Algorithmic Analysis of the Maximum Queue Length in a Busy Period for the M/M/c Retrial Queue

Authors:
Jesus R. Artalejo;Antonis Economou;M. J. Lopez-Herrero
Affiliations:
Department of Statistics and Operations Research, Faculty of Mathematics, Complutense University of Madrid, Madrid 28040, Spain;Department of Mathematics, University of Athens, Panepistemioupolis, Athens 15784, Greece;School of Statistics, Complutense University of Madrid, Madrid 28040, Spain
Venue:
INFORMS Journal on Computing
Year:
2007

Citing 2
Cited 2

Introduction to numerical linear algebra and optimisation

Introduction to numerical linear algebra and optimisation
Accessible bibliography on retrial queues

Mathematical and Computer Modelling: An International Journal

The M/G/1 retrial queue: New descriptors of the customer's behavior

Journal of Computational and Applied Mathematics
Heavy-traffic extreme value limits for Erlang delay models

Queueing Systems: Theory and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper deals with the maximum number of customers in orbit (and in the system) during a busy period for the M/M/c retrial queue. Determining the distribution for the maximum number of customers in orbit is reduced to computation of certain absorption probabilities. By reducing to the single-server case we arrive at a closed analytic formula. For the multi-server case we develop an efficient algorithmic procedure for computation of this distribution by exploiting the special block-tridiagonal structure of the system. Numerical results illustrate the efficiency of the method and reveal interesting facts concerning the behavior of the M/M/c retrial queue.