Frequency design in urban transit networks with variable demand: Model and algorithm

Abstract

The goal of this study is to present a methodology for modeling the transit frequency design problem with variable demand. A bilevel optimization model based on a non-cooperative Stackelberg game is used to describe the problem. The upper-level operator problem is formulated as a non-linear optimization model to maximize demand while considering fleet size and frequency constraints. The lower-level user problem is formulated as a capacity-constrained stochastic user equilibrium assignment model with variable demand, considering transfer delays between transit lines. An efficient algorithm is also developed for solving the proposed model. The upper-level model is solved by a gradient projection method. The gradient of the objective function is calculated at each iteration considering the fixed equilibrium overload delays determined by the lower-level model. The lower-level model is solved by an extant iterative balancing method, which was slightly modified for this study. An application of the proposed model and algorithm is presented using a small test network. The results of this application show that the developed algorithm converges well to an optimal point.