Optimal sectional fare and frequency settings for transit networks with elastic demand

Abstract

Sectional fares have beenused in transit services in practice but are rarely examined analytically andcompared with flat and distance-based fares, especially under theconsiderations of path choice, elastic demand, service frequency, andprofitability. This paper proposes a bilevel programming model to jointlydetermine the fare and frequency setting to maximize transit operator's profit.The preceding three fare structures can be incorporated into the bilevel model.To consider the path choice and elastic demand in the bilevel model, theexisting approach-based stochastic user equilibrium transit assignment modelfor the fixed demand was extended to the elastic demand case and the resultantmodel was used in the lower level model. To solve the bilevel model, thesensitivity-based descent search method that takes into account theapproach-based formulation for the elastic demand transit assignment isproposed, in which the approach-based formulation was solved by thecost-averaging self-regulated averaging method. Numerical studies andmathematical analyses were performed to examine the model properties andcompare the three fare structures. The result of the Tin Shui Wai networkinstance is also provided to illustrate the performance of the solution method.