On Effect of Model Parameters on Departure Process in a Production System with Failures

Abstract

A queueing system of the M/M/1/N type with cyclic failure-free and repair times is used as a model of a single-machine manufacturing line. Jobs arrive according to a Poisson process and are being served with exponentially distributed processing time. Successive working (failure-free) and repair times have exponential distributions, too. Basing on a system of integral equations for double transforms of conditional probability distributions of the number of jobs completely processed before the fixed time (departure process), comprehensive numerical analysis of the impact of system parameters on the mean number of departures before the fixed epoch T>0 is carried out.