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Bulk Arrival Queue System With Balking,Reneging And Multiple Working Vacations

Posted on:2013-08-29Degree:MasterType:Thesis
Country:ChinaCandidate:Y M GuoFull Text:PDF
GTID:2230330371470847Subject:Applied Mathematics
Abstract/Summary:PDF Full Text Request
In this paper, a queuing system is considered with reneging, balking, batch arrival and multiple working vacations under the conditions of the limited site. The customers arrive in batch, and the number of each batch is a random quantity. The interval of time between the two batch customers obeys index distribution, and the service time of servers obeys index distribution. The single-server queuing model and the multi-server queuing model are considered respectively and established the corresponding working vacation queuing system. By using relevant knowledge, the steady-state probability equations are obtained. Finally, the relevant conclusions are derived by using the matrix method and iterative method.Firstly, this thesis studies a MX/M/l/Nqueuing system with balking, reneging and multiple working vacations. The two-dimensional Markov chain is established by studying the number of customers at some point. Through the Markov process method, the steady-state probability equations and transition rate matrix are obtained at one time. The matrix form equation of the steady-state probability is derived by using the block matrix solution method. Some performance measures of the system such as the expected number of customers in the system or in the queue, the average rate of the customer balking and reneging are also presented.Second, the MX/M/m//N queuing system is considered with balking, reneging, and synchronous multiple working vacations, and one point is assumed that the system can choose customers into the servicer. The steady-state probability equations of the system are derived by using the similar approach in the third chapter. By rewriting the transition rate matrix as a block one, the steady-state probability solution in matrix form is obtained by using the matrix solution method. At the same time, some performance measures of the system are worked out.Finally, at the end of the article, the problems which should been solved in the future have been briefly introduced. Meanwhile, the future direction of the research is pointed out.
Keywords/Search Tags:Batch arrival, Performance measures, Multiple working vacations
PDF Full Text Request
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