Convergence of the stationary distributions of M/M/s/K retrial queue as K tends to infinity

We investigate the convergence of the stationary distributions x(K) of M/M/s/K retrial queue to the stationary distribution pi of M/M/s queue as K tends to infinity. It is showed that x(K) converges geometrically to pi in l(1)-sense and the convergence rate is characterized by the traffic intensity rho = lambda/s mu' where lambda and mu are the arrival rate and service rate, respectively. (C) 2007 Elsevier B.V. All rights reserved.