Stochastic routing mechanism on multiclass switching network using game theory

Game theory conceptions apply in many areas especially in commu-nication network, which provides a scaold to design the model and an-alyze conict among decision making process. Over the last few decadesstream control mechanism has more attention in the early stages of re-search in communication network. The motivation of this work is deepunderstanding on the stream control mechanism problem in multi-classnetworks. In this paper, game theoretic perspectives are presented andthe appropriate frame work for the study of stream control mechanismproblem is analyzed. Consider a min-max routing problem, where thecontrol mechanism has to decide to which of N queues that the arrivingcustomer should be sent. The service rate in each queue is dependenton the state of the system, may change in time and is unknown to thecontrol mechanism. The goal of the control mechanism is to design anecient policy which guarantees the best performance under the worstcase service conditions. ie., Arriving customers are routed by a controlmechanism, with the purpose of minimizing the total discounted holdingcost under worst-case service conditions. Then the problem is viewedas a zero-sum (Stochastic) Markov game between the routing controlmechanism and a service control mechanism. In zero-sum (Stochastic)Markov game, where the server acts as player 1 and the stream controlmechanism acts as a player 2. Each player assumed to have the infor-mation of all the previous action of players as well as the current andthe past states of the system. The main results obtained are to identifythe optimal strategy for both players. A value iteration technique isused to establish properties of the value of the game, which are relatedto super modularity and convexity.