Queueing system with batch arrivals, batch service and disasters
Problemy fiziki, matematiki i tehniki, no. 3 (2011), pp. 78-80.

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We consider a single-server queueing system with batch arrivals and batch service. Besides, the flow of the disaster enters the queueing system. The disaster completely clears the queue of the system if it is not empty, and renders no influence if the queue of the system is empty. Stationary distribution of the states of the process describing the queueing system behavior is found.
Keywords: queueing system, batch arrivals, batch service, disaster.
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A. N. Starovoitov. Queueing system with batch arrivals, batch service and disasters. Problemy fiziki, matematiki i tehniki, no. 3 (2011), pp. 78-80. http://geodesic.mathdoc.fr/item/PFMT_2011_3_a12/

[1] G. Jain, K. Sigman, “A Pollaczeek–Khinchine formula for $\mathrm{M/G/1}$ queues with disasters”, J. Appl. Prob., 1996, no. 33, 1191–1200 | DOI | MR | Zbl

[2] A. Chen, E. Renshaw, “The $\mathrm{M/M/1}$ queue with mass exodus and mass arrivals when empty”, J. Appl. Prob., 1997, no. 34, 192–207 | DOI | MR | Zbl

[3] O. V. Semenova, “A queueing system with two operation modes and a disaster flow: its stationary state probability distribution”, Automation and Remote Control, 63:10 (2002), 1597–1608 | DOI | MR | Zbl

[4] A. Dudin, S. Nishimura, “A $\mathrm{BMAP/SM/1}$ queueing system with markovian arrival input of disasters”, J. Appl. Prob., 36 (1999), 868–881 | DOI | MR | Zbl

[5] A. Dudin, O. Semenova, “A stable algorithm for stationary distribution calculation for a $\mathrm{BMAP/SM/1}$ queueing system with markovian arrival input of disasters”, J. Appl. Prob., 41 (2004), 547–556 | DOI | MR | Zbl

[6] M. Miyazawa, P. G. Taylor, “Geometric product-form distribution for a queueing network with non-standard batch arrivals and batch transfers”, Adv. Appl. Prob., 29:2 (1997), 1–22 | DOI | MR

[7] Yu. S. Boyarovich, “Statsionarnoe raspredelenie zamknutoi seti massovogo obsluzhivaniya s gruppovymi perekhodami zayavok”, Avtomatika i telemekhanika, 2009, no. 11, 80–86 | MR | Zbl

[8] Yu. V. Malinkovskii, E. V. Korobeinikova, “Kharakterizatsiya statsionarnogo raspredeleniya setei s gruppovymi peremescheniyami v forme proizvedeniya smeschennykh geometricheskikh raspredelenii”, Avtomatika i telemekhanika, 2010, no. 12, 43–56 | MR | Zbl

[9] V. A. Ivnitskii, Teoriya setei massovogo obsluzhivaniya, Fizmatlit, M., 2004, 772 pp.

[10] F. P. Kelly, Reversibility and stochastic networks, Wiley, N.Y., 1979, 230 pp. | MR