A bi-level programming approach for trip matrix estimation and traffic control problems with stochastic user equilibrium link flows

Abstract

Article:Maher, M.J., Zhang, X. and van Vliet, D. (2001) Abstract ⎯ This paper deals with two mathematically similar problems in transport network analysis: trip matrix estimation and traffic signal optimisation on congested road networks.These two problems are formulated as bi-level programming problems with stochastic user equilibrium assignment as the second-level programming problem. We differentiate two types of solutions in the combined matrix estimation and stochastic user equilibrium assignment problem (or, the combined signal optimisation and stochastic user equilibrium assignment problem): one is the solution to the bi-level programming problem and the other the mutually consistent solution where the two sub-problems in the combined problem are solved simultaneously. In this paper, we shall concentrate on the bi-level programming approach although we shall also consider mutually consistent solutions so as to contrast the two types of solutions. The purpose of the paper is to present a solution algorithm for the two bi-level programming problems and to test the algorithm on several networks.

Route choice and traffic signal control: A study of the stability and instability of a new dynamical model of route choice and traffic signal control

“…Allsop (1974), Gartner (1976), Smith (1979a, c), Bentley and Lambe (1980) and Dickson (1981) were among the first to point to the need to combine models of route choice and traffic signal control; in part so that optimal controls taking account of routeing reactions might be found. The study of traffic control and route choice has been pursued by Meneguzzer (1996Meneguzzer ( , 1997, Maher et al (2001), Wong et al (2001), and many others. Taale and van Zuylen (2001) provide an overview.…”

Disaggregate Path Flow Estimation in an Iterated Dynamic Traffic Assignment Microsimulation

“…Far more common are iterated microsimulations that constrain themselves to the equilibration of route choice (and a strictly trip-based demand (van Zuylen and Willumsen, 1980), Bayesian estimation (Maher, 1983), generalized least squares (Bell, 1991;Bierlaire and Toint, 1995;Cascetta, 1984), and maximum likelihood estimation (Spiess, 1987) have been applied. These methods can be carried over at least approximately to congested networks (Maher et al, 2001;Yang, 1995;Yang et al, 1992;Bierlaire and Crittin, 2006;Cascetta and Posterino, 2001). The further addition of a time dimension, yielding various dynamic OD estimators, is also possible (Cascetta et al, 1993;Ashok, 1996;Bierlaire, 2002;Sherali and Park, 2001;Zhou, 2004).…”

A traffic flow simulator for short‐term travel time forecasting

“…M(q) is the assignment map and/or link choice proportion, which relates the link flows v with the 0-D matrix q. In most of the aforementioned models, the linear relationship is used as below: Maher and Zhang;and Maher et al, 2001) have focused on formulating a bi-level programming problem for 0-D estimation of road traffic. Therefore, the bi-level programming approach, in which the lower level problem is a UE assignment and the upper level problem is a generalized least squares estimation, is used to ensure consistency in the link choice proportions (Yang et al, 1992).…”

“…It is because SUE assignment does consider the perceived error of travel time (Sheffi, 1985). Recently, Maher et al (2001) proposed a bi-level programming approach for ME and traffic count problems with SUE link flows. Based on the heuristic iterative algorithm (Maher et al, 2001), solution algorithm is developed for solving the proposed bi-level programming problem, The constrained generalized least squares (GLS) method (Bell, 1991) is used for solving the upper-level ME problem.…”