On Loss Process in a Queueing System Operating Under Single Vacation Policy

Abstract

A finite-buffer queueing model with Poisson arrivals and generally distributed processing times is analyzed. Every time when the service station becomes idle a single vacation period is being initialized, during which the processing is suspended. A system of integral equations for the probability distribution of the length of the first loss series is built, using the idea of embedded Markov chain and the total probability law. The solution of the is obtained in a compact form by using the linear algebraic approach. The corresponding result for next series of losses is hence derived. Numerical utility of analytical formulae is presented in a computational example.