An Incentive Mechanism for M/M/1 Queues with Selfish Users

In this paper, we study an incentive mechanism design problem for network congestion control. We investigate the behavior of a single store-and-forward router (a.k.a. "server" in this work). The scenario is modeled as an M/M/1 queueing game with each packet generator (a.k.a. "player") optimizing the throughput-delay tradeoff in a selfish distributed manner. We first show that the original game has an inefficient unique Nash Equilibrium (NE). In order to improve the outcome efficiency, we propose a packet dropping scheme that can be easily implemented at the server. We then show that if the packet dropping scheme is a function of the sum of arrival rates, this new M/M/1 queueing game is a potential game with unique NE. We further propose a linear packet dropping scheme, which is similar to the Random Early Detection (RED) algorithm used with TCP. Our investigation shows that with this RED-like mechanism, the social welfare (summation of utilities of all players) at the equilibrium point can be arbitrarily close to the social welfare at the global optimal point.