Traffic signal control and route choice: A new assignment and control model which designs signal timings

Abstract This paper outlines a dynamical assignment and control model which calculates stage green-times for a signal-controlled network. In the dynamical model route flows, bottleneck delays and stage green-times all change simultaneously over iterations. It is shown that if the initial problem is feasible and the P 0 policy is utilised to move stage green-times then convergence is certain in the vertical queueing case. The model makes some reasonable systematic allowance for travellers’ route choices by encouraging congestion-reducing route choices in the future; the model (in generating signal timings) maximises network capacity (taking account of route choices) when queueing is vertical. Blocking back however appears difficult to deal with (while retaining the convergence guarantee) and represents an area for further study. The model may be used to design fixed-time or time of day signal timings; it may also be used to pre-prepare timings for rapid implementation in case of a predictable incident; finally if computation speeds are high enough the method may possibly be used responsively, in real-time.

[1]  T Van Vuren,et al.  Route Choice and Signal Control: The Potential for Integrated Route Guidance , 1992 .

[2]  Henk Taale,et al.  Integrated anticipatory control of road networks: A game-theoretical approach , 2008 .

[3]  Pravin Varaiya,et al.  Max pressure control of a network of signalized intersections , 2013 .

[4]  C S Fisk.  OPTIMAL SIGNAL CONTROLS ON CONGESTED NETWORKS , 1984 .

[5]  H. M. Zhang,et al.  Models and algorithms for the traffic assignment problem with link capacity constraints , 2004 .

[6]  Chen Cai,et al.  Adaptive Dynamic Control for Road Traffic Signals , 2007, 2007 IEEE International Conference on Networking, Sensing and Control.

[7]  Mike Smith,et al.  Dynamics of route choice and signal control in capacitated networks , 2011 .

[8]  Michael J. Smith,et al.  The Stability of a Dynamic Model of Traffic Assignment - An Application of a Method of Lyapunov , 1984, Transp. Sci..

[9]  Hai Yang,et al.  Traffic assignment and signal control in saturated road networks , 1995 .

[10]  Markos Papageorgiou,et al.  Store-and-forward based methods for the signal control problem in large-scale congested urban road networks , 2009 .

[11]  Claudio Meneguzzer,et al.  REVIEW OF MODELS COMBINING TRAFFIC ASSIGNMENT AND SIGNAL CONTROL , 1997 .

[12]  R D Bretherton,et al.  THE SCOOT ON-LINE TRAFFIC SIGNAL OPTIMISATION TECHNIQUE , 1982 .

[13]  Giulio Erberto Cantarella,et al.  Dynamic Processes and Equilibrium in Transportation Networks: Towards a Unifying Theory , 1995, Transp. Sci..

[14]  M O Ghali,et al.  DESIGNING TIME-OF-DAY SIGNAL PLANS WHICH REDUCE URBAN TRAFFIC CONGESTION , 1994 .

[15]  Claudio Meneguzzer.  Computational Experiments with a Combined Traffic Assignment and Control Model with Asymmetric Cost Functions , 1996 .

[16]  Xiaolei Guo,et al.  A link-based day-to-day traffic assignment model , 2010 .

[17]  Mike J. Smith,et al.  Equilibrium in Capacitated Network Models with Queueing Delays, Queue-storage, Blocking Back and Control☆ , 2013 .

[18]  Hani S. Mahmassani,et al.  Day-to-day evolution of network flows under real-time information and reactive signal control , 1997 .

[19]  J. G. Wardrop,et al.  Some Theoretical Aspects of Road Traffic Research , 1952 .

[20]  Mike Smith.  Intelligent Network Control: Using an Assignment–Control Model to Design Fixed Time Signal Timings , 2010 .

[21]  K Wood.  URBAN TRAFFIC CONTROL : SYSTEMS REVIEW , 1993 .

[22]  Thomas J. Dickson,et al.  A NOTE ON TRAFFIC ASSIGNMENT AND SIGNAL TIMINGS IN A SIGNAL-CONTROLLED ROAD NETWORK , 1981 .

[23]  Richard Mounce,et al.  Existence of equilibrium in a continuous dynamic queueing model for traffic networks with responsive signal control , 2007 .

[24]  M. J. Smith,et al.  Traffic Equilibrium with Responsive Traffic Control , 1993, Transp. Sci..

[25]  Wang,et al.  Review of road traffic control strategies , 2003, Proceedings of the IEEE.

[26]  Giulio Erberto Cantarella.  Signal Setting with Dynamic Process Assignment , 2010 .

[27]  M J Smith,et al.  A LOCAL TRAFFIC CONTROL POLICY WHICH AUTOMATICALLY MAXIMISES THE OVERALL TRAVEL CAPACITY OF AN URBAN ROAD NETWORK , 1980 .

[28]  Richard Mounce,et al.  A splitting rate model of traffic re-routeing and traffic control , 2011 .

[29]  L. Armijo.  Minimization of functions having Lipschitz continuous first partial derivatives. , 1966 .

[30]  Benjamin G. Heydecker,et al.  Objectives, Stimulus and Feedback in Signal Control of Road Traffic , 2004, J. Intell. Transp. Syst..

[31]  Carlos F. Daganzo,et al.  Queue Spillovers in Transportation Networks with a Route Choice , 1998, Transp. Sci..

[32]  Hai Yang,et al.  Equilibrium Network Traffic Signal Setting Under Conditions of Queuing and Congestion , 1996 .

[33]  Warren B. Powell,et al.  Optimal Signal Settings Over Transportation Networks , 1983 .

[34]  Giulio Erberto Cantarella,et al.  A General Fixed-Point Approach to Multimode Multi-User Equilibrium Assignment with Elastic Demand , 1997, Transp. Sci..

[35]  Mike Smith,et al.  The existence, uniqueness and stability of traffic equilibria , 1979 .

[36]  André de Palma,et al.  Stationary Dynamic Solutions in Congested Transportation Networks: Summary and Perspectives , 2003 .

[37]  Henk Taale,et al.  THE COMBINED TRAFFIC ASSIGNMENT AND CONTROL PROBLEM: AN OVERVIEW OF 25 YEARS OF RESEARCH , 2001 .

[38]  M. Smith,et al.  A descent algorithm for solving monotone variational inequalities and monotone complementarity problems , 1984 .

[39]  M. Patriksson,et al.  An augmented lagrangean dual algorithm for link capacity side constrained traffic assignment problems , 1995 .

[40]  Nathan H. Gartner,et al.  Area Traffic Control and Network Equilibrium , 1976 .

[41]  Bart De Schutter,et al.  Influencing route choice in traffic networks: A model predictive control approach based on mixed-integer linear programming , 2008, 2008 IEEE International Conference on Control Applications.

[42]  Thomas. Van Vuren,et al.  The interaction between signal control policies and route choice. , 1990 .

[43]  M J Smith.  TRAFFIC CONTROL AND TRAFFIC ASSIGNMENT IN A SIGNAL-CONTROLLED NETWORK WITH QUEUEING , 1987 .

[44]  D I Robertson,et al.  "TRANSYT" METHOD FOR AREA TRAFFIC CONTROL , 1969 .

[45]  F. Webster.  TRAFFIC SIGNAL SETTINGS , 1958 .

[46]  M J Smith,et al.  THE INTERACTIONS BETWEEN SIGNAL CONTROL POLICIES AND ROUTE CHOICE , 1987 .

[47]  Michiel C.J. Bliemer,et al.  Quasi-dynamic network loading: adding queuing and spillback to static traffic assignment , 2012 .

[48]  Mike Smith,et al.  Traffic control and route-choice; a simple example , 1979 .