Exact convergence rate for the distribution of GI/M/c/K queue as K tends to infinity

摘要

We obtain the exact convergence rate of the stationary distribution π (K) of the embedded Markov chain in GI/M/c/K queue to the stationary distribution π of the embedded Markov chain in GI/M/c queue as K→∞. Similar result for the time-stationary distributions of queue size is also included. These generalize Choi and Kim's results of the case c =1 by nontrivial ways. Our results also strengthen the Simonot's results 5