Small work-load mode in a queueing system with random nonstationary intensity
Matematičeskie zametki, Tome 80 (2006) no. 3, pp. 339-349.

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We consider a queueing system of $M_tR|GI|1|\infty$ type with doubly stochastic Poisson arrival stream. The case of a small work load in such a system is studied. We derive an asymptotic expansion in the work-load smallness parameter of the distribution function of the virtual waiting time.
Keywords: single-server queueing system, doubly stochastic Poisson arrival stream, virtual waiting time, periodic random process.
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E. E. Bashtova. Small work-load mode in a queueing system with random nonstationary intensity. Matematičeskie zametki, Tome 80 (2006) no. 3, pp. 339-349. http://geodesic.mathdoc.fr/item/MZM_2006_80_3_a2/

[1] T. Rolski, “Queues with nonstationary inputs”, Queueing Systems Theory Appl., 5:1–3 (1989), 113–129 | DOI | MR | Zbl

[2] T. Rolski, “Upper bounds for single server queues with doubly stochastic Poisson arrivals”, Math. Oper. Res., 11:3 (1986), 442–450 | DOI | MR | Zbl

[3] N. Bäuerle, T. Rolski, “A monotonicity result for the workload in Markov-modulated queues”, J. Appl. Probab., 35 (1998), 741–747 | DOI | MR | Zbl

[4] R. Szekli, R. L. Disney, S. Hur, “$MR/GI/1$ queues with positive correlated arrival stream”, J. Appl. Probab., 31 (1994), 497–514 | DOI | MR | Zbl

[5] C. Chang, X. Chao, M. Pinedo, “Monotonicity result for queues with doubly stochastic Poisson arrivals: Ross's conjecture”, Adv. in Appl. Probab., 23 (1991), 210–228 | DOI | MR | Zbl

[6] A. A. Borovkov, Veroyatnostnye protsessy v teorii massovogo obsluzhivaniya, Nauka, M., 1972 | MR | Zbl

[7] L. G. Afanaseva, “Stokhasticheskaya ogranichennost tsiklicheskikh sistem obsluzhivaniya”, Problemy ustarevshikh stokhasticheskikh modelei, Trudy seminara VNIISI, 1989

[8] L. G. Afanas'eva, E. E. Bashtova, “The queue with periodic double stochastic Poisson input”, Transactions of the XXIV Intern. Sem. on Stab. Probl. for Stoch. Models, Jurmala, 2004