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Algorithm for computing the queue length distribution at various time epochs in DMAP/G(1, a, b)/1/N queue with batch-size-dependent service time

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  • Yu, Miaomiao
  • Alfa, Attahiru Sule

Abstract

This paper presents a discrete-time single-server finite-buffer queue with Markovian arrival process and generally distributed batch-size-dependent service time. Given that infinite service time is not commonly encountered in practical situations, we suppose that the distribution of the service time has a finite support. Recently, a similar continuous-time system with Poisson input process was discussed by Banerjee and Gupta (2012). But unfortunately, their method is hard to apply in the analysis of discrete-time case with versatile Markovian point process due to the fact that the difference equation governing the boundary state probabilities is more complex than the continuous one. If we follow their ideas, we will eventually find that some important joint queue length distributions cannot be computed and thus some key performance measures cannot be derived. In this paper, replacing the finite support renewal distribution with an appropriate phase-type distribution, the joint state probabilities at various time epochs (arbitrary, pre-arrival and departure) have been obtained by using matrix analytic method and embedded Markov chain technique. Furthermore, UL-type RG-factorization is employed in numerical computation of block-structured Markov chains with finitely-many levels. Some numerical examples are presented to demonstrate the feasibility of the proposed algorithm for several service time distributions. Moreover, the impact of the correlation factor on loss probability and mean sojourn time is also investigated.

Suggested Citation

  • Yu, Miaomiao & Alfa, Attahiru Sule, 2015. "Algorithm for computing the queue length distribution at various time epochs in DMAP/G(1, a, b)/1/N queue with batch-size-dependent service time," European Journal of Operational Research, Elsevier, vol. 244(1), pages 227-239.
    • Handle: RePEc:eee:ejores:v:244:y:2015:i:1:p:227-239
    DOI: 10.1016/j.ejor.2015.01.056
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    References listed on IDEAS

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    1. Claeys, Dieter & Walraevens, Joris & Laevens, Koenraad & Bruneel, Herwig, 2010. "A queueing model for general group screening policies and dynamic item arrivals," European Journal of Operational Research, Elsevier, vol. 207(2), pages 827-835, December.
    2. Bar-Lev, Shaul K. & Parlar, Mahmut & Perry, David & Stadje, Wolfgang & Van der Duyn Schouten, Frank A., 2007. "Applications of bulk queues to group testing models with incomplete identification," European Journal of Operational Research, Elsevier, vol. 183(1), pages 226-237, November.
    3. Bar-Lev, S.K. & Parlar, M. & Perry, D. & Stadje, W. & van der Duyn Schouten, F.A., 2007. "Applications of bulk queues to group testing models with incomplete identification," Other publications TiSEM 0b1bfa5e-c1e6-43ec-9684-1, Tilburg University, School of Economics and Management.
    4. Samanta, S.K. & Gupta, U.C. & Sharma, R.K., 2007. "Analyzing discrete-time D-BMAP/G/1/N queue with single and multiple vacations," European Journal of Operational Research, Elsevier, vol. 182(1), pages 321-339, October.
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    Cited by:

    1. S. Pradhan & U. C. Gupta, 2019. "Analysis of an infinite-buffer batch-size-dependent service queue with Markovian arrival process," Annals of Operations Research, Springer, vol. 277(2), pages 161-196, June.
    2. A. D. Banik & M. L. Chaudhry, 2017. "Efficient Computational Analysis of Stationary Probabilities for the Queueing System BMAP / G /1/ N With or Without Vacation(s)," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 140-151, February.
    3. Srinivas R. Chakravarthy & Shruti & Alexander Rumyantsev, 2021. "Analysis of a Queueing Model with Batch Markovian Arrival Process and General Distribution for Group Clearance," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1551-1579, December.

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