Modeling Machine Failures in a Queueing System

Abstract

When we want to model a system where there is stochastic variability, we usually use a queueing system. In a queueing system, we handle random customer arrivals and random service times. Service times are considered to be a random variable in a queueing system. In addition to the stochastic variability in service times, there can occur another random impacts. As one of those impacts, machine break down can affect a queueing system. In this paper we consider a queueing system where the server sometimes breaks down. Machine failures are said to occur when the server breaks down and cannot process customers. As one way to handle the machine break down, we can adjust the mean and the variance of service times such that the effective mean and variance be identical. But this method is not accurate other than the first and the second moments. We would like to handle the machine failure more directly.