Optimal adaptive routing and traffic assignment in stochastic time-dependent networks

A stochastic time-dependent (STD) network is defined by treating all link travel times at all time periods as random variables, with possible time-wise and link-wise stochastic dependency. A routing policy is a decision rule which specifies what node to take next out of the current node based on the current time and online information. A formal framework is established for optimal routing policy problems in STD networks, including generic optimality conditions, and a comprehensive taxonomy with insights into variants of the problem. A variant pertinent to road traffic networks is studied in detail, where a discrete joint distribution of link travel times is used to accommodate the most general stochastic dependency among link travel times, and the access to perfect online information about link travel times is assumed. Both exact and approximation solution algorithms are designed and tested. The criteria of optimality are then extended to reliability measures, such as travel time variance and expected early/late schedule delays. The first routing-policy-based stochastic dynamic traffic assignment (DTA) model is established. A general framework is provided and the equilibrium problem is formulated as a fixed point problem with three components: the optimal routing policy generation module, the routing policy choice model and the policy-based dynamic network loader. An MSA (method of successive averages) heuristic is designed. Computational tests are carried out in a hypothetical network, where random incidents are the source of stochasticity. The heuristic converges satisfactorily in the test network under the proposed test settings. The adaptiveness in the routing policy based model leads to travel time savings at equilibrium. As a byproduct, travel time reliability is also enhanced. The value of online information is an increasing function of the incident probability. Travel time savings are high when market penetrations are low. However, the function of travel time saving against market penetration is not monotonic. This suggests that in a travelers’ information system or route guidance system, the information penetration needs to be chosen carefully to maximize benefits. Thesis Supervisor: Moshe E. Ben-Akiva Title: Edmund K. Turner Professor of Civil and Environmental Engineering

[1]  R. Cheung.  Iterative methods for dynamic stochastic shortest path problems , 1998 .

[2]  Pitu Mirchandani,et al.  Generalized Traffic Equilibrium with Probabilistic Travel Times and Perceptions , 1987, Transp. Sci..

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

[4]  Ismail Chabini,et al.  Discrete Dynamic Shortest Path Problems in Transportation Applications: Complexity and Algorithms with Optimal Run Time , 1998 .

[5]  Daniele Pretolani,et al.  A directed hypergraph model for random time dependent shortest paths , 2000, Eur. J. Oper. Res..

[6]  John W. Polak,et al.  STATIONARY STATES IN STOCHASTIC PROCESS MODELS OF TRAFFIC ASSIGNMENT: A MARKOV CHAIN MONTE CARLO APPROACH , 1996 .

[7]  Peter Nijkamp,et al.  Information policy in road transport with elastic demand: Some welfare economic considerations , 1998 .

[8]  Chelsea C. White,et al.  A Heuristic Search Approach for a Nonstationary Stochastic Shortest Path Problem with Terminal Cost , 2002, Transp. Sci..

[9]  Robert B. Noland,et al.  Travel-time uncertainty, departure time choice, and the cost of morning commutes , 1995 .

[10]  L. B. Fu,et al.  Expected Shortest Paths in Dynamic and Stochastic Traf c Networks , 1998 .

[11]  Carlos F. Daganzo,et al.  On Stochastic Models of Traffic Assignment , 1977 .

[12]  Mark David Abkowitz.  The impact of service reliability on work travel behavior , 1980 .

[13]  John N. Tsitsiklis,et al.  Dynamic Shortest Paths in Acyclic Networks with Markovian Arc Costs , 1993, Oper. Res..

[14]  Tim Lomax,et al.  THE 2003 ANNUAL URBAN MOBILITY REPORT , 2003 .

[15]  E. Cascetta.  A stochastic process approach to the analysis of temporal dynamics in transportation networks , 1989 .

[16]  André de Palma,et al.  Dynamic Model of Peak Period Traffic Congestion with Elastic Arrival Rates , 1986, Transp. Sci..

[17]  Dimitri P. Bertsekas,et al.  Dynamic Programming and Optimal Control, Two Volume Set , 1995 .

[18]  Stefano Pallottino,et al.  Equilibrium traffic assignment for large scale transit networks , 1988 .

[19]  Song Gao,et al.  Optimal routing policy problems in stochastic time-dependent networks , 2006 .

[20]  Adaptive least-expected time paths in stochastic, time-varying transportation and data networks , 2001 .

[21]  Gary A. Davis,et al.  Large Population Approximations of a General Stochastic Traffic Assignment Model , 1993, Oper. Res..

[22]  Martin L. Hazelton.  Some Remarks on Stochastic User Equilibrium , 1998 .

[23]  J. Tsitsiklis,et al.  Stochastic shortest path problems with recourse , 1996 .

[24]  George H. Polychronopoulos.  Stochastic and dynamic shortest distance problems , 1992 .

[25]  Elise Miller-Hooks,et al.  Adaptive routing considering delays due to signal operations , 2004 .

[26]  Mohamed Abdel-Aty,et al.  Exploring route choice behavior using geographic information system-based alternative routes and hypothetical travel time information input , 1995 .

[27]  Hong Kam Lo,et al.  Network with degradable links: capacity analysis and design , 2003 .

[28]  J. Scott Provan,et al.  A polynomial‐time algorithm to find shortest paths with recourse , 2003, Networks.

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

[30]  Mohamed Abdel-Aty,et al.  INVESTIGATING EFFECT OF TRAVEL TIME VARIABILITY ON ROUTE CHOICE USING REPEATED-MEASUREMENT STATED PREFERENCE DATA , 1995 .

[31]  H. Mahmassani,et al.  Least expected time paths in stochastic, time-varying transportation networks , 1999 .

[32]  Jon Alan Bottom,et al.  Consistent anticipatory route guidance , 2000 .

[33]  David P. Watling,et al.  A Second Order Stochastic Network Equilibrium Model, II: Solution Method and Numerical Experiments , 2002, Transp. Sci..

[34]  André de Palma,et al.  Does providing information to drivers reduce traffic congestion , 1991 .

[35]  David K. Smith,et al.  Dynamic Programming and Optimal Control. Volume 1 , 1996 .

[36]  Haris N. Koutsopoulos,et al.  DEVELOPMENT OF A ROUTE GUIDANCE GENERATION SYSTEM FOR REAL-TIME APPLICATION , 1997 .

[37]  Bin Ran,et al.  Analytical Dynamic Traffic Assignment Model with Probabilistic Travel Times and Perceptions , 2002 .

[38]  Warren B. Powell,et al.  An algorithm for the equilibrium assignment problem with random link times , 1982, Networks.

[39]  David P. Watling,et al.  A Second Order Stochastic Network Equilibrium Model, I: Theoretical Foundation , 2002, Transp. Sci..

[40]  Song Gao,et al.  Optimal routing policy problems in stochastic time-dependent networks. I. Framework and taxonomy , 2002, Proceedings. The IEEE 5th International Conference on Intelligent Transportation Systems.

[41]  Liping Fu,et al.  An adaptive routing algorithm for in-vehicle route guidance system with real-time information , 2001 .

[42]  Giovanni Andreatta,et al.  Stochastic shortest paths with recourse , 1988, Networks.

[43]  J. Croucher.  A note on the stochastic shortest‐route problem , 1978 .

[44]  Pierre Hansen,et al.  Commuters' Paths with Penalties for Early or Late Arrival Time , 1990, Transp. Sci..

[45]  Randolph W. Hall,et al.  The Fastest Path through a Network with Random Time-Dependent Travel Times , 1986, Transp. Sci..

[46]  Robin Lindsey,et al.  DEPARTURE TIME AND ROUTE CHOICE FOR THE MORNING COMMUTE , 1990 .