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Performance Analysis of a Block-Structured Discrete-Time Retrial Queue with State-Dependent Arrivals



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Artalejo, Jesús R. and Li, Quan-Lin (2010) Performance Analysis of a Block-Structured Discrete-Time Retrial Queue with State-Dependent Arrivals. Discrete Event Dynamic Systems, 20 (3). pp. 325-347. ISSN 0924-6703

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In this paper, we introduce a new discrete block state-dependent arrival (D-BSDA) distribution which provides fresh insights leading to a successful generalization of the discrete-time Markovian arrival process (D-MAP). The D-BSDA distribution is related to structured Markov chains and the method of stages. The consideration of this new discrete-time state-dependent block description gives one the ability of construct new stochastic models. The retrial queue analyzed in this paper gives an example of application of the D-BSDA distribution to construct more general and sophisticated models. We assume that the primary arrivals and the retrials follow the D-BSDA description and the service times are of discrete phase-type (PH). We study the underlying level dependent Markov chain of M/G/1-type at the epochs immediately after the slot boundaries. To this end, we employ the UL-type RG-factorization which provides an expression for the stationary probabilities. We also perform an analysis of waiting times. Numerical experiments are presented to study the system performance.

Item Type:Article
Uncontrolled Keywords:Service; System; Queueing; Discrete-time; Structured Markov chain; Retrial; LU-factorizations; Waiting time
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:15001
Deposited On:25 Apr 2012 08:45
Last Modified:06 Aug 2018 08:37

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