OPTIMAL ADAPTIVE SIGNAL CONTROL FOR DIAMOND INTERCHANGES USING DYNAMIC PROGRAMMING

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OPTIMAL ADAPTIVE SIGNAL CONTROL FOR DIAMOND INTERCHANGES USING DYNAMIC PROGRAMMING

ABSTRACT

 

The signalization of two closely spaced intersections in interchanges presents a major challenge in providing efficient traffic operations within the highway system. In current practice, PASSER III is the only existing signal optimization model for diamond interchanges. It optimizes the pre-timed signal plan based on off-line demand and cannot adapt itself to fluctuating demand situations. The two most popular adaptive signal control systems (i.e., OPAC and RHODES) have some limitations: OPAC cannot guarantee a globally optimum solution, both systems cannot be applied to optimize phase sequence, and the arrival patterns used for optimization horizons may not be reliable. Therefore, this research develops a methodology and a corresponding implementation algorithm using dynamic programming (DP) to provide optimal signal control of diamond interchanges in response to real-time traffic fluctuations. The problem is formulated as to find a phase sequencing decision with a  phase duration that makes a pre-specified performance measure minimized over a finite horizon that rolls forward. The problem is solved by DP forward value iterations method. The optimization performance measure can be, for example, delay, queue length, number of stops, or any combination of these. A horizon of 10 seconds is divided into an integral number of intervals, each having 2.5 seconds. The optimal signal switches over each 2.5-second interval are found for each horizon. The optimization process proceeds one horizon after another and is based on the advanced vehicle information obtained from loop detectors set back a certain distance from the stop-line. A dynamic model of future vehicular detections, arrivals and departures is developed at the microscopic level in this study to estimate the traffic flows at the stop-line for each horizon.

 

The DP algorithm is coded in C++ language and dynamically linked to AIMSUN, a stochastic micro-simulation package, which is used for evaluation of the developed methodology. AIMSUN simulates a signalized diamond interchange instrumented with loop detectors that can provide vehicle counts and speeds to the DP algorithm. Based on this, the algorithm calculates the optimal phase sequence and the duration of each

 

horizon, and passes them back to AIMSUN, which subsequently controls the interchange in real time. To enable the algorithm to implement practical scenarios, a so-called majority rolling technique was also developed.

 

A sensitivity analysis using simulation results is conducted to study the characteristics of the DP algorithm.  The results have shown that queue length and storage ratio defined performance measures are the best ones in minimizing system delays. A general rule of choosing the weight of an approach is that a larger weight applied for approaches having more demand. The study has also demonstrated the benefits of using dynamic weights without manually requiring the changing of weights. Dynamic weights can reduce system delay by 36 percent – 49 percent than fixed weights when the demand varies unpredictably every 15 minutes and is unbalanced. Moreover, the real-time DP algorithm has revealed the capability to accommodate various demand situations.

 

The real-time DP algorithm has also been compared to two off-line optimization packages: PASSER III and TRANSYT-7F. The optimized pre-timed signal plans from TRANSYT-7F and PASSER III are implemented in AIMSUN, and the results are compared to those from the DP algorithm. The simulation has exhibited that the real-time adaptive signal algorithm is superior to PASSER III and TRANSYT-7F in handling demand fluctuations for medium to high flow scenarios when the field demand is increased from the one used in off-line optimization. The performance of the three algorithms is almost identical if the simulation demand is the similar to off-demand situation and dose not vary much.

 

 

 

TABLE OF CONTENTS

LIST OF TABLES…………………………………………………………………………………………… viii

LIST OF FIGURES…………………………………………………………………………………………… ix

ACKNOWLEDGEMENTS…………………………………………………………………………………. x

CHAPTER 1  INTRODUCTION ……………………………………………………………………….. 1

1.1 Diamond Interchange Operational Problems and Signal Plans……………………. 1

1.2 Optimal Adaptive Signal Control……………………………………………………………….. 2

1.3 Dynamic Programming (DP)……………………………………………………………………… 4

1.4 Objectives of the Thesis……………………………………………………………………………… 5

1.5 Thesis Overview…………………………………………………………………………………………. 7

CHAPTER 2  LITERATURE REVIEW……………………………………………………………… 8

2.1 Intersection Traffic Signal Control and Optimization…………………………………. 8

2.1.1 Intersection Traffic Signal Control………………………………………………………….. 8

2.1.2 Performance Measures – Delay Models…………………………………………………… 9                        

2.1.3 Optimization Methods for Signalized Intersection Operation……………………. 10           

2.1.3.1 Optimal Phase Splits Using the Time Budget Concept…………………… 10                 

2.1.3.2 Optimization Methods for Adaptive Signal Control……………………….. 12                      

– Binary Choice Process…………………………………………………………………….. 13 

– Signal Sequencing Process Using DP……………………………………………….. 15 

– Parameters Optimization Models……………………………………………………… 18  

2.2 Diamond Interchange Signal Control and Optimization……………………………. 20                         

2.2.1 Diamond Interchange Signal Control……………………………………………………… 20                        

– Three-phase Plan……………………………………………………………………………. 21

-Four-phase plan………………………………………………………………………………. 22

2.2.2 Performance Measures of Diamond Interchanges……………………………………. 23                       

2.2.3 Optimization of Diamond Interchange Signal Operations…………………………. 24                   

2.3 Summary of Literature Review………………………………………………………………… 25

CHAPTER 3  OPTIMIZATION METHODOLOGY…………………………………………. 28                       

3.1 Decision Network Formulation…………………………………………………………………. 28 

3.1.1 Adaptive Signal Plan for Diamond Interchanges……………………………………… 28                       

3.1.2 Decision Network Formulation of Diamond Interchanges Signal Control…… 29

3.1.3 Decision-Making Process……………………………………………………………………… 32

3.2 Dynamic Programming for Interchange Signal Control…………………………….. 32

3.2.1 Background………………………………………………………………………………………… 32

3.2.2 Dynamic Programming Formulation……………………………………………………… 33

3.2.2.1 Introduction………………………………………………………………………………. 33

3.2.2.2 Terminology and Symbols for DP adaptive Signal Control Problem… 35

3.2.2.3 Forward Recurrence Equation……………………………………………………… 39

3.2.3.4 Signal State Transition……………………………………………………………….. 42

3.2.3.5 Immediate Return Equation and Terminal Values………………………….. 42

3.2.3.6 Algorithm Discussion…………………………………………………………………. 44

3.3 Vehicle Arrival-Discharge Projection Dynamics……………………………………….. 47

3.3.1 Introduction…………………………………………………………………………………. 47

3.3.2 Queued Vehicles at the Stop-line……………………………………………………. 47

3.3.3 Vehicle Travel Time…………………………………………………………………….. 50

3.3.4 Vehicle Projection Dynamics and Detection Range………………………….. 51

3.4 Calculation of Performance Measures for one DP Interval………………………… 56

CHAPTER 4  ALGORITHM IMPLEMENTATION…………………………………………. 58

4.1 Basic Parameters for Implementing DP Algorithm……………………………………. 58

4.2 Detectors Setup………………………………………………………………………………………… 60

4.3 DP Optimization Horizon and the Corresponding Detection Range…………… 62

4.4 Implementation of Optimized Signal Plan…………………………………………………. 65 

4.5 Framework of Algorithm Implementation………………………………………………… 66

CHAPTER 5  USING SIMULATION TO EVALUATE THE DP ALGORITHM.. 70

5.1 Using Simulation for Evaluation……………………………………………………………….. 70

5.1.1 Simulation Evaluation Procedure…………………………………………………………… 70

5.1.2 Selection of a Simulation Model……………………………………………………………. 71                        

5.1.3 Calibration of the Selected Simulation Model…………………………………………. 74   

5.1.4 Signal Timing Optimization Models for Diamond Interchanges………………… 78

5.1.5 Simulation of the Proposed DP Algorithm……………………………………………… 80

5.2 Simulation of the DP Algorithm in AIMSUN…………………………………………….. 81

5.2.1 GETRAM Extension Module………………………………………………………………… 81

5.2.2 DP Algorithm Simulation Scheme…………………………………………………………. 82

5.2.3 Flow Structure and Time Logic of the DP Algorithm Coding……………………. 86 

CHAPTER 6  SENSITIVITY ANALYSIS…………………………………………………………. 91

6.1 Overview…………………………………………………………………………………………………. 91

6.2 Delay vs. Performance Measure Index (PMI)……………………………………………. 92

6.2.1 PMI Definitions…………………………………………………………………………………… 92

6.2.2 Fixed Weights…………………………………………………………………………………….. 94

6.2.3 Dynamic Weights………………………………………………………………………………… 98

6.3 Delay vs. Weights……………………………………………………………………………………. 107

6.3.1 Delay vs. Ramp Weights…………………………………………………………………….. 107

6.3.2 Delay vs. Arterial Weights………………………………………………………………….. 110

6.3.3 Delay vs. Internal Link Left Turning Weights……………………………………….. 112

6.4 Delay vs. Various Demand Scenarios………………………………………………………. 114

6.5 Summary……………………………………………………………………………………………….. 119

CHAPTER 7  COMPARISONS OF DIFFERENT OPTIMIZATION METHODS 121

7.1 Overview……………………………………………………………………………………………….. 121

7.2 Low Demand………………………………………………………………………………………….. 121

7.3 Varying Demand……………………………………………………………………………………. 126

7.3.1 Introduction………………………………………………………………………………………. 126

7.3.2 Case A: Unbalanced Demand with Varying Demand on Ramps……………… 126

7.3.3 Case B: Varying Demand on Arterials………………………………………………….. 135

7.3.4 Case C: Varying Demand on Ramps and Arterials…………………………………. 148

7.4 Summary……………………………………………………………………………………………….. 160

CHAPTER 8  SUMMARY, CONCLUSIONS AND FUTURE RESEARCH……… 162

8.1 A Summary of the Thesis Research…………………………………………………………. 162

8.2 Contributions and Conclusions……………………………………………………………….. 164

8.3 Future Research…………………………………………………………………………………….. 167

BIBLIOGRAPHY…………………………………………………………………………………………… 169

APPENDIX  C++ CODE OF THE DP ALGORITHM……………………………………… 175

CHAPTER 1 INTRODUCTION

 

1.1  Diamond Interchanges Operational Problems and Signal Plans

 

Signalized interchanges serve a critical function in highway systems. The most common interchange types are the diamond interchanges, which consist of two intersections, with one connection made for each freeway direction. These intersections are typically signalized when demand flows are high. The signalized intersections connecting to the arterial cross street are often the key operational element within the interchange system.

 

 

Figure 1.1    Geometric Layout of Diamond Interchange (Koonce et al, 1999)

 

The distance between the two intersections varies from less than 400 ft in densely developed urban areas to 800 ft or more in suburban areas (Messer et al, 1997). The close proximity of the two intersections creates a number of interactive effects that complicate the operation. This distance limits the storage available for queued vehicles.  Thus if the signal timing is not properly set, the queue from the downstream intersection will spill back and block the upstream approaches. Another phenomenon that adversely affects interchange operation is called demand starvation. It occurs when portions of the green at the downstream intersection are not used because conditions prevent vehicles at the upstream intersection from reaching the downstream stop-line (HCM, 2000). Additionally, diamond interchanges usually have predominant left-turn movements that adversely affect progression and platoon cohesion along the surface street. To mitigate these unique operational problems at diamond interchanges, it is essential to provide optimal signal control of these two closed-space signalized intersections for efficiently accommodating all movements involved.

 

The most common diamond interchange timing plans are three-phase or fourphase. Each of them has advantages and disadvantages in minimizing delay and queuing, but none of them is optimal for every possible diamond interchange geometry and traffic pattern.  From the literature review undertaken, the only existing optimization model for diamond interchanges is PASSER III, developed by Texas Transportation Institute (TTI) (Messer, et al, 1977, Fambro, et al, 1991). PASSER III is a model designed specifically for diamond interchange signal optimization. The optimization principle of PASSER III is to search for a signal plan or a value of the parameter (such as cycle length, phase duration, offset, etc.) that results in the minimum delay from the restricted alternatives provided to the program. Every search focuses on one variable such as cycle length, phase duration, etc. Thus, the optimal solution provided by PASSER III may not be the globally optimum one. Moreover, PASSER III is an off-line, pre-timed signalized diamond interchange model and does not consider real-time demand fluctuations.

 

 1.2  Optimal Adaptive Signal Control

 

Signal control in practice usually includes pre-timed, actuated and adaptive control. The pre-timed control operates on predetermined, fixed intervals and phase timings. The number and sequence of phases and the cycle length are also fixed. Thus when the traffic conditions change substantially, the timing plan will become less effective. More advanced than pre-timed, actuated control uses the gap-seek logic to respond to traffic fluctuations. The controller extends the green beyond a minimum time until a gap in the traffic flow on the approaches currently with green has been detected or until the (pre-specified) maximum green time has been reached.  Actuated signal control has certain limitations including the tendency to extend green inefficiently under low traffic flow conditions, and great sensitivity to incorrectly set maximum green times (Bell, 1990). Also, its effectiveness deteriorates rapidly as traffic demand increases. Actuated control works well only within certain ranges of demands. Both pre-timed and actuated control use pre-defined timing plans. The green time variation range (including minimum green, maximum green time, etc.) in actuated control is pre-defined.  In contrast to these, adaptive control generates and implements the signal plan dynamically based upon real time traffic conditions, which are measured through a traffic detection system. The algorithm differs between the various adaptive control systems. Compared to pre-timed and actuated control, adaptive signal control has the potential to increase the operational efficiency of existing roadways, particularly for high demands or for varying traffic conditions.

 

Adaptive control can be defined as any signal control strategy that can adjust signal operations in response to fluctuating traffic demand in real time according to certain criteria (Lin and Vijayayumar, 1988).  While the methods used to achieve such signal operations vary, adaptive control makes signal timing decisions based on detected or identified current and short-term or long-term future flow. The adaptive signal control concept was initiated by Miller (1963b). He described an algorithm for adjusting signal timings in small time intervals of 1~2 seconds.  A decision to be made is whether to extend the current green duration or terminate it immediately. The algorithm calculates the difference in vehicle-seconds of delay between the gain made during an extension and the loss in the cross-street resulting from that extension.

 

Since Miller’s pioneering work, considerable research has been done in the United Kingdom, Australia, and the United States to develop adaptive systems. Systems such as SCOOT (Hunt, et al, 1982), SCATS (Luk, 1984; Charles, 2001), OPAC (Gartner, 1983, Gartner and Pooran, 2001) and RHODES (Sen and Head, 1997, Mirchandani and Head, 2001) are among the best known. Some of them were tested and implemented in many cities worldwide. The adaptive control systems demonstrate the effectiveness of integrating Advanced Traffic Management Systems (ATMS) in Intelligent Transportation Systems (ITS) to reduce delay, reduce traffic accidents and improve the efficiency at intersections and networks. These systems include algorithms that provide signal timing plans in response to real-time traffic conditions. They require extensive surveillance, usually in the form of pavement loop detectors, and a communications infrastructure that allows for two-way communication with the central and/or local controllers.

 

1.3  Dynamic Programming (DP)

 

Among the other adaptive control systems listed above, OPAC and RHODES are two promising American systems that are based on dynamic programming and operate using the rolling horizon concept. They have been developed primarily for individual intersections and are being extended to networks. Both systems have their limitations. OPAC does not use a dynamic programming solution procedure; instead, a restricted optimal sequential constrained search (OSCO) is applied. Thus, the OPAC optimization methodology can be classified as trial-and-error enumeration that cannot guarantee a globally optimum solution.  RHODES requires a fixed sequence of phases and a much longer projection time.  Either one of these formulations cannot be applied to optimize phase sequence under phase constraints that are involved in the control for diamond interchanges. Nevertheless, both systems have demonstrated the potential of using DP to optimize the signal plan for a certain future horizon.

 

Earlier signal optimization algorithms considered a short future interval (i.e., 2 seconds), which cannot ensure an overall optimum solution and frequent computing of each interval is not appropriate for on-line implementation.  More recent ones (i.e., OPAC and RHODES) take into account a longer future horizon (i.e., greater than 20 seconds).  However, longer future time involves evaluating a large number of alternative signal timing sequences. One possible approach to solve this problem is to enumerate all possible phase sequencing paths. The number of possible alternatives is huge, and having to calculate the performance measures for each path is not an appealing task and not appropriate for on-line implementation. Compared to the exhaustive enumeration methodology, DP is able to find a global optimal solution with much less effort and time, and thus can be implemented on-line. DP is a proven useful mathematical technique for selecting a sequence of interrelated decisions. It provides a systematic and efficient procedure for determining the optimal combination of decisions (Hillier and Lieberman, 2001).

 

In view of the above, DP should be a promising signal optimization technique for diamond interchange adaptive signal control. In this study DP is proposed to solve the phase sequencing and duration optimization problem at signalized diamond interchanges.

 

1.4   Objectives of the Thesis

 

This study aims at developing a methodology and the corresponding implementation algorithm to provide optimal traffic adaptive signal control of diamond interchanges using DP. To achieve this, two major objectives have been identified:

 

To develop a methodology for optimal solution of signal plan at diamond interchanges and the corresponding implementation algorithm.

 

The methodology will be based on DP because it provides great computational savings over exhaustive enumeration to find the best combination of phase sequencing decisions from a large number of alternatives.  The proposed DP methodology in this study will be defined and formulated in a way that especially suits diamond interchange timing plans and will also lead to an efficient solution to the optimal signal plan. The framework and procedure to implement the proposed scheme will also be developed as part of this dissertation.

 

A vehicle arrival-discharge projection model will be built at the microscopic level for a diamond interchange. Mathematical expressions of various performance measures, such as vehicle delay, queue length and number of stops will be developed. These models will be used in the DP algorithm and therefore influence the optimization performance.

 

To evaluate the proposed optimal signal control for diamond interchanges using micro-simulation.

 

One of the existing commercially available simulation models will be selected to simulate the proposed algorithm and the signal plans from other models with respect to various traffic scenarios and operational conditions. The model will be calibrated using field data.  The proposed DP algorithm will be evaluated and compared to other signal optimization models using pre-selected performance measures.

 

The proposed DP algorithm will attempt to provide global optimal solutions to both phase sequence and phase duration, which would be a new contribution in the field of real-time signal control. The microscopic vehicle projection, arrival and discharge models to be developed will eliminate limitations and inadequacy of existing models. One of the most challenging tasks is the DP formulation of the problem. It must accommodate the optimization of both phase order and phase duration while taking into account the complexity of microscopic arrival-discharge dynamics in view of computational burden for real-time implementation. The evaluation and simulation of the proposed DP algorithm is another challenging task. It requires building an interface between the optimal signal plan from the algorithm and simulation model. To do so, the capabilities of individual simulation models and their programming implications must be carefully examined. The internal data structure of the simulation models has to be examined in order to select an appropriate model. A further challenging task is the modeling of the arrival trajectories and discharge process because they directly affect the optimization performance of the proposed DP algorithm.

 

The primary output of the dissertation will be a new and enhanced methodology for optimal signal control of diamond interchanges, including the decision network expression of the problem, the DP solution methodology, and the models for vehicle trajectories from detector arrival to discharging of the stop-line. The secondary output is the corresponding implementation procedure and algorithms.

 

 1.5  Thesis Overview

 

A critical literature review on intersection traffic signal control and optimization, and diamond interchange signal control and optimization is included in Chapter 2. Chapter 3 presents the proposed methodology for optimal traffic adaptive signal control of diamond interchange using DP, and the model for vehicle arrival-discharge projection dynamics at the stop-line. This is followed by a discussion on the algorithm implementation in Chapter 4. The evaluation of the algorithm using simulation along with the selection of a micro-simulation model and the algorithm coding are given in Chapter 5. Chapter 6 conducts three types of sensitivity analysis to study the characteristics of the DP algorithm. The performance of dynamic weights and fixed weights is also discussed. Chapter 7 compares the performance of the DP algorithm with other two off-line signal optimization tools under various demand scenarios. Finally, Chapter 8 summarizes the contributions, findings and conclusions drawn from the research and also presents the future research.

OPTIMAL ADAPTIVE SIGNAL CONTROL FOR DIAMOND INTERCHANGES USING DYNAMIC PROGRAMMING

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