Game theoretical control of service rates in closed jackson networks

The servers´ competition for resources is a common phenomena in queueing systems. In this paper, we discuss the service rate control problem of queueing networks from a game theoretical perspective. The payoff function of each server is composed of two parts, the holding cost and the operating cost. Each server independently chooses their service rates in order to maximize their own average payoff. We formulate this problem as a game and prove that the average payoff of each server has a monotonic property. We further develop an iterative algorithm to find the Nash equilibrium of this game. Simulation experiments are conducted to demonstrate the main idea of the paper.