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M~x/M/1/Nqueue with Balking,Reneging and Single Working Vacations
Pages: 125-133
Year: Issue:  7
Journal: Mathematics in Practice and Theory

Keyword:  queuesteady-state probabilityperformance measuresmatrix solution methodsingle working vacationsbalkrenege;
Abstract: In this paper,we consider an queue with balking,reneging and single working vacations.Customers arrive in batch and every arriving customer either decides to enter the queue with a probability b or balk(do not enter) with a probability 1 — 6 The impatient customer in the queue may leave the system(renege) if it has not been served after a period of waiting time.The server takes single working vacations immediately when it becomes idle at a service completion instant.First,we obtain the steady-state probability equations by the Markov process method.Second,by the matrix solution method we derive the matrix form solution of the steady-state probability.Some performance measures of the system such as the expected number of the customers in the system or in the queue and the average loss probability of customers are also presented.Finally the effects of the parameters of the system are investigated,such as the lower service rate and the vacation rate on the expected queue length of the system by numerical examples.
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