be set to avoid progression disruptions. Assuming demand does not exceed capacity, long segment travel times implicitly indicate if an “early return to green” has occurred for a signal controller or if downstream queues are adversely impacting platoon progression on the arterial. The following example explains how travel time between two intersections can infer the quality of platoon progression. Example of Offset Impact on Travel Time Imagine that the ideal travel time for a given arterial link is calculated. This ideal link travel time can be computed based on a mathematical function incorporating link length, design speed, and queue discharge times (11). With the ideal travel time known, if observed vehicle travel times exceed this calculated time, ideal progression is not being achieved. In the majority of cases for a coordinated actuated arterial, the progression disruption is the result of two situations: 1) an “early return to green” causes vehicles to December 11, 1998
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be released from an upstream intersection prior to the desired release time for coordination efforts or 2) downstream queues are causing vehicle platoons to stop or slow down. However, if link travel times are observed in the proximity of the ideal link travel time, vehicle progression through the intersections is being achieved and neither the “early return to green” nor downstream queues are adversely affecting progression. Thus, real-time adaptive offsets based on travel time account for the two most important parameters that affect vehicle progression in a coordinated actuated arterial. These two parameters are: •
The average split times occurring in the field for the coordinated phases of a signal controller
•
The affect of downstream queues on progression
Consequently, an online methodology incorporating adaptive offset tuning based on travel time could provide a significant benefit. To determine the steps and procedures needed for a real-time adaptive offset algorithm, an offline methodology is developed based on vehicle travel times observed for a testbed arterial created in CORSIM. TESTBED ARTERIAL To illustrate how travel time can be used to compute offsets, a testbed arterial with three actuated signalized intersections was created. Figure 3 shows the link-node diagram of the testbed arterial. The purpose for creating this testbed arterial was as follows: (1) To define a network that demonstrated an “early return to green” in a controlled situation. All offsets for intersection 3 were exhaustively evaluated to identify the ideal offset range between intersections 3 and 2. (2) Replicate an offset within the previously computed ideal offset range based solely on the travel time of several probe vehicles. The geometric characteristics for the testbed arterial consisted of approximately equal intersection spacing with 2 through lanes and 250’ left turn bays provided on the arterial for each intersection approach. Additionally, a 100 second background cycle and a design speed of 40 mph were specified. Traffic volumes and turning movements were assigned below signal capacity levels for the non-coordinated phases to ensure that side street phases gapped out early and an “early return to green” occurred at each controller. Traffic volumes for the coordinated phase of the arterial were initially assigned 1200 vph for both the northbound and southbound entrances. Subsequently, the northbound entrance volume was increased to 1500 vph and later to 1800 vph to conduct a volume sensitivity analysis for the offset at intersection 3.
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TESTBED ARTERIAL ANALYSIS AND RESULTS Measures of effectiveness consisting of average link travel time (sec/veh), delay time (per-min), and stop percentages were tabulated for the arterial link between intersections 3 and 2. To accurately account for the stochastic properties of traffic, twenty 15-minute CORSIM simulation runs based on different random seed numbers were compiled for each offset analyzed. Graphical results are shown in Figure 4 and represent the results of 2,400 15-minute simulations. Figure 4a, Figure 4b, and Figure 4c show the ideal offset ranges which best provide progression through intersections 3 and 2. All noted graphs show similar ranges of ideal offsets, however, it is observed that Figure 4c based on stop percentages provides the most restrictive range of all three. Therefore, to ensure that our offline methodology provides offsets which facilitate progression, the offset set by travel time observations must fall within the ideal offset range shown in Figure 4c. OFFLINE OFFSET TUNING METHODOLOGY The first step with our offline algorithm is to establish the initial offsets for the arterial prior to conducting any offset tuning. It was decided that initial offsets should be set in such a way to ensure that the maximum bandwidth is provided to the coordinated arterial phase. Establishing offsets in relation to the end of cycle coordination point ensures that the maximum bandwidth is obtained. Initial offsets are calculated by dividing each arterial link length by the design speed for the link. Then, starting with the most downstream intersection, the relative offsets are subtracted from each cycle coordination point in a step-wise procedure until all offsets are set. Figure 5a shows the rounded initial offsets established for the testbed arterial (Figure 3) using this procedure. Unfortunately, as Figure 5a shows, drivers at the beginning of a platoon experience a disruptive stop and go movement at intersection 2 because phases prior to the coordinated phase gap out early. Hence, while the maximum bandwidth is being provided with the initial offsets, vehicle progression fails to occur. This lack of perceived progression was noted for fixed timed signal systems in a previous research study (12). That study indicated that achieving maximum bandwidth for an arterial in no way guarantees perceived driver progression, particularly when a two-way bandwidth approach is used to determine offsets. To achieve perceived progression on an arterial, the offset for intersection 3 shown in Figure 5a must be adjusted. Adjustments to the initial offsets are based on the link travel times observed for the first vehicle in a platoon. Only the first vehicle travel time is needed because it is the most sensitive to an “early return to green” and any downstream queues that may disrupt progression. The disrupted link travel time is recorded as the time between when the first through vehicle of an arrival platoon stops and when the same first vehicle enters the adjacent downstream link. The disrupted link travel time is recorded first at the most downstream link of the coordinated actuated arterial. Then, once these travel times are computed, the most adjacent upstream signal offset is adjusted upward by the disrupted travel time. Travel time calculations begin at the most downstream link and proceed upstream to ensure that the maximum bandwidth is not encroached upon unless interior December 11, 1998
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queues require that the offset be advanced significantly. Due to the stochastic properties associated with traffic, disrupted travel times should be collected over several cycles to form a sample. Then, the average disrupted travel time for the sample is computed, and the upstream intersection offset is adjusted by the average disrupted travel time. In the event that no vehicles are stopped over the entire sample size, the most adjacent upstream offset is not adjusted and the tuning procedure is continued at the next upstream signal controller. The discussed offset tuning procedure is easily implemented by observing vehicle travel times in the TRAFVU component of TSIS. The eight steps necessary to conduct offset fine-tuning are summarized in Table 1. Applying the 8-step offset tuning procedure to the testbed arterial results in the offsets and time-space diagram shown in Figure 5b. Figure 5b shows that maximum progression opportunities between intersection 3 and 1 are obtained. Further, an analysis of the offset between intersections 3 and 2 indicates that the fine-tuned offset lies within the ideal offset range as determined by Figure 4c. Therefore, initial results suggest that offsets determined by a vehicle’s travel time can facilitate progression. To verify that the 8-step offset tuning procedure is also applicable to more general real-world arterials, a six intersection coordinated actuated system located on State Route 26 in Lafayette, Indiana was fine-tuned following the 8-step procedure. OFFSET TUNING CASE STUDY: STATE ROUTE 26 State Route 26 is classified as a principal arterial and is the main thoroughfare connecting Interstate 65 with State Route 52 in the eastern portion of Lafayette, Indiana. The section of State Route 26 analyzed consists of six actuated signalized intersections operating in coordination via an interconnected master controller. All intersections are standard four leg design and contain left turn bays varying from 100 to 550 feet on State Route 26. The posted speed limit is 45 mph between all intersections except the speed limit between nodes 1 and 2 is 35 mph. Figure 6 shows a link-node diagram for the section of State Route 26 analyzed. The traffic period analyzed is the mid-afternoon daily time period. This period was selected due to the low side street volumes resulting in an “early return to green” for the main street phases at several intersections. Traffic controller timings and phases were obtained from the Indiana Department of Transportation. Volume and turning movements were obtained by field data collection. It was arbitrarily decided that the eastbound direction of State Route 26 be the direction to apply the offset fine-tuning procedure. Both the east and west directional volumes are approximately equal for the majority of arterial links, and no significant advantages in applying the fine-tuning procedure definitively to either direction were intuitively apparent. State Route 26 was fine-tuned offline with the proposed 8-step offset tuning procedure (Table 1). Figure 7 shows the time-space diagram that resulted. Once the offsets were fine-tuned for each controller, twenty 40-minute CORSIM simulation runs based on different random seed numbers were compiled for the cases of State Route 26 operating
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with existing offsets and with newly proposed fine-tuned offsets. A quantitative comparison of State Route 26 operating with each offset scheme was then conducted. Comparison of the measures of effectiveness computed with the fine-tuned offsets versus existing offsets indicate that travel time (sec/veh), delay (per-min) and stops for the arterial through movement can be significantly reduced by applying fine-tuned offsets. Fine-tuned offsets reduce the eastbound cumulative travel time by 7.2% and cumulative delay time by 12.1%. Further, eastbound stops on the arterial are reduced from 853 to 725 for a 15.0% reduction. Table 2 shows tabulated eastbound reductions. Similarly, even though the eastbound direction was selected as the arterial direction to be finetuned, considerable reductions in travel time, delay, and stops for the westbound arterial movement were also obtained. Westbound cumulative travel times are reduced by 8.2% and cumulative delay times by 13.1%. Additionally, westbound stops are reduced from 1273 to 1089 for a reduction of 14.5%. See Table 3 for tabulated westbound reductions and Table 4 for a summary of t-statistics comparing mean values of the measures of efficiency for State Route 26. One may be surprised to observe that although the eastbound through movement was the direction selected to be fine-tuned, measures of effectiveness for the westbound through movement were also substantially improved. For the specific case of State Route 26, the westbound through movement achieved an even greater reduction in travel time and delay. While our research efforts are focused only at this time on definitively providing progression for one direction rather than attempting a two-way bandwidth approach, several reasons may explain why measures of effectiveness are reduced for both arterial directions. One probable reason for both reductions is that the existing offsets used for State Route 26 were not recently tuned. Thus reductions in cumulative stops, travel time, and delay are based on comparing an offset fine-tuning methodology with poor existing offsets. Further, the intersection spacing, the average green times for the coordinated phases, and the locations of critical intersections are conducive to improving measures of effectiveness in both the eastbound and westbound directions. DISCUSSION The results from the testbed arterial and State Route 26 study suggest the following: (1) Vehicle travel time can be used to calculate the offsets needed to achieve progression. Progression is based on the arterial through movement for one direction. (2) Using vehicle travel times to set offsets implicitly accounts for the two most influential factors that may disrupt vehicle progression on a coordinated actuated arterial. These factors are the average green times allocated to the coordinated main street phases and the presence of downstream queues. Adjusting offsets based on travel time significantly reduces the adverse affects occurring from an “early return to green” at a signal. (3) When basing offsets on only one through movement of an arterial, it does not necessarily imply that the opposing arterial direction must experience poor December 11, 1998
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progression opportunities and delay. Contrarily, two-way bandwidth is more than a function of only offsets, but also of intersection spacing, phasing, and cycle length. Further, the concept of obtaining two-way progression for an arterial is often misunderstood. Frequently, the objective of trying to obtain two-way bandwidth often results in situations where drivers of both directions do not perceive progression and are thus both aggravated. (4) A methodology was created that could be applied to a real-time adaptive offset algorithm based on vehicle travel times and the average start of green for coordinated phases. Such an adaptive algorithm appears promising and would be of great benefit to traffic engineers. CONCLUSION An offline procedure to fine-tune offsets based on travel time was presented. Fine-tuning offsets in a coordinated actuated system mitigates the problem of the “early return to green” and downstream queues that may negatively impact arterial progression. The offline tuning procedure is easily implemented using the TSIS simulation package and provided encouraging results when compared to existing offset settings for a real-world arterial. In its current form (Table 1), this algorithm can be used by practicing engineers to tune a coordinated actuated system before it is deployed on field equipment. More importantly, this offline offset tuning procedure will serve as the foundation for implementing an online algorithm that dynamically adjusts offsets using real-time link travel time data. Advances in vehicle reidentification algorithms are approaching the point where implementing such an online system will soon be feasible. ACKNOWLEDGEMENTS Part of the support for this research effort was provided by Alumni gift funds to the Purdue School of Civil Engineering and the Joint Transportation Research Program.
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REFERENCES 1. Ficklin, N.C. For and Against Semi-actuated Signals. Traffic Engineering, March 1973. 2. Jovanis, P.P., and J.A. Gregor. Coordination of Actuated Arterial Traffic Signal Systems. Journal of Transportation Engineering, ASCE, Vol. 112, No. 4, July 1986. 3. Skabardonis, A. Determination of timings in signal systems with traffic-actuated controllers. In Transportation Research Record 1554, TRB, National Research Council, Washington, D.C., 1996, pp. 18-26. 4. Chang, E. C. P. Guidelines for actuated controllers in coordinated systems. In Transportation Research Record 1554, TRB, National Research Council, Washington D.C., 1996, pp. 61-73. 5. Kuzbari, Ray. Early green start analysis for time-of-day signal coordination. In ITE Journal, August 1996. 6. Skabardonis, A. Progression through a Series of Intersections with Traffic Actuated Controllers. Report FHWA/RD-89-132, Vol. 1.FHWA, U.S. Department of Transportation, Oct. 1988. 7. Skabardonis, A. Progression through a Series of Intersections with Traffic Actuated Controllers. Report FHWA/RD-89-133, Vol. 2, User’s Guide. FHWA, U.S. Department of Transportation, Oct. 1988. 8. Coifman, B. A New Algorithm for Vehicle Reidentification and Travel Time Measurement on Freeways, Applications of Advanced Technologies in Transportation, ASCE, Newport Beach, California, 1998, pp. 167-174. 9. Coifman, B. Vehicle Reidentification and Travel Time Measurement in Real-Time on Freeways Using the Existing Loop Detector Infrastructure, presented at the Transportation Research Board, 1998 meeting, paper no. 981498. 10. Kuhne, R., Palen, J., Gardner, C., Ritchie, S. Loop-based Travel Time Measurement, Applications of Advanced Technologies in Transportation, ASCE, Newport Beach, California, 1998, pp. 175-182. 11. McShane, W.R., and R.P. Roess. Traffic Engineering, Prentice Hall, Inc., Englewood Cliffs, N.J., 1990, pp. 533. 12. Wallace, Charles E. and Kenneth G. Courage. Arterial Progression – New Design Approach. In Transportation Research Record 881, TRB, National Research Council, Washington, D.C., 1982, pp. 53-59.
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φ2 φ6 Phase 1 F.O.
Phase 5 F.O.
Phase 4 F.O.
Phase 8 F.O.
Phase 3 F.O.
Phase 7 F.O.
F.O. = Force off
(a) All phases max out and are forced off
φ2 φ6 Phase 1 F.O.
Phase 5 F.O.
Phase 4 F.O.
Phase 8 F.O. Phase 5 gaps out
Phase 1 gaps out
Phase 8 gaps out
Phase 4 gaps out
Phase 7 F.O.
Phase 3 F.O.
Phase 7 gaps out
Phase 3 gaps out F.O. = Force off
(b) Phases gap out before reaching force offs and extra green time is allocated to φ2 and φ6
Figure 1: Coordinated ring structure
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φ2 φ6 φ2 φ6
φ2 φ6
Time (s)
φ2 φ6
Distance (ft)
(a) Start of green band when all phases max out
φ2 φ6 φ2 φ6
φ2 φ6
Front of Platoon must stop
Phase 1 F.O.
Time (s)
φ2 φ6
Front of Platoon must stop
Phase 1 gaps out
Distance (ft)
(b) Start of green band when some phases gap out early Figure 2: Time-space diagrams
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N
N
W
E 1200 vph
W S
E S
400 vph
5
400 vph
20 60
1
90
1
5 55 25
20
20 5
5 90 5 85 10
845’ 550 vph
600 vph 30
50
2
2
50 20
20
30 5
790’ 125 vph
3
75 vph
845’
40 40
3
90 90
3
5
790’
7 35 30
20
35 90
5
Period I. 1200 vph Period II. 1500 vph Period III. 1800 vph
5
(a) Demand Volumes
b) Turning Movement Percentages
Figure 3: Three intersection testbed arterial
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TESTBED ARTERIAL ANALYSIS LINK 3-2 TRAVEL TIMES NORTHBOUND
80
TRAVEL TIME (sec/veh)
70
60 IDEAL OFFSET RANGE NB Volume=1800 vph
50
NB Volume=1500 vph 40
NB Volume=1200 vph
30
20 0
10
20
30
40
50
60
70
80
90
100
OFFSETS (sec)
(a) Ideal Range of Offsets determined by Aggregated Travel Time TESTBED ARTERIAL ANALYSIS LINK 3-2 DELAY TIMES NORTHBOUND
520 470 420
DELAY TIME (per-min)
370 IDEAL OFFSET RANGE 320 270
NB Volume=1800 vph
220
NB Volume=1500 vph NB Volume=1200 vph
170 120 70 20 0
10
20
30
40
50
60
70
80
90
100
OFFSETS (sec)
(b) Ideal Range of Offsets determined by Delay Time TESTBED ARTERIAL ANALYSIS LINK 3-2 STOP PERCENTAGES NORTHBOUND
100
90
STOP PERCENTAGES
80
70
IDEAL OFFSET RANGE NB Volume=1800 vph
60
NB Volume=1500 vph 50
NB Volume=1200 vph 40
30
20 0
10
20
30
40
50
60
70
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90
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OFFSETS (sec)
(c) Ideal Range of Offsets determined by Stop Percentages
Figure 4: Ideal range of offsets for testbed arterial link 3-2 December 11, 1998
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Intersection 3
Relative Offset =
distance 3-2 design speed
Intersection 2
Intersection 1 Relative Offset =
= 13.5 s
distance 2-1 design speed
= 14.4 s
φ2φ6 φ2φ6
Time (s)
φ2φ6
Discontinuity indicates a bad offset
790’ Avg. green times: φ2 = 68 s φ6 = 67 s Offset = 46 s
845’
Avg. green times: φ2 = 49 s φ6 = 51 s Offset = 60 s
Avg.green times: φ2 = 57 s φ6 = 57 s Offset = 74 s
Distance (ft)
(a) Initial offsets for fine-tuning procedure of testbed arterial
Intersection 3
Intersection 2
Intersection 1
φ2φ6 φ2φ6
Time (s)
φ2φ6
790’
845’
Offset =62 s
Offset = 60 s
Offset = 74 s
Adjusted Offset
Distance (ft)
(b) Final offsets for fine-tuning procedure of testbed arterial
Figure 5: Time-space diagrams for testbed arterial
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N W
E S
3003’ 590 vph
618’ 130 vph
235 vph
515 vph
674’ 170 vph
1188’
1070 vph
786’
960 vph 101
1
2
3
4
5
6
7
8
670 vph
65 vph
370 vph
30 vph
410 vph
1165 vph
590 vph
(a) Demand Volumes
N W
E S
786’
10 9
101
82
66
1
24 71
9 11
27 62
1188’
16 17
20
12
20
60
13
62
2
68
674’
58
22 47
19
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10
27
3
87
0
3
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42 82
16 9 2
50
0
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618’
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28
4
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78 5
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8 75
3003’
91
3
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49 16
42 94
4
16
6 2
62
19
19
58
35
7
65 14
8
21
26 29
57
14
(b) Turning movement percentages
Figure 6: State Route 26 in Lafayette, Indiana
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NODE 7
NODE 5
NODE 4
NODE 3 NODE 2
NODE 1
Time (s)
Additional progression opportunities provided with fine-tuned offsets
Additional progression opportunities provided with fine-tuned offsets
Distance (ft) KEY Phase 2 Avg. green time
Phase 6 Avg. green time
Phase 1 F.O.
Phase 5 F.O.
Phase 1 gaps out
Phase 5 gaps out
F.O. = Force off
Figure 7: Time-space diagram for fine-tuned offsets of State Route 26
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FINE-TUNING STEP
1
2
DESCRIPTION Establish initial offsets for the coordinated actuated arterial. Initial offsets between controllers are calculated by dividing each arterial link length by the link design speed. Then, starting with the most downstream intersection on the arterial, the relative offsets are subtracted from each end of main street green in a step-wise manner until all arterial offsets are set. Beginning at the most downstream intersection of the arterial, record the time when the first vehicle in the arrival platoon stops (< 3 fps) and the time when that same vehicle enters the adjacent downstream link. Repeat Step 2 until a desired cycle sampling size is achieved. Determine the disrupted travel time of the first vehicle in the platoon for each sampled cycle. TFVE − TVFS if first vehicle stops TD = 0 if first vehicle does not stop
3
TD = Disrupted Travel Time (sec) TFVE = Time first vehicle of arrival platoon enters downstream link (sec)
4 5
6
7 8
TVFS = Time first vehicle of arrival platoon stops (sec) Average the first vehicle’s disrupted travel times over all sampled cycles for the given link. Adjust the adjacent upstream signal controller offset upward by adding the average disrupted travel time. Modify the CORSIM file per the newly calculated offset. The CORSIM file is modified to account for queuing and spillback affects that will be mitigated by implementing the new offset. Repeat Steps 1 through 6 at the next most downstream signalized intersection. Repeat Steps 1 through 7 until all offsets for the coordinated actuated arterial are fine-tuned.
Table 1: 8-step offset fine-tuning procedure
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Start
End
101 1 2 3 4 5 6
1 2 3 4 5 6 7
Travel Delay Time Time (s) (per-min) 32.6 78.3 60.1 253.1 23.6 59.6 16.4 62.7 15.7 86.2 25.0 41.6 59.7 302.8
Stops (unit) 113 221 38 79 88 0 314
Cumulative Cumulative Travel Delay Cumulative Time Time Stops (s) (per-min) (unit) 32.6 78.3 113 92.8 331.5 334 116.3 391.0 372 132.7 453.8 451 148.4 540.0 539 173.4 581.6 539 233.2 884.4 853
(a) Eastbound State Route 26 MOEs with existing offsets
Start
End
101 1 2 3 4 5 6
1 2 3 4 5 6 7
Travel Delay Time Time (s) (per-min) 32.2 75.5 53.5 213.2 24.9 73.9 23.5 135.7 15.8 87.1 25.2 44.4 41.3 148.0
Stops (unit) 110 173 63 158 91 0 130
Cumulative Cumulative Travel Delay Cumulative Time Time Stops (s) (per-min) (unit) 32.2 75.5 110 85.7 288.7 283 110.6 362.6 346 134.1 498.3 504 149.9 585.4 595 175.1 629.8 595 216.4 777.8 725
(b) Eastbound State Route 26 MOEs with fine-tuned offsets
Reduction in Eastbound Cumulative Travel Time
= 7.2 %
Reduction in Eastbound Cumulative Delay Time
= 12.1 %
Reduction in Eastbound Cumulative Stops
= 15.0 %
Table 2: State Route 26 Eastbound through movement performance summary
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Start
End
8 7 6 5 4 3 2
7 6 5 4 3 2 1
Travel Delay Time Time (s) (per-min) 37.3 199.9 28.0 60.2 34.6 167.0 22.1 147.1 16.0 64.2 80.5 384.5 61.8 411.1
Stops (unit) 221 0 200 154 72 254 372
Cumulative Cumulative Travel Delay Cumulative Time Time Stops (s) (per-min) (unit) 37.3 199.9 221 65.3 260.2 221 99.9 427.2 421 121.9 574.3 575 138.0 638.5 647 218.4 1022.9 901 280.3 1434.0 1273
a) Westbound State Route 26 MOEs with existing offsets
Start
End
8 7 6 5 4 3 2
7 6 5 4 3 2 1
Travel Delay Time Time (s) (per-min) 37.1 199.1 28.0 61.0 39.5 233.6 18.8 110.0 17.0 74.9 82.4 397.1 34.4 170.1
Stops (unit) 221 0 308 108 88 235 129
Cumulative Cumulative Travel Delay Cumulative Time Time Stops (s) (per-min) (unit) 37.1 199.1 221 65.2 260.1 221 104.6 493.7 529 123.4 603.8 637 140.4 678.7 725 222.8 1075.8 960 257.3 1245.9 1089
(b) Westbound State Route 26 MOEs with fine-tuned offsets
Reduction in Westbound Cumulative Travel Time
= 8.2 %
Reduction in Westbound Cumulative Delay Time
= 13.1 %
Reduction in Westbound Cumulative Stops
= 14.5 %
Table 3: State Route 26 Westbound through movement performance summary
December 11, 1998
19
Shoup and Bullock
Measure of Effectiveness
Before
After
Percent Reduction
Calculated t-statistic
Test statistic for 95% C.I.
Cumulative Eastbound Travel Time
233.2 (3.6)
216.4 (3.8)
7.2 %
-14.353
-1.688
Cumulative Eastbound Delay Time
884.4 (40.5)
777.8 (42.9)
12.1 %
-8.081
-1.688
Cumulative Eastbound Stops
853 (40.5)
725 (33.4)
15.0 %
-10.904
-1.689
Cumulative Westbound Travel Time
280.3 (16.9)
257.3 (12.3)
8.2 %
-4.921
-1.692
Cumulative Westbound Delay Time
1434.0 (121.3)
1245.9 (100.8)
13.1 %
-5.334
-1.689
Cumulative Westbound Stops
1273 (44.4)
1089 (50.6)
14.5 %
-12.224
-1.688
(#) Standard deviation; n1 = n2 = 20 replications
Table 4: Tabulation of before and after data for State Route 26
December 11, 1998
20
Shoup and Bullock
