A splitting rate model of traffic re-routeing and traffic control

The paper presents an idealised dynamical model of day-to-day or within-day re-routeing using splitting rates at nodes, or node-exit flows, rather than route-flows. It is shown that under certain conditions the dynamical model gives rise to a sequence of link flow vectors which converges to a set of approximate Wardrop equilibria. A special dynamical signal green-time re-allocation model is added; the combination is also shown (in outline) to converge to the set of approximate consistent equilibria under certain conditions. Finally the paper uses model network results to illustrate a method of designing fixed time signal timings to meet different scenarios.

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

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

[3]  M J Smith,et al.  A DESCENT ALGORITHM FOR SOLVING A VARIETY OF MONOTONE EQULIBRIUM PROBLEMS , 1984 .

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

[5]  D. Boyce,et al.  Solving a Non-Convex Combined Travel Forecasting Model by the Method of Successive Averages with Constant Step Sizes , 2006 .

[6]  D. Watling.  STABILITY OF THE STOCHASTIC EQUILIBRIUM ASSIGNMENT PROBLEM: A DYNAMICAL SYSTEMS APPROACH , 1999 .

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

[8]  D I Robertson,et al.  TRANSYT: A TRAFFIC NETWORK STUDY TOOL , 1969 .

[9]  M J Maher.  SAM - A STOCHASTIC ASSIGNMENT MODEL , 1992 .

[10]  G Skrobanski,et al.  Two-direction methods for variable demand traffic assignment , 2007 .

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

[12]  P. Hughes,et al.  A PROBIT-BASED STOCHASTIC USER EQUILIBRIUM ASSIGNMENT MODEL , 1997 .

[13]  Robert B. Dial,et al.  A PROBABILISTIC MULTIPATH TRAFFIC ASSIGNMENT MODEL WHICH OBVIATES PATH ENUMERATION. IN: THE AUTOMOBILE , 1971 .

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

[15]  Dimitri P. Bertsekas,et al.  Data Networks , 1986 .

[16]  Samer H. Hamdar,et al.  Modeling Driver Behavior as Sequential Risk-Taking Task , 2008 .

[17]  R E Allsop.  SOME POSSIBILITIES FOR USING TRAFFIC CONTROL TO INFLUENCE TRIP DISTRIBUTION AND ROUTE CHOICE , 1974 .

[18]  D Van Vliet,et al.  101 USES FOR PATH-BASED ASSIGNMENT , 1999 .

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

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

[21]  Tien Fang Fwa,et al.  Applications of Advanced Technologies in Transportation Engineering , 2004 .

[22]  Guido Gentile,et al.  Linear User Cost Equilibrium: The New Algorithm for Traffic Assignment in VISUM , 2009 .

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

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

[25]  Hong Kam Lo,et al.  Stability and attraction domains of traffic equilibria in a day-to-day dynamical system formulation , 2010 .

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

[27]  D. Watling.  Asymmetric problems and stochastic process models of traffic assignment , 1996 .

[28]  Yu Nie,et al.  A class of bush-based algorithms for the traffic assignment problem , 2009 .

[29]  Martin L. Hazelton,et al.  The Dynamics and Equilibria of Day-to-Day Assignment Models , 2003 .

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

[31]  Mike Maher,et al.  Algorithms for logit-based stochastic user equilibrium assignment , 1998 .

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

[33]  Hillel Bar-Gera,et al.  Traffic Assignment by Paired Alternative Segments , 2010 .

[34]  Mike Smith,et al.  A Two-direction Method of Solving Variable Demand Equilibrium Models with and without Signal Control , 2009 .

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

[36]  Mike Smith,et al.  Bilevel Optimisation of Prices and Signals in Transportation Models , 2006 .

[37]  Hillel Bar-Gera,et al.  Origin-Based Algorithm for the Traffic Assignment Problem , 2002, Transp. Sci..

[38]  G. Gentile,et al.  A within-day dynamic traffic assignment model for urban road networks , 2005 .

[39]  T. Koopmans,et al.  Studies in the Economics of Transportation. , 1956 .

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

[41]  Mike Smith,et al.  Distributed computation of dynamic traffic equilibria , 1997 .

[42]  Yosef Sheffi,et al.  Urban Transportation Networks: Equilibrium Analysis With Mathematical Programming Methods , 1985 .

[43]  Robert B. Dial,et al.  A path-based user-equilibrium traffic assignment algorithm that obviates path storage and enumeration , 2006 .

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

[45]  Torbjörn Larsson,et al.  Simplicial Decomposition with Disaggregated Representation for the Traffic Assignment Problem , 1992, Transp. Sci..

[46]  Hani S. Mahmassani,et al.  DYNAMICS OF COMMUTING DECISION BEHAVIOR UNDER ADVANCED TRAVELER INFORMATION SYSTEMS , 1999 .

[47]  Stella Dafermos,et al.  Traffic Equilibrium and Variational Inequalities , 1980 .

[48]  T. A. Lambe,et al.  ASSIGNMENT OF TRAFFIC TO A NETWORK OF SIGNALIZED CITY STREETS , 1980 .

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

[50]  J. Clegg,et al.  Bilevel programming applied to optimising urban transportation , 2001 .

[51]  Suzanne P. Evans,et al.  DERIVATION AND ANALYSIS OF SOME MODELS FOR COMBINING TRIP DISTRIBUTION AND ASSIGNMENT , 1976 .

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

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

[54]  Nathan H. Gartner,et al.  OPAC: A DEMAND-RESPONSIVE STRATEGY FOR TRAFFIC SIGNAL CONTROL , 1983 .

[55]  T. Magnanti,et al.  Equilibria on a Congested Transportation Network , 1981 .

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

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

[58]  David E. Boyce,et al.  Origin-based algorithms for combined travel forecasting models , 2003 .

[59]  A. Liapounoff,et al.  Problème général de la stabilité du mouvement , 1907 .