A mixed-integer linear programming formulation is proposed to solve the combined system optimal dynamic traffic assignment and signal optimization problem. Traffic conditions are modeled with the cell transmission model, a convergent numerical approximation to the hydrodynamic model of traffic flow. The formulation is suited to respond to oversaturated traffic conditions. It also can be adapted to account for turning movements, protected and permissive phases (gap acceptance), and multiple signal controller types: dynamic (traffic adaptive) and pretimed. Trials with a test network validated the formulation and achieved promising results. Specifically, dynamic signal control proved to be substantially more effective than pretimed control for incident conditions. In addition, potential benefits of rerouting vehicles in both directions of a roadway were revealed even when only one direction is closed.
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References
1.
WebsterF. V.Traffic Signal Settings.Road Research Technical Paper 39.Her Majesty's Stationery Office, London, 1958, pp. 1–24.
2.
RobertsonD. I.TRANSYT: A Traffic Network Study Tool. Transport and Road Research Laboratory Report LR 253. Transportation Research Laboratory, 1969.
3.
LittleJ. D. C., KelsonM. D., and GartnerN. H.. MAXBAND: A Program for Setting Signals on Arteries and Triangular Networks. In Transportation Research Record 795, TRB, National Research Council, Washington, D.C., 1981, pp. 40–46.
4.
HuntP. B., RobertsonD. I., BrethertonR. D., and RoyaleM. C.. SCOOT On-Line Traffic Signal Optimization Technique.Traffic Engineering and Control, Vol. 23, 1982, pp. 190–192.
5.
LowrieP. R.SCATS Principles, Methodology, Algorithm.IEE Conference on Road Traffic Signaling. IEE Publication 207. IEE, London, 1982, pp. 67–70.
6.
WoodK.Urban Traffic Control: A Systems Review. Project Report 41. Transportation Research Laboratory, Crowthorne, Berkshire, United Kingdom, 1993.
7.
ParkB., MesserC. J., and UrbanikT.IIEnhanced Genetic Algorithm for Signal-Timing Optimization of Oversaturated Intersections. In Transportation Research Record: Journal of the Transportation Research Board, No. 1727, TRB, National Research Council, Washington, D.C., 2000, pp. 32–41.
8.
LiebermanE. B., ChangJ., and PrassasE. S.. Formulation of Real-Time Control Policy for Oversaturated Arterials. In Transportation Research Record: Journal of the Transportation Research Board, No. 1727, TRB, National Research Council, Washington, D.C., 2000, pp. 77–88.
9.
GiriannaM., and BenekohalR. F.. Dynamic Signal Coordination for Networks with Oversaturated Arterials. In Transportation Research Record: Journal of the Transportation Research Board, No. 1811, Transportation Research Board of the National Academies, Washington, D.C., 2002, pp. 122–130.
10.
WeyW.-M., and JayakrishnanR.. Network Traffic Signal Optimization Formulation with Embedded Platoon Dispersion Simulation. In Transportation Research Record: Journal of the Transportation Research Board, No. 1683, TRB, National Research Council, Washington, D.C., 1999, pp. 150–159.
11.
WeyW.-M.Model Formulation and Solution Algorithm of Traffic Signal Control in an Urban Network.Computers, Environment and Urban Systems, Vol. 24, No. 4, 2000, pp. 355–377.
12.
WeyW.-M., and JayakrishnanR.. Applying a Network Programming Algorithm to a Networkwide Traffic Control Scheme: Simulation-Based Performance Studies. In Transportation Research Record: Journal of the Transportation Research Board, No. 1882, Transportation Research Board of the National Academies, Washington, D.C., 2004, pp. 105–112.
13.
LoH. K.A Novel Traffic Signal Control Formulation.Transportation Research, Vol. 33A, No. 6, 1999, pp. 433–448.
14.
LoH. K.A Cell-Based Traffic Control Formulation: Strategies and Benefits of Dynamic Timing Plans.Transportation Science, Vol. 35, No. 2, 2001, pp. 148–164.
15.
LoH. K., ChangE., and ChanY. C.. Dynamic Network Traffic Control.Transportation Research, Vol. 35A, No. 8, 2001, pp. 721–744.
16.
LoH. K., and ChowA. H.. Control Strategies for Oversaturated Traffic.Journal of Transportation Engineering, Vol. 130, No. 4, 2004, pp. 466–478.
17.
MichalopoulosP., StephanopoulosG., and StephanopoulosG.. Modelling and Analysis of Traffic Queue Dynamics at Signalized Intersections.Transportation Research, Vol. 13A, No. 5, 1979, pp. 295–307.
18.
LinW. H., and WangC.. An Enhanced 0-1 Mixed-Integer Linear Program Formulation for Traffic Signal Control.IEEE Transactions on Intelligent Transportation Systems, Vol. 5, No. 5, 2004, pp. 238–245.
19.
AllsopR. E.Some Possibilities for Using Traffic Control to Influence Trip Distribution and Route Choice.Proc., 6th International Symposium on Transportation and Traffic Theory, 1974, pp. 345–373.
20.
SmithM. J.The Existence of an Equilibrium Solution to the Traffic Assignment Problem When There Are Junction Interactions.Transportation Research, Vol. 15B, No. 6, 1981, pp. 443–451.
21.
SmithM. J.Properties of a Traffic Control Policy Which Ensure the Existence of a Traffic Equilibrium Consistent with the Policy.Transportation Research, Vol. 15B, No. 6, 1981, pp. 453–462.
22.
MeneguzzerC.Review of Models Combining Traffic Assignment and Signal Control.Journal of Transportation Engineering, Vol. 123, No. 2, 1997, pp. 148–155.
23.
MerchantD. K., and NemhauserG. L.. A Model and an Algorithm for the Dynamic Traffic Assignment Problems.Transportation Science, Vol. 12, No. 3, 1978, pp. 183–199.
24.
VariaH. R., and DhingraS. L.. Dynamic Optimal Traffic Assignment and Signal Timing Optimization Using Genetic Algorithms.Computer-Aided Civil and Infrastructure Engineering, Vol. 19, No. 4, 2004, pp. 260–273.
25.
AbdelfatahA. S., and MahmassaniH. S.. System Optimal Time-Dependent Path Assignment and Signal Timing in Traffic Network. In Transportation Research Record 1645, TRB, National Research Council, Washington, D.C., 1998, pp. 185–193.
26.
DaganzoC. F.The Cell Transmission Model: A Simple Dynamic Representation of Highway Traffic Consistent with Hydrodynamic Theory.Transportation Research, Vol. 28B, No. 4, 1994, pp. 269–287.
27.
DaganzoC. F.The Cell Transmission Model, Part II: Network Traffic.Transportation Research, Vol. 29B, No. 2, 1995, pp. 79–93.
28.
LighthillM. J., and WhithamJ. B.. On Kinematic Waves, I: Flow Movement in Long River; II: A Theory of Traffic Flow in Long Crowded Roads.Proc., Royal Society, A, 229, 1955, pp. 281–345.
29.
RichardsP. I.Shock Waves on the Highway.Operational Research, Vol. 4, 1956, pp. 42–51.
30.
ZiliaskopoulosA. K.A Linear Programming Model for the Single Destination System Optimum Dynamic Traffic Assignment Problem.Transportation Science, Vol. 34, No. 1, 2000, pp. 37–49.
31.
ZiliaskopoulosA. K., and LeeS.. Cell Transmission Based Assignment Simulation Model for Integrated Freeway/Surface Street Systems. Presented at 76th Annual Meeting of the Transportation Research Board, Washington D. C., 1997.
32.
LiY.Development of Dynamic Traffic Assignment Models for Planning Applications.PhD thesis. Northwestern University, Evanston, Ill., 2001.
33.
Highway Capacity Manual.TRB, National Research Council, Washington, D.C., 2000.
