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)x(K) of M/M/s/K   retrial queue to the stationary distribution ππ of M/M/s queue as K   tends to infinity. It is showed that x(K)x(K) converges geometrically to ππ in l1-sense and the convergence rate is characterized by the traffic intensity ρ=λsμ, where λ and μ are the arrival rate and service rate, respectively.