Analysis of the queue with phase type distributions and inverse service discipline with interruptions

The queueing system of GI/GI/1/r type with phase type distribution functions for input flow (non-Poisson flow) and service time and with inverse service discipline with interruptions is investigated. In accordance with this discipline the new claim has the highest priority and interrupted claims are serviced in the sequel. Thus the discipline 'Last Come First Served Preemptive Resume' (LCFCPR) is considered. Tensor-multiplicative stationary distribution of the queue and recursive formula for the calculation of first moments for the time of staying of the claim in the system are obtained. The numerical results show that for hyperexponential distribution function the probability of losses is less for the discipline LCFSPR. Repetition (LCFSPRR) in comparison with disciplines LCFSPR and LCFS. Vice versa for Erlang distribution the discipline LCFSPRR gives the highest probability of losses.