OF E2/E2/1/m QUEUEING SYSTEM SUBJECT TO OPERATEDEPENDENT SERVER BREAKDOWNS

Abstract

The paper deals with modelling of a finite single-server queueing system with a server subject to breakdowns. Customers interarrival times and customers service times follow the Erlang distribution defined by the shape parameter k=2 and the scale parameter 2λ or 2μ respectively. We consider that server failures can occur when the server is busy (so called operate-dependent failures). Further we assume that service of a customer is interrupted by the occurrence of the server failure (the preemptive-repeat discipline. We assume that random variables relevant to server failures and repairs are exponentially distributed. The queueing system is modelled using method of stages. We present a state transition diagram, a system of linear equations describing the system behaviour in the steady-state and formulas for several performance measures computation. To validate the mathematical model a simulation model was created using simulation software Witness. At the end of the paper some graphical dependencies are shown.