Asymptotic upper bounds for an M/M/C/K retrial queue with a guard channel and guard buffer

Nesrine Zidani () and Natalia Djellab ()
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Nesrine Zidani: University Chadli Bendjedid El-Tarf
Natalia Djellab: University of Annaba

Mathematical Methods of Operations Research, 2024, vol. 99, issue 3, No 6, 365-407

Abstract: Abstract The paper deals with Markovian multiserver retrial queuing system with exponential abandonments, two types of arrivals: Fresh calls and Handover calls and waiting places in the service area. This model can be used for analysing a cellular mobile network, where the service area is divided into cells. In this paper, the number of customers in the system and in the orbit form a level-dependent quasi-birth-and-death process, whose stationary distribution is expressed in terms of a sequence of rate matrices. First, we derive the Taylor series expansion for nonzero elements of the rate matrices. Then, by the expansion results, we obtain an asymptotic upper bound for the stationary distribution of both the number of busy channels and the number of customers in the orbit. Furthermore, we present some numerical results to examine the performance of the system.

Keywords: Taylor series expansion; Asymptotic; Multiserver retrial queue; QBD (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00186-024-00865-0

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