• Journal of Korean Society of Transportation
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• v.27 no.6
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• pp.147-156
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• 2009

We present a methodology for modeling and solving the transit frequency design problem with variable demand. The problem is described as a bi-level model based on a non-cooperative Stackelberg game. The upper-level operator problem is formulated as a non-linear optimization model to minimize net cost, which includes operating cost, travel cost and revenue, with 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 delay between transit lines. An efficient algorithm is also presented for solving the proposed model. The upper-level model is solved by a gradient projection method, and the lower-level model is solved by an existing iterative balancing method. An application of the proposed model and algorithm is presented using a small test network. The results of this application show that the proposed algorithm converges well to an optimal point. The methodology of this study is expected to contribute to form a theoretical basis for diagnosing the problems of current transit systems and for improving its operational efficiency to increase the demand as well as the level of service.