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A single-server batch arrival queue with returning customers

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  • Falin, G.I.

Abstract

We consider a new class of batch arrival retrial queues. By contrast to standard batch arrival retrial queues we assume if a batch of primary customers arrives into the system and the server is free then one of the customers starts to be served and the others join the queue and then are served according to some discipline. With the help of Lyapunov functions we have obtained a necessary and sufficient condition for ergodicity of embedded Markov chain and the joint distribution of the number of customers in the queue and the number of customers in the orbit in steady state. We also have suggested an approximate method of analysis based on the corresponding model with losses.

Suggested Citation

  • Falin, G.I., 2010. "A single-server batch arrival queue with returning customers," European Journal of Operational Research, Elsevier, vol. 201(3), pages 786-790, March.
    • Handle: RePEc:eee:ejores:v:201:y:2010:i:3:p:786-790
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    References listed on IDEAS

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    1. Dudin, A. N. & Krishnamoorthy, A. & Joshua, V. C. & Tsarenkov, G. V., 2004. "Analysis of the BMAP/G/1 retrial system with search of customers from the orbit," European Journal of Operational Research, Elsevier, vol. 157(1), pages 169-179, August.
    2. Kim, Chesoong & Klimenok, Valentina I. & Orlovsky, Dmitry S., 2008. "The BMAP/PH/N retrial queue with Markovian flow of breakdowns," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1057-1072, September.
    3. Quan-Lin Li & Yu Ying & Yiqiang Zhao, 2006. "A BMAP/G/1 Retrial Queue with a Server Subject to Breakdowns and Repairs," Annals of Operations Research, Springer, vol. 141(1), pages 233-270, January.
    4. A. G. Pakes, 1969. "Some Conditions for Ergodicity and Recurrence of Markov Chains," Operations Research, INFORMS, vol. 17(6), pages 1058-1061, December.
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    Cited by:

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    2. Joanna Rodríguez & Rosa E. Lillo & Pepa Ramírez-Cobo, 2016. "Nonidentifiability of the Two-State BMAP," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 81-106, March.

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