Algorithmic Analysis of the Maximum Queue Length in a Busy Period for theM/M/cRetrial Queue
Jesus R. Artalejo, Antonis Economou, M. J. Lopez-Herrero
INFORMS Journal on Computing · 2007 · Volume 19 · Issue 1
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.
Keywords
M/M/c retrial queue, maximum orbit size, busy period, continuous-time Markov chain, tridiagonal linear system
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