Abstract
The paper deals with a research of bivariate Markov process \(\{X(t), t\ge 0\}\) whose state space is a lattice semistrip \(S(X)=\{0,1,{\ldots },c\} \times Z_{+}\). The process \(\{X(t), t\ge 0\}\) describes the service policy of a multi-server retrial queue in which the rate of repeated flow does not depend on the number of sources of retrial calls. In this class of queues, a vector–matrix representation of steady-state distribution was obtained. This representation allows to write down the stationary probabilities through the model parameters in closed form and to propose the closed formulas of its main performance measures. The investigative techniques use an approximation of the initial model by means of the truncated one and the direct passage to the limit.
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References
Artalejo JR (1996) Stationary analysis of the characteristics of the M/M/2 queue with constant repeated attempts. Opsearch 33:83–95
Artalejo JR, Gomez-Corral A, Neuts MF (2001) Analysis of multiserver queues with constant retrial rate. Eur J Oper Res 135:569–581
Artalejo JR, Gomez-Corral A (2008) Retrial queueing systems: a computational approach. Springer, Berlin
Avrachenkov K, Yechiali U (2008) Retrial networks with finite buffers and their application to internet data traffic. Probab Eng Inf Sci 22:519–536
Choi BD, Shin YW, Ahn WC (1992) Retrial queues with collision arising from unsoltted CSMA/CD protocol. Queueing Syst 11:335–356
Choi BD, Park KK, Pearce CEM (1993) An M/M/1 retrial queue with control policy and general retrial times. Queueing Syst 14:275–292
Efrosinin D, Sztrik J (2011) Performance analysis of a two server heterogeneous retrial queue with threshold policy. Qual Technol Quant Manag 8:211–236
Falin G (1995) Heavy traffic analysis of a random walk on a lattice semi-strip. Stoch Model 11(3):395–409
Falin GI, Templeton JGC (1997) Retrial queues. Chapman & Hall, London
Fayolle G (1986) A simple telephone exchange with delayed feedbacks. Teletraffic Anal Comput Perform Eval 7:245–253
Gomez-Corral A, Ramalhoto MF (1999) The stationary distribution of a Markovian process arising in the theory of multiserver retrial queueing systems. Math Comput Model 30:141–158
Gomez-Corral A, Ramalhoto MF (2000) On the waiting time distribution and the busy period of a retrial queue with constant retrial rate. Stoch Model Appl 3(2):37–47
Roger AH, Charles RJ (1986) Matrix analysis. Cambridge University Press, Cambridge
Walrand J (1988) An introduction to queueing networks. Prentice Hall, Englewood Cliffs, NJ
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Lebedev, E., Ponomarov, V. Steady-state analysis of M/M/c/c-type retrial queueing systems with constant retrial rate. TOP 24, 693–704 (2016). https://doi.org/10.1007/s11750-016-0414-3
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DOI: https://doi.org/10.1007/s11750-016-0414-3