Logarithmic Asymptotics for the

Abstract

We study tail asymptotics of the stationary distribution for the GI=G=1-type Markov chain with finitely many background states. Decay rate in the logarithmic sense is identified under a number of conditions on the transition probabilities. The results are applied to the BMAP=G=1queuewithvacations.Therelationshipbetweenvacationtimeandthedecayrate of the queue length distribution is investigated.