M^x/G/1 Queue with Multiple Vacations

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.

Keywords:

• Busy period analysis
• Multiple vacations
• Queueing system
• Stationary queue length
• Stationary waiting time

Mathematics Subject Classification:

• 60K25

Acknowledgments

This project was supported by the National Natural Science Foundation of China.