The Study Of Solutions Of The Queueing Game Model

There are the cooperation and competition in the queueing system. If Game Theory is a very good solution, every payoff in the queueing system will be Pareto-payoff. Queueing game model began to be studied in the last decade, by now, Queueing game has been a challenging work. And queueing game has been applied to various fields, For example, in service costs, computer communication networks, medical and other high-tech fields.Firstly this paper studied M/M/1 queueing stochastic cooperative game model, and showed the Properties of solutions, unique existence theorem and proof. Then, we considered the Mξ/M/1 queuing system that is more complex and more meaningful than the M/M/1 queuing system. And we built the Mξ/M/1 queuing game. This is a new game model by now.The first chapter briefly described the concept of game theory, the background of the paper, and showed the main work. This chapter also gave a brief review for the history of game theory and methods, and prepared for the model on the theory and symbols.The second chapter studied the basic knowledge of the non-cooperative games, cooperative games and stochastic cooperative games, two the important theorems'proof are given, prepared for the solution of the queue model .The third chapter built M/M/1 queuing stochastic cooperative game model, showed the axiomatic description of the Shapley value and unique existence theorem.Final chapter created Mξ/M/1 queuing game, proved the existence of Nash equilibrium; gave every player's the marginal contribution and the Shapley value.