On Two Modifications of E2/E2/1/m Queueing System with a Server Subject to Breakdowns

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. The paper demonstrates two modifications of the queueing system. In both cases we consider that server failures can occur when the server is busy (operate-dependent failures). Further we assume that service of a customer is interrupted by the occurrence of the server failure (the preemptive-repeat discipline) or the system empties when the server is broken (the failure-empty discipline). We assume that random variables relevant to server failures and repairs are exponentially distributed. Both modifications are modelled using method of stages. For each modification we present the state transition diagram, the system of linear equations describing the system behavior in the steady state and the formulas for several performance measures computation. At the end of the paper some graphical dependencies are shown.