Enactment of Stochastic Model Stream Mechanism on Multi class Queueing Network

Abstract

Over the last few decades stream control mechanism has more attention in the early stages of research in communication network. The motivation of this work is deep understanding on the stream control mechanism problem in multi-class networks. In this paper, game theoretic perspectives are presented and the appropriate frame work for the study of stream control mechanism problem is analysed. Consider a min-max routing problem, where the control mechanism has to decide to which of N queues that the arriving customer should be sent. The service rate in each queue is dependent on the state of the system, may change in time and is unknown to the control mechanism. The goal of the control mechanism is to design an efficient policy which guarantees the best performance under the worst case service conditions. ie., Arriving customers are routed by a control mechanism, with the purpose of minimizing the total discounted holding cost under worst-case service conditions. Then the problem is viewed as a zero-sum (Stochastic)Markov game between the routing control mechanism and a service control mechanism. In zero-sum (Stochastic)Markov game, where the server acts as player 1 and the stream control mechanism acts as a player 2. Each player is assumed to have the information of all the previous actions of both players as well as the current and the past states of the system. The main results obtained are to identify the optimal strategy for both players. A value iteration technique is used to establish properties of the value of the game, which are related to super modularity and convexity.