And Analysis For The Retrial And Vacation Queues

:In the research work of traditional queueing theory, the vast majority are using stochastic process or dynamic programming technology to analyse the system’s performence. In recent years, the economists and researchers of queueing theory begin to study queueing systems from an economic viewpoint based on game and queueing theory. In their models, according to a reward-cost structure, customers are allowed to make their decisions independently in order to maximize their welfare. The resulting description can be thought of as an equilibrium among the customers. however, the self optimization does not ordinarily lead to social optimization, so our basic problem is to find equilibrium strategies, socially optimal strategies and the optimal control of the system to achieve the social optimality.The rapid development economy and modern management provide important application background for the retrial and vacation queuing systems. Retrial queueing systems have applications in many areas such as Tele-traffic Theory, Computer and Communication Networks. And multiple vacation policies are simulating the actual operation principles of management organization and communication network, to reduce resource wastage and system cost, improve work efficiency and provide flexible choice for system optimization. However, there are few literature discuss this problem from an economic viewpoint. So the economics-based analysis of the retrial and vacation queues can not only enrich the existing theories, but also have important practical significance.In many service systems arising in OR/MS applications, the server needs a setup time when it is turned on and the service time may be non-Markovian as usually assumed. In the present paper, we first study the balking behavior of customers in a single-server queue with two-phase Erlangian service time and exponential setup time. Then, we consider the classical retrial queueing system with non-Markovian service time to simulate actual economics cases. Specially, we consider a single-server retrial queue with two-phase Erlangian service time. Finally, this paper is considered with the strategic behavior and social optimization with respect to N-policy of the M/M/1queue with constant retrial rate. And our model is special in that both types of behaviors may exist in our system:it may be FTC when the sever’s state is dormant and ATC when the server’s state is normal working. And consequently, both multiple and unique equilibrium arrival rates could exist. We also show that self optimization does not ordinarily lead to social optimization, so we give some suggestions for optimal control of the system to achieve the social optimality. And some numerical examples are also presented.