(The) loss probability in GI/M/1/K queue by the dual sequence of the embedded Markov chain

Abstract

In this thesis we define a dual sequence of the discrete time EMC of a GI/M/1/K queue by inverting the roles of a customer and an empty position. One of the advantage of dual sequence is that the dual sequence of the EMC of the GI/M/1/K queue is stochastically equivalent to the EMC of the M/G/1/K+1 queue. By using the duality we give an explicit expression of the stationary distribution of the EMC and the loss probability for the GI/M/1/K queue in terms of a stationary measure of the EMC of an M/G/1 queue. We also find the asymptotic behavior of the loss probability for the GI/M/1/K queue as K→∞.