M/M/1 Retrial Queue with Collisions and Transmission Errors

Lamia Lakaour (), Djamil Aïssani (), Karima Adel-Aissanou () and Kamel Barkaoui ()
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Lamia Lakaour: Bejaia University
Djamil Aïssani: Bejaia University
Karima Adel-Aissanou: Bejaia University
Kamel Barkaoui: Conservatoire National des Arts et Métiers

Methodology and Computing in Applied Probability, 2019, vol. 21, issue 4, 1395-1406

Abstract: Abstract In this paper, an M/M/1 retrial queue with collisions and transmission errors is considered. The collision may occur when a primary arriving customer finds the server busy while the transmission errors usually occur due to an erroneous packet or due to a non-ideal channel condition. We apply the generating function method to derive the joint distribution of the server state and the orbit length in steady state and we obtain important system characteristics. Finally, we present numerical examples to show the applicability of the model.

Keywords: Retrial queue; Collisions; Transmission errors; Classical retrial rate; Generating function; 60K25; 68M20 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s11009-018-9680-x

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