A Discrete-Time Geo/G/1 Retrial Queue with General Retrial Times

Authors:
Ivan Atencia;Pilar Moreno
Affiliations:
Departamento de Matemática Aplicada, E.T.S.I. Telecomunicación, Universidad de Málaga, Campus de Teatinos, 29071 Málaga, Spain iatencia@ctima.uma.es;Departamento de Economía y Empresa, Facultad de Ciencias Empresariales, Universidad Pablo de Olavide, Ctra. de Utrera, km. 1, 41013 Sevilla, Spain mpmornav@dee.upo.es
Venue:
Queueing Systems: Theory and Applications
Year:
2004

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Abstract

We consider a discrete-time Geo/G/1 retrial queue in which the retrial time has a general distribution and the server, after each service completion, begins a process of search in order to find the following customer to be served. We study the Markov chain underlying the considered queueing system and its ergodicity condition. We find the generating function of the number of customers in the orbit and in the system. We derive the stochastic decomposition law and as an application we give bounds for the proximity between the steady-state distributions for our queueing system and its corresponding standard system. Also, we develop recursive formulae for calculating the steady-state distribution of the orbit and system sizes. Besides, we prove that the M/G/1 retrial queue with general retrial times can be approximated by our corresponding discrete-time system. Finally, we give numerical examples to illustrate the effect of the parameters on several performance characteristics.