Effects of Slow-Downs and Failure on Stochastic Service Systems

The reliability and efficiency of a stochastic service system subject to break-downs and slow-downs is investigated. A mathematical model of such a system is a single server queue with Poisson input and exponential service time. However, the server is subject to break-downs and slow-downs, the lengths of which are exponentially distributed. During these periods he serves at varying rates. Analytic expressions are derived for the mean waiting time and the mean queue length. © 1963 Taylor & Francis Group, LLC.