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 l1-sense and the convergence rate is characterized by the traffic intensity , where [lambda] and [mu] are the arrival rate and service rate, respectively.