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

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.