Solution approaches to the bus operator problem

We study urban traffic equilibrium involving three classes of agents: car users, bus users or passengers and bus operators. A partially unregulated transit system is assumed, where bus fares are exogenously determined by municipal or transportation authorities, but bus operators are allowed to choose the routes where they offer service. The paper deals specifically with the bus operators submodel, for which several algorithms are proposed to find equilibrium solutions. Convergence properties of the proposed algorithms are analyzed and computational results, on both small test networks and the Santiago de Chile urban transit network, are reported. Various methods to deal with the problem posed by limited bus capacities are discussed.