In this paper, we investigate how fast the stationary distribution π(K) of an embedded Markov chain (time-stationary distribution q(K)) of the GI/M/1/K queue converges to the stationary distribution π of the embedded Markov chain (time-stationary distribution q) of the GI/M/1 queue as K tends to infinity. Simonot (1997) proved certain equalities. We obtain sharper results than these by finding limit values lim K → ∞ σ-K ∥π(K) -π∥ and limK → ∞ σ -K ∥q(K) -q∥ explicitly.
- GI/M/1/K queue; dual sequence; stationary measure; stationary distribution; convergence rate
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty