Self-interested routing in queueing networks

We study self-interested routing in stochastic networks, taking into account the discrete stochastic dynamics of such networks. We analyze a two-station multiclass queueing network in which the system manager chooses the scheduling rule and individual customers choose routes in a self-interested manner. We show that this network can be unstable in Nash equilibrium under some scheduling rules. We also design a nontrivial scheduling rule that negates the performance degradation resulting from self-interested routing and achieves a Nash equilibrium with performance comparable to the first-best solution.