English

Variable Demand and Multi-commodity Flow in Markovian Network Equilibrium

Optimization and Control 2021-10-19 v4

Abstract

Markovian network equilibrium generalizes the classical Wardrop equilibrium in network games. At a Markovian network equilibrium, each player of the game solves a Markov decision process instead of a shortest path problem. We propose two novel extensions of Markovian network equilibrium by considering 1) variable demand, which offers the players a quitting option, and 2) multi-commodity flow, which allows players to have heterogeneous ending time. We further develop dynamic-programming-based iterative algorithms for the proposed equilibrium problems, together with their arithmetic complexity analysis. Finally, we illustrate our network equilibrium model via a multi-commodity ride-sharing example, and compare the computational efficiency of our algorithms against state-of-the-art optimization software Mosek over extensive numerical experiments.

Keywords

Cite

@article{arxiv.1901.08731,
  title  = {Variable Demand and Multi-commodity Flow in Markovian Network Equilibrium},
  author = {Yue Yu and Dan Calderone and Sarah H. Q. Li and Lillian J. Ratliff and Behçet Açıkmeşe},
  journal= {arXiv preprint arXiv:1901.08731},
  year   = {2021}
}
R2 v1 2026-06-23T07:21:53.309Z