MAP/G/1 QUEUES UNDER N-POLICY WITH AND WITHOUT VACATIONS

Shoji Kasahara · Tetsuya Takine · Yutaka Takahashi · Toshiharu Hasegawa

39 citations0/0 files storedJournal of the Operations Research Society of Japan

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Advanced Queuing Theory Analysis Probability and Risk Models Age of Information Optimization

Abstract

This paper considers MAP/G/1 queueing systems under the following two situations: (1) At the end of a busy period, the server is turned off and inspects the queue length every time a customer arrives. When the queue length reaches a pre-specified value N, the server turns on and serves customers continuously until the system becomes empty. (2) At the end of a busy period, the server takes a sequence of vacations. At the end of each vacation, the server inspects the queue length. If the queue length is greater than or equal to a pre-specified value N at this time, the server begins to serve customers continuously until the system becomes empty. For each case, we analyze the stationary queue length and the actual waiting time distributions, and derive the recursive formulas to compute the moments of these distributions. Furthermore, we provide a numerical algorithm to obtain the mass function of the stationary queue length. The numerical examples show that in light traffic, correlation in arrivals leads to a smaller mean waiting time.

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References

1986Queueing systems with vacations ? A survey 1985Stochastic Decompositions in the M/G/1 Queue with Generalized Vacations 1990A single-server queue with server vacations and a class of non-renewal arrival processes 1988A stable recursion for the steady state vector in markov chains of m/g/1 type 1993Marked point processes as limits of Markovian arrival streams 1989Control Policies for the MX/G/1 Queueing System 1989The threshold policy in theM/G/1 queue with server vacations 1991Vacation and priority systems

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2005Factorization and Stochastic Decomposition Properties in Bulk Queues with Generalized Vacations 1998On the relationship between queue lengths at a random instant and at a departure in the stationary queue with bmap arrivals 2005Computing queue length distributions in MAP/G/1/N queue under single and multiple vacation 2008The infinite-buffer single server queue with a variant of multiple vacation policy and batch Markovian arrival process 2009On the BMAP/G/1 G-queues with second optional service and multiple vacations

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