Steady-state analysis of M/M/c/c-type retrial queueing systems with constant retrial rate

Eugene Lebedev () and Vadym Ponomarov ()
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Eugene Lebedev: Taras Shevchenko National University of Kyiv
Vadym Ponomarov: Taras Shevchenko National University of Kyiv

TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 2016, vol. 24, issue 3, No 8, 693-704

Abstract: Abstract The paper deals with a research of bivariate Markov process $$\{X(t), t\ge 0\}$$ { X ( t ) , t ≥ 0 } whose state space is a lattice semistrip $$S(X)=\{0,1,{\ldots },c\} \times Z_{+}$$ S ( X ) = { 0 , 1 , … , c } × Z + . The process $$\{X(t), t\ge 0\}$$ { X ( t ) , t ≥ 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.

Keywords: Queue; Repeated calls; Constant retrial rate; Stationary regime; 60K20; 60K25; 90B22 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s11750-016-0414-3

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