Geodesic
Stability conditions for retrial queueing systems with regenerative input flow
Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2018) no. 3, pp. 5-18.

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We consider two classes of multiserver retrial queueing systems. For the first class, the rate of retrial requests depends on the number of customers on the orbit, and for the second class, the rate is constant. The input flow is supposed to be a regenerative one and service time has an arbitrary distribution. Based on the synchronization of the input flow and an auxiliary service process, we establish necessary and sufficient stability conditions for models of both classes. 
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L. G. Afanaseva. Stability conditions for retrial queueing systems with regenerative input flow. Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2018) no. 3, pp. 5-18. http://geodesic.mathdoc.fr/item/FPM_2018_22_3_a0/

[1] Afanaseva L. G., Tkachenko A., “Mnogokanalnye sistemy obsluzhivaniya s regeneriruyuschim vkhodyaschim potokom”, Teoriya veroyatn. i ee primen., 58:2 (2013), 210–234 | DOI

[2] Sevastyanov B. A., “Ergodicheskaya teorema dlya markovskikh protsessov i ee prilozhenie k telefonnym sistemam s otkazami”, Teoriya veroyatn. i ee primen., 2:1 (1957), 106–116 | MR | Zbl

[3] Afanaseva L. G., Bashtova E. E., “Coupling method for asymptotic analysis of queue with regenerative input and unreliable server”, Queueing Systems, 76:2 (2014), 125–147 | DOI | MR

[4] Artalejo S. R., “Stationary analysis of the characteristics of the $M|M|2$ queue with constant repeated attempts”, Opsearch., 33 (1996), 83–95 | MR | Zbl

[5] Artalejo S. R., Gómez-Corral A., Neuts M. F., “Analysis of multiserver queues with constant retrial rate”, Europ. J. Operat. Res., 135 (2001), 569–581 | DOI | MR | Zbl

[6] Choi B. D., Rhee K. H., Park K. K., “The $M| G| 1$ retrial queue with retrial rate control policy”, Probab. Eng. Inform. Sci., 7 (1993), 29–46 | DOI

[7] Choi B. D., Rhee K. H., Park K. K., Pearce C. E. M., “An $M| M| 1$ retrial queue with control policy and general retrial times”, Queueing Systems, 14 (1993), 175–292 | DOI | MR

[8] Choi B. D., Shin J. W., Ahn W. C., “Retrial queues with collision arising from unslotted CSMA|CD protocol”, Queueing Systems, 11 (1992), 335–356 | DOI | MR | Zbl

[9] Cohen S. W., “Basic problems of telephone traffic theory and influence of repeated calls”, Philips Telecommunic. Rev., 18 (1957), 49–100

[10] Falin G. I., Artalejo J. R., “Approximation for multiserver queues with bulking/retrial discipline”, OR Spectrum, 17 (1995), 239–244 | DOI | MR | Zbl

[11] Falin G. I., Templeton S. G. C., Retrial Queues, Chapman Hall, London, 1997 | Zbl

[12] Fayolle G., “A simple telephone exchange with delayed feedback”, Teletraffic Analysis in Computer Performance Evaluation, eds. O. S. Boxma, S. W. Cohen, H. C. Tijms, Elsevier, Amsterdam, 1986

[13] Feller W., An Introduction to Probability Theory and Its Applications, v. II, Wiley, 1950 | MR | Zbl

[14] Gómez-Corral A., Ramalhoto M. F., “On the stationary distribution of Markovian process arising in the theory of multiserver retrial queueing systems”, Math. Comput. Modelling, 30 (1999), 141–158 | DOI | MR | Zbl

[15] Grandell J., Doubly Stochastic Poisson Process, Springer, Berlin, 1976 | MR

[16] Neuts M. F., Structured Stochastic Matrices of $M|G|1$ Type and Their Applications, Marcel Dekker, New York, 1989 | MR | Zbl

[17] Thorisson H., Coupling, Stationarity and Regeneration, Springer, New York, 2000 | MR | Zbl

[18] Wilkinson R. I., “Theories for toll traffic engineering in the USA”, Bell System Tech. J., 35 (1950), 421–514 | DOI | MR

[19] Zeifman A., Satin Y., Morozov E., Nekrasova R., Gorshenin A., “On the ergodicity bounds for a constant retrial rate queueing model”, 8th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT), 2016, 269–272