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M\(^X\)/G/1 queue with multiple vacations. (English) Zbl 1112.60073

The authors consider a batch arrival \(\text{M}^X/\text{G}/1\) queueing system with exhaustive service and multiple vacations and obtain the probability generating function of stationary queue length and Laplace Stieltjes transform of stationary waiting time by employing an imbedded Markov chain method. This approach is adaptible to stochastic decomposition theory and can be useful in computer network flow.

MSC:

60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
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References:

[1] DOI: 10.1016/0167-6377(91)90063-U · Zbl 0747.60090 · doi:10.1016/0167-6377(91)90063-U
[2] DOI: 10.1016/0377-2217(92)90161-2 · Zbl 0762.60087 · doi:10.1016/0377-2217(92)90161-2
[3] DOI: 10.1016/0167-6377(93)90029-G · Zbl 0792.60094 · doi:10.1016/0167-6377(93)90029-G
[4] DOI: 10.1016/0167-6377(94)90085-X · Zbl 0820.68021 · doi:10.1016/0167-6377(94)90085-X
[5] DOI: 10.1016/0305-0548(94)00038-A · Zbl 0838.90047 · doi:10.1016/0305-0548(94)00038-A
[6] DOI: 10.1016/S0362-546X(97)00017-5 · Zbl 0914.90116 · doi:10.1016/S0362-546X(97)00017-5
[7] DOI: 10.1016/S0377-2217(98)00085-X · Zbl 0947.90028 · doi:10.1016/S0377-2217(98)00085-X
[8] Madan K.C., Applied Mathematics and Computation 160 pp 909– (2005)
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