Abstract
We study in this paper an M/G/1 quorum queueing system under T-policy. First, we consider the system size stochastic process embedded at departure epoch times and show that it is an ergodic Markov chain. Then, we consider the system size stochastic process at arbitrary instants of time and show that it is an ergodic semi-regenerative process. We derive the steady-state distribution for both processes. Various system characteristics of related processes (idle and busy periods) are also obtained and special cases are discussed.
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References
Bailey NTJ (1954). On queueing processes with bulk service. J R Stat Soc Ser B 16: 80–87.
Chaudhry ML and Templeton JGC (1983). A First Course in Bulk Queues. Wiley: New York.
Dshalalow JH and Tadj L (1992). A queueing system with a fixed accumulation level, random server capacity, and capacity dependent service time. Int J Math Math Sci 15: 189–194.
Abolnikov L and Dshalalow JH (1991). A first passage problem and its applications to the analysis of a class of stochastic models. J Appl Math Stoch Anal 5: 83–98.
Dshalalow JH (ed) (1997). Queueing systems with state dependent parameters. In: Frontiers in Queueing: Models and Applications in Science and Engineering 1997. CRC Press: Boca Raton, FL, pp 61–116.
Bloemena AR (1960). On queueing processes with a certain type of bulk service. Bull Inst Int Stat 37: 219–226.
Fabens AJ (1961). The solution of queueing and inventory models by semi-Markov processes. J R Stat Soc Ser B 23: 113–117.
Heyman DP (1968). The T-policy for the M/G/1 queue. Mngt Sci 23: 775–778.
Tanenbaum AS and Van Renesse R (1985). Distributed operating systems. Comput Surv 17: 419–470.
Abolnikov L and Dukhovny A (1991). Markov chains with transition delta matrix: ergodicity conditions, invariant probability measures and applications. J Appl Math Stoch Anal 4: 333–356.
Bruneel H (1983). Buffers with stochastic output interruptions. Electron Lett 19: 735–737.
Fuhrmann SW and Cooper RB (1985). Stochastic decomposition in the M/G/1 queue with generalized vacations. Opns Res 36: 566–569.
Acknowledgements
I thank an anonymous referee for bringing to my attention reference 11, for correcting numerous mistakes, and for making many suggestions that greatly enhanced the readability and quality of the paper.
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Tadj, L. On an M/G/1 quorum queueing system under T-policy. J Oper Res Soc 54, 466–471 (2003). https://doi.org/10.1057/palgrave.jors.2601536
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DOI: https://doi.org/10.1057/palgrave.jors.2601536