Capacitated transit service network design with boundedly rational agents. (November 2016) - Liu, Jiangtao; Zhou, Xuesong
Highlights: Provide an alternative framework to model boundedly rational decision rules of travelers with tight capacity constraints. Develop a set of integer linear inequalities on a space-time network that consists of transit service arcs and waiting arcs. Single-level integer linear programming model can avoid the use of possible nonlinear and non-convex functions. Proposed model can be decomposed and solved efficiently on the large scale networks through Lagrangian relaxation. Abstract: This paper proposes a new alternative modeling framework to systemically account for boundedly rational decision rules of travelers in a dynamic transit service network with tight capacity constraints. Within a time-discretized space-time network, the time-dependent transit services are characterized by traveling arcs and waiting arcs with constant travel times. Instead of using traditional flow-based formulations, an agent-based integer linear formulation is proposed to represent boundedly rational decisions under strictly imposed capacity constraints, due to vehicle carrying capacity and station storage capacity. Focusing on a viable and limited sets of space-time path alternatives, the proposed single-level optimization model can be effectively decomposed to a time-dependent routing sub-problem for individual agents and a knapsack sub-problem for service arc selections through the Lagrangian decomposition. In addition, several practically important modeling issues are discussed, such as dynamic and personalized transit pricing, passenger inflow control as part of network restraint strategies, and penalty for early/late arrival. Finally, numerical experiments are performed to demonstrate the methodology and computational efficiency of our proposed model and algorithm.