Sensitivity analysis of stochastic user equilibrium flows in a bi-modal network with application to optimal pricing

Sensitivity analysis methods for transport systems having an automobile road network and a physically separate transit network are studied. For the case that both the automobile and transit networks are congested in the sense that link cost functions increase with the flow, a general computational method is presented for sensitivity analysis. For another case where the automobile network is congested but the transit network simply consists of independent lines connecting Origin-Destination pairs and may have economies of scale with the increase of the passengers, conditions under which sensitivity analysis can be properly conducted are investigated. The sensitivity analysis algorithm is applied to the optimal pricing problem in a combined network with transit lines exhibiting economies of scale as well as congestion diseconomies.