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MRSPN analysis of Semi-Markovian finite source retrial queues

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Abstract

In this paper, the analysis of Semi-Markovian single server retrial queues by means of Markov Regenerative Stochastic Petri Nets (MRSPN) is considered. We propose MRSPN models for the two retrial queues M/G/1/N/N and M/G/1/N/N with orbital search. By inspecting the reduced reachability graph of both MRSPN models, the qualitative analysis is obtained. The quantitative analysis is carried out after constructing their one step transition probability matrix and computing the steady state probability distribution of each tangible marking. As an example, the queue \(M/Hypo_{2}/1/2/2\) is treated in order to illustrate the functionality of the MRSPN approach. The exact performance measures (mean number of customers in the system, mean response time, mean waiting time,...) are computed for different parameters of the two systems by an algorithm elaborated in Matlab environment.

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Authors and Affiliations

  1. Research Unit LaMOS (Modeling and Optimization of Systems), Bejaia University, Béjaïa, Algeria

    Lyes Ikhlef, Ouiza Lekadir & Djamil Aïssani

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  1. Lyes Ikhlef
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  2. Ouiza Lekadir
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  3. Djamil Aïssani
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Correspondence to Lyes Ikhlef.

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Ikhlef, L., Lekadir, O. & Aïssani, D. MRSPN analysis of Semi-Markovian finite source retrial queues. Ann Oper Res 247, 141–167 (2016). https://doi.org/10.1007/s10479-015-1883-8

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