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Equilibrium results for the M/G/k group-arrival loss system

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Abstract

In this paper we consider a specific M/G/k group-arrival loss system, under statistical equilibrium and two cases of acceptance policy. In the first case the system works under the partial acceptance policy. Explicit results are obtained for the corresponding stationary distribution, which extend previous relevant results. In the second case, where the system works under the all-or-nothing acceptance policy, a sufficient condition is given for the stationary distribution to have a closed-product form. In both cases customers depart individually, while the joint service time distribution of the accepted members of a group may depend both on its initial and the accepted size plus an additional condition.

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References

  • Chao X, Miyazawa M, Pinedo M (1999) Queueing networks: customers, signals and product form solutions. Wiley, Chichester

    Google Scholar 

  • Chen SP (2004) A mathematical programming approach to fuzzy queues with batch arrivals. Eng Optim 36:635–644

    Article  Google Scholar 

  • Economou A, Fakinos D (1999) Product form stationary distributions for the M/G/k group-arrival group-departure loss system under a general acceptance policy. Eur J Oper Res 112:196–206

    Article  Google Scholar 

  • Fakinos D (1982) The M/G/k group-arrival group-departure loss system. J Appl Probab 19:826–834

    Article  Google Scholar 

  • Fakinos D (1990) On the M/G/k group-arrival loss system. Eur J Oper Res 44:75–83

    Article  Google Scholar 

  • Fakinos D, Sirakoulis K (1989) Product-form distributions for an M/G/k group-arrival group-departure loss system. Adv Appl Probab 21:721–724

    Article  Google Scholar 

  • Kelly FP (1979) Reversibility and stochastic networks. Wiley, New York

    Google Scholar 

  • Papier F, Wolff RW, Thonemann UW (2007) On the convexity of loss probabilities when arrivals occur in batches and servers are heterogeneous. Oper Res Lett 35:467–471

    Article  Google Scholar 

  • Whittle P (1986) Partial balance, insensitivity and weak coupling. Adv Appl Probab 18:706–723

    Article  Google Scholar 

  • Wolff RW (1989) Stochastic modeling and the theory of queues. Prentice Hall, Englewood Cliffs

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Athens, Panepistimiopolis, Athens, 15784, Greece

    Spiros Dimou & Demetrios Fakinos

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  1. Spiros Dimou
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  2. Demetrios Fakinos
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Correspondence to Spiros Dimou.

Additional information

D. Fakinos’ research was supported partially by the University of Athens (ELKE) Grant 70/4/3401.

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Dimou, S., Fakinos, D. Equilibrium results for the M/G/k group-arrival loss system. TOP 21, 163–181 (2013). https://doi.org/10.1007/s11750-010-0168-2

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  • DOI: https://doi.org/10.1007/s11750-010-0168-2

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