EQUILIBRIUM SOLUTION IN NON-COOPERATIVE QUEUING GAMES ON OPEN NETWORK WITH UN-EQUAL ARRIVAL RATES

Abstract

This paper studies the equilibrium solution in a class of 2-player queueing games played on a network of a single server. While much research has been done on equilibrium solutions in such games, the case of unequal arrival rates for players has not been thoroughly addressed. The objective of both players is to minimize the mean expected time their clientsspend in the system. Each player can choose either a single path or distribute clients over multiple paths. We demonstrate that this game may or may not have a pure strategy Nash equilibrium (PNE) under discrete strategies, using the finite improvement path property. When players can split trac, existence and uniqueness of PNE is shown using Lagrange multipliers and the KarushKuhnTucker conditions. Pure and mixed strategy equilibria arediscussed, along with the price of anarchy. We also explore the congestion game formulation of this queueing setup.