The inclusion of storage in a queueing system

Service operations involving an intermediate store are modelled using an extended definition of the system state which is a conventional definition of state supplemented with an indicator of the live capacity in the store. Additional to the parameters of mean service rate and mean arrival rate, a mean discharge rate of the store is introduced and the steady state probabilities are calculated in terms of these three quantities. Both finite source and infinite source cases are considered under the assumption of exponential distributions. The models permit production comparisons for systems with and for systems without storage devices.