Operation of Traffic Signal Systems in Oversaturated Conditions, Volume 2 β Final Report (2014) / Chapter Skim
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Chapter 2: Research Approach This research project resulted in several significant findings and developments: β’ Development of new quantitative measures of oversaturation β’ A research methodology for developing signal timing plans for oversaturated conditions β’ A software tool that can select pre-planned mitigation strategies based on the new quantitative measures β’ Evaluation of many combinations of strategies in real world examples β’ Development of guidance and a process to help practitioners identify which strategies apply when and where In this chapter, we will present the following: β’ A series of definitions and framing concepts β’ The motivation and theory for calculation of quantitative metrics of oversaturation β’ The multi-objective methodology for developing and evaluating signal timing plans for oversaturated operation β’ The design and concept of the online software tool for selection of strategies In Chapter 3, we will summarize the findings and test cases of these research and development efforts: β’ Testing and evaluation of the multi-objective development and evaluation methodology β’ Testing and evaluation of the quantitative measures of oversaturation β’ Testing and evaluation of a heuristic for green time re-allocation using quantitative measurement of oversaturation β’ Testing and evaluation of the online strategy selection framework Chapter 4 presents the findings, conclusions, and directions for future research. Definitions Oversaturated conditions can be described according to the following attributes: β’ Spatial extent β’ Temporal extent β’ Recurrence β’ Cause(s)
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The details of these five dimensions comprise a specific "scenario" of traffic conditions that warrant some mitigation strategies. To further clarify these dimensions, we present a series of definitions.
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Common sense dictates that a scenario where a queue of vehicles is dispersed and one or two vehicles are remaining after the termination of the green time is probably not a serious issue to address with alternative traffic control strategies, at least if it only lasts for one or two cycles. However, from general queuing theory we know that a sustained arrival rate (traffic demand)
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Significantly oversaturated conditions existing on a single movement can be handled by re-timing the signal to shift green time from other under-saturated phases to the phase serving the oversaturated movement. Extension of the Definition for Spatial Extent From this basic condition of oversaturation on a movement, the next level of characterization of oversaturation is oversaturation on an approach to an intersection.
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Figure 4 illustrates the case where both the through movement and the left-turn movement are oversaturated. The "subject vehicle" tags in the figure indicate that both movements are oversaturated since neither vehicle proceeds through the intersection during the green signal.
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Figure 5. Illustration of oversaturated approach due to starvation A traffic control phase would be considered oversaturated if all movements that are served by the phase are oversaturated.
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Figure 6 below illustrates an oversaturated intersection where the vehicles in the northbound left turn bay are blocking the movement of the vehicles on the eastbound approach. In a non-blocking situation at an oversaturated intersection, there is no impedance of one approach flow by another incompatible flow.
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oversaturated at the same time. Oversaturation on a route can also be a source of blocking conditions at intersections.
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Figure 8. Illustration of an oversaturated network Special Cases of Network Oversaturation Several special cases of oversaturated scenarios on networks can be defined.
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Table 2. Special cases of network oversaturation Special Case Description Two-way arterial Two or more consecutive approaches in both travel directions that are simultaneously oversaturated.
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Figure 9. Illustration of oversaturated condition on a two-way arterial Large-Scale Problems and Gridlock Wide-spread or regional oversaturated conditions are the most complicated situations to be handled by any mitigation strategy.
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Figure 10. A challenging regional network scenario Strategic restriction of demand to the network (i.e.
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occurrence that provides the definition. As the condition persists for more cycles continuously the condition would be considered to be more severe when combined with the severity level presented by the length of the persistent queue with respect to the storage area for the movement or approach.
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Table 4. Causal factors Factor Description Traffic Demand Heavier traffic flow than can be processed by the traffic signal system regardless of modifications and enhancements to geometrics, signal timings, or both.
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Table 5. Frequency of oversaturation Frequency Description Recurrent Oversaturated conditions characterized by relatively predictable and repeatable occurrences at certain times of day and days of the week.
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Spillback occurs when a queue from a downstream intersection uses up all the space on a link and prevents vehicles from entering the upstream link on green. Some literature has defined this condition as causing "de facto red" to the upstream movement since no progression is possible.
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Storage bay spillback, shown in Figure 13, occurs when turning traffic uses up the entire space of the storage lane and blocks the through traffic. The blocked through movement then experiences starvation.
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Figure 15. Cross blocking effects Identification of these symptoms of oversaturated conditions is an important component of the identification of appropriate mitigation strategies.
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Oversaturation Problem Characterization and System Dynamics Oversaturated conditions might be characterized as being both easy and hard to identify. A motorist that takes a specific route on a daily basis might easily predict where the oversaturated links will occur on their route and knows almost instinctively when the conditions on certain parts of their route are more heavily congested than normal.
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Figure 16. Loading, oversaturation, and recovery regimes of operation During the loading regime, the traffic volumes are increasing, route proportions are changing, and in the case of non-recurrent events, the triggering event(s)
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strategies applied during this phase also serve to help the system return to steady-state operation sooner during the recovery phase than continuing to apply the "normal" operational strategies. During the recovery regime, traffic volumes, route proportions, or restrictive downstream capacity (e.g.
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Measuring Length of Queue and Overflow Queuing Effects In the previous section, we defined the key qualitative characteristics of an oversaturated traffic scenario. To characterize the nature of an oversaturated problem quantitatively, the primary method is to measure queue lengths.
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The amount of green time that is now used to service the overflow queue is quantified by TOSI, ranging from 0% to 100%. When TOSI = 100%, all of the green time for the phase is used to disperse the overflow queue.
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where qa and qb are arrival rates for two conflicting directions; sa and sb are saturation flow rates for two directions; L is the total lost time; and C is the cycle length. Direct application of these definitions to detect the onset and quantify the duration and extent of oversaturation is difficult partly because of the uncertainty of the capacity and saturation flow, and partly due to the difficulty to measure the arrival flow.
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measure of oversaturation by quantifying its detrimental effects. The detrimental effect of oversaturation can be described in temporal and/or spatial dimensions, both of which lead to the reduction of usable green time in a cycle for a signalized approach.
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perspective, the presence of TOSI >0 and SOSI>0 in a series of compatible approaches is the primary method by which to judge a critical route in an oversaturated system. The differentiation of TOSI and SOSI identifies the causal relationship of arterial traffic congestion.
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Monitoring of Arterial Road Traffic and Signals) developed at the University of Minnesota (Liu & Ma, 2009; Liu et al., 2009a, 2009b)
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shockwave (v4)
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Break point C (TC) represents the time when the departure shockwave (v3)
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of the downstream traffic. Using the estimated shockwave speeds from the above equation, the maximum queue (both length max nL and time max nT )
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Under such conditions, the complete queue profile cannot be recovered from the detector data. However, since the entire green time has been used for queue discharge the number of vehicles passing the detector location during the green time can be counted (between TB and Tgn+1)
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Distance Time 1v 2v n gT n rT maxmin( )
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overflow queue cannot be measured with stop-line detection only, it is sufficient to say that oversaturation may have occurred at this intersection for this cycle, i.e.
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The second type of QOD, which occurs outside of the time interval 4 2[ / , / ] n n g d r dT L v T L v+ + , indicates that a spillover has happened at a downstream location.
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vehicle for a relatively long period of time or the detector is placed at or near a bus stop and a transit vehicle stays on the detector for some time)
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the arterial. Advance detectors are located on the major approaches and stop-bar detectors on the minor approaches.
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08:09:15.012, D8 on, 7.902s 08:09:15.481, D8 off, 0.468s 08:09:16.761, G3 off, 29.389s 08:09:16.761, Y3 on, 179.021s 08:09:17.620, D9 on, 2.686s 08:09:18.151, D10 on, 2.593s 08:09:18.307, D9 off, 0.687s 08:09:18.823, D10 off, 0.671s 08:09:20.244, Y3 off, 3.482s 08:09:21.649, D22 on, 80.953s 08:09:22.008, D22 off, 0.359s 08:09:23.242, G1 on, 172.806s Detector #8 on at 08:09:15.012; Vacant time is 7.902s Green Phase #3 off at 08:09:16.761; Green duration time is 29.389s Detector #9 off at 08:09:18.307; Occupy time is 0.687s Yellow Phase #3 off at 08:09:20.244; Yellow duration time is 3.482s Green Phase #1 on at 08:09:23.242; Red duration time is 172.806s Figure 24. Sample data collected at the test site Estimation Results of Overflow Queue Length Using the event-based data from the SMART-Signal system, the queue length estimation method discussed above was applied for the estimation of overflow queue lengths.
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Case of Oversaturation 0 100 200 300 400 500 600 700 16:48:00 16:49:26 16:50:53 16:52:19 16:53:46 16:55:12 16:56:38 16:58:05 Queue Length Profile at Eastbound Glenwood Distance (feet) Time Residual Queue Figure 25.
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Example Results for Detection of Spillover The spatial detrimental effect caused by oversaturation is characterized by spillover, which can be diagnosed by identifying the second type of QOD. In Figure 27, we present the detector occupancy time within an afternoon peak hour cycle on Nov.
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Traj 7000 7500 8000 8500 9000 17:12:03 17:12:46 17:13:29 17:14:12 17:14:56 17:15:39 17:16:22 17:17:05 Distance (feet) Intersection Winnetka Intersection Rhode Island Location of Advance Detector Location of Advance Detector Time Spillover Vehicle Trajectories in the Case of Spillover from Winnetka to Rhode Island Figure 28.
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0300 600 900 1200 1500 1800 17:05:17 17:12:29 17:19:41 17:26:53 17:34:05 17:41:17 Time Queue Length Profile at the Intersection of WinnetkaDistance (feet) Figure 29.
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Table 7. Oversaturation Severity Indices (OSI)
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Summary of Diagnostics for Severity of Oversaturation In this section, we presented a methodology for measurement of oversaturation (overflow queue lengths) from conventional detectors and high-resolution phase timing data and two derived metrics for the severity of oversaturation.
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described in the next section of the report. Two simulation examples of applying the methodology on real-world test networks are described in Chapter 4.
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A Multi-Objective Methodology for Designing and Evaluating Signal Timing Plans Under Oversaturated Conditions In the previous section we described algorithms to calculate the intensity of oversaturation on an individual approach. This detailed information is necessary from a bottom-up perspective to quantify the presence and effects of oversaturated conditions.
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that might be taken to mitigate any specific scenario. The systematic mathematical optimization procedure described in this section was developed in an attempt to provide a rational approach for arriving at specific timing plan parameters that take into account both oversaturated conditions and critical route flows.
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Figure 30. Framework for determination of control strategies used in this research Framework for Determination of the Traffic Flows on Critical Routes Volumes on critical routes can be determined using detailed theoretical analysis, including synthetic O-D estimation, volume correlation analysis, and clustering of detector data.
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contribution to the design of the control strategy. The second key principle is the concept of volume spillover.
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critical routes and attempts to prevent spillback and starvation which results in several sets of timing parameters. Since we now have a range of possible timing values, simulation is then used to evaluate the performance of the generated timing plans for the three principle optimization objectives: minimize delay, maximize throughput, and manage queues.
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capacities of the approaches in the system. In oversaturated conditions, however, cycle length is a function of the storage capacity of the links, the arrival rate during red intervals along the arterial, and the green split ratio at each intersection.
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Figure 34. Upper-bound of cycle length that prevents spillback Roess et.
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Figure 35. Upper-bound of cycle length as a function of saturation flow rate As illustrated in the figures, short link distances create the most severe limits on cycle length during high demand periods.
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green splits are initially allocated based on the v/c ratios given a specific cycle time. In the case of phase failure (i.e., v/c> 1)
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value of (p) is the design value used for computing maximum and minimum offset values, such that ( )
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Figure 37. Starvation avoidance offset Similar to the computation of the spillback avoidance bound on offsets, a design value for Ο must be assumed.
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queue ratio is 0.5 (half of the 800 ft link length is filled with a queue) then the relative offset is constrained in the region of offsets between (-30s, 10s)
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Figure 39. Split-offset calculation procedure 1-Volume per cycle (VPC)
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πππ β β β οΏ½π£πππ πππποΏ½ οΏ½πβπ½πβπΌπβπ
Eq. 21 Subject to the following constraints: Cycle length constraint β (πππ + πππ)
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d(k) I : mean departure rate from approach (i)
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fronts. A Pareto front is the combination of compromise solutions of all of the objectives being considered in the problem.
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Delay Minimization Most offline optimization tools use some kind of formulation for minimizing delay and stops, perhaps balanced with some consideration for providing progression on an arterial route. In undersaturated conditions, this objective is handled sometimes quite loosely to perhaps include solutions that might only be considered to be effective or only acceptable and not really a true minimum total delay.
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vehicles to continue through a sequence of intersections without stopping. By carefully setting the offset values, the objective of minimizing delay (equity treatment for all users)
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overall output processing rate of the intersections in the system closely matches the input processing rate and overflow storage of vehicles in the system does not occur. In oversaturated conditions, the output rate is less than the input rate and overflow queuing begins to build up within the system at various points.
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of actuated-coordinated control by commanding patterns with different parameters. The coordination of actions between intersections for queue management must closely resemble the operation of a diamond interchange with a carefully orchestrated sequence of actions, with rapid feedback between the detection of queue extent and the application of rapid-response mitigation strategies such as phase truncation and green extension.
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Cycle length constraint β (πππ + πππ)
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Cycle length constraint β (πππ + πππ)
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πππ: Approach (j) green time at intersection (i)
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For all critical routes in the network: β π β π
,β π β πΌ, βπ β π½ Eq. 50 Where: C : cycle length c : capacity v : volume, and g : effective green Qb: size of initial queue T : analysis period, hour t : duration of oversaturation within T, h u : delay parameter si : adjusted saturation flow rate per lane of approach (i)
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In addition, the methodology considers the time-varying nature of the traffic demands. Particularly for oversaturated conditions, the process of generating the timing plans must consider that any un-served demand must be serviced in the next time period.
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during time period 5, instead of allowing the westbound queues to grow until the timings for time period 9 are finally implemented. These kind of trade-offs are analyzed and brought to light by the multi-objective Pareto front analysis process.
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Figure 44. Concept of volume profiles that generate un-served demand Optimization Procedure The optimization problems for minimizing delay, maximizing throughput, and managing queues are mixed integer nonlinear problems with nonlinear constraints.
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The surface for total delay uses the HCM equation to compute the performance of the timing plan for each time period. Similarly, the surface for total throughput uses the Abu-Lebdeh (2000)
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Figure 46. Throughput surface representing the performance of each timing plan for each time period Switching Between Control Strategies The decision to switch between control strategies is based on several factors: 1.
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ο§ Throughput maximization -Queue management -Throughput maximization A timing plan that is optimal for the first objective would be applied during the loading regime. A timing plan that is optimal for the second objective would be applied during the processing regime.
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Figure 47. Example of optimal timing plans and scheduling based on the minimum delay objective Figure 48.
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3. the selection of the objective function to solve for optimal timings with respect to a particular objective, and 4.
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Online Implementation of Mitigation Strategies In the previous two sections we described quantitative measures for estimating the severity of an oversaturated condition and a process for generating timing plans that are designed to mitigate oversaturated conditions. When the oversaturated scenario is recurrent, either of these methods can be used to generate mitigation timing plans and apply those timing plans on a TOD scheduled basis.
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mitigation strategies. Traditional occupancy measurements can also be used with the logic processor application, given that the detectors are located appropriately and aggregation of the data is configured appropriately.
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Figure 49. Recommended placement of oversaturation detection zones Placement of Detectors for Online Recognition of a Scenario In simple situations involving an individual approach or an individual intersection, it is straightforward to identify where detection zones are needed since they should be placed on the approaches where the queuing is experienced.
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Figure 50. Example placement of oversaturation detection points Detector Data Aggregation Intervals and Persistence Time Aggregation of detector occupancy data is also important in balancing the occurrence of false positive and false-negative conditions.
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β’ Configuration of the detection points β’ Configuration of the logic clauses β’ Configuration of the mitigation timing plans This setup is illustrated in Figure 51. In this example, not all of the oversaturation detectors are used as inputs.
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Table 9. Example logic conditions and actions Table 10.
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Figure 52. Logic engine example As shown in this example, thresholds for each detector input can be selected independently and ANDβ¦OR logic can be applied between the inputs for a certain logic clause.
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of all the detectors drop below, 50%. This reduces waffling in the timing plan decision if just a single lane drops below 50% for several cycles.
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Figure 53. Online oversaturation management research software integration The online process is implemented in a software-in-the-loop framework as illustrated below.
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The first step of the evaluation process, as shown above in Figure 53, is to obtain access to the traffic signal phase timing information and detector actuations inside of the simulation model and use that data to estimate queue lengths and compute oversaturation estimates. The queue length and oversaturated conditions measurement module was developed by the University of Minnesota.
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Figure 55. Research software integration β Step 3 D4 then acts on the plan commands sent by the congestion manager and implements the requested change to the traffic control strategy, such as phase omits, phase reservice, split and cycle time modifications, simultaneous offsets, and other strategies, by running the newlyrequested plan.
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Figure 56. Research software integration β Step 4 After the new plans are implemented during the oversaturated conditions, the Vissim model collects the performance data such as delays, throughput, stops, and so on for effectiveness evaluation as identified below in Figure 57.
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Figure 57. Research software integration β Step 5 A similar process is applied in the offline case, except the congestion manager module is not used to dynamically change signal timing strategies based on the congestion estimates.
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the extremely challenging nature of the chosen problem. The process and the tool, however, were proven to be a viable method to tie together the design of mitigation strategies with the measurement of oversaturation severity estimates and queue length measurement.
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