Bi-level Formulation for Equilibrium Traffic Flow and Signal Settings

Abstract

A bi-level programming approach has been used to tackle an area traffic control optimisation problem subject to user equilibrium traffic flows. In the upper level problem, the signal timing plan for coordinated fixed time control has been defined. In the lower level problem, user equilibrium traffic assignment obeying Wardrop's first principle has been formulated as a variational inequality problem. Mathematical expressions for various components of the performance index in the upper level problem and the average delay in the lower level problem have been derived and reported (Chiou 1997a). A mixed search procedure has been proposed as the solution method to the bi-level problem and a range of numerical tests have been carried out (Chiou 1997b, 1998a,b). In this paper, further numerical tests are performed on Allsop and Charlesworth's (1977) road network in which various traffic loads are taken into account. Effectiveness in terms of the robustness and reliability of the mixed search procedure in congested and uncongested road networks is thus investigated further. Comparisons of the performance index resulting from the mixed search procedure and that of mutually consistent TRANSYT-optimal signal settings and traffic flows are made for the congested road network.

Citation

Chiou, S.-W. (1998), "Bi-level Formulation for Equilibrium Traffic Flow and Signal Settings", Griffiths, J.D. (Ed.) Mathematics in Transport Planning and Control, Emerald Group Publishing Limited, Leeds, pp. 59-68. https://doi.org/10.1108/9780585474182-006