Mx/G/1 Queue with Multiple Vacations

Qingzhen Xu · Zhanyou Ma · Naishuo Tian

15 citations0/0 files storedStochastic Analysis and Applications

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Advanced Queuing Theory Analysis Probability and Statistical Research Age of Information Optimization

Abstract

In this article, we study a queueing system M x /G/1 with multiple vacations. The probability generating function (P.G.F.) of stationary queue length and its expectation expression are deduced by using an embedded Markov chain of the queueing process. The P.G.F. of stationary system busy period and the probability of system in service state and vacation state also are obtained by the same method. At last we deduce the LST and mean of stationary waiting time in the service order FCFS and LCFS, respectively.

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References

1999Optimal control for an MX/G/1 queue with two service modes 2004On the Mx/G/1 queue with feedback and optional server vacations based on a single vacation policy 1993The Mx/G/1 queue with single and multiple vacations under the LIFO service regime 1991Priority queues with batch Poisson arrivals 1995Optimal control of the MX/G/1/K queue with multiple server vacations

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2012On an M[X]/G/1 queuing system with random breakdowns, server vacations, delay times and a standby server 2019Distribution of the time to buffer overflow in the M/G/1/N-type queueing model with batch arrivals and multiple vacation policy

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