On Transient Queue-Size Distribution in a Single-Machine Production System with Breakdowns

Abstract

An operation of a single-machine manufacturing system is modeled by an unreliable finite-buffer-type queuing system with Poisson arrivals, in which service times, failure-free times and times of repairs are totally independent and exponentially distributed random variables. Applying the idea of embedded Markov chain and the formula of total probability a system of integral equations for the transient conditional queue-size distributions of jobs present in the system at fixed time t is built. The solution of the corresponding system written for Laplace transforms is obtained in a compact form using the potential technique.