Matrix-geometric queue distribution under LCFS discipline with interruption and phase-type distributions

The queuing system of GI - GI - 1 - r type with phase-type distribution function (PH-distribution) of input flow and serving time is considered. It is supposed that forthcoming claim ousts the served one in the queue and the interrupted claim is served afterwards anew. This procedure corresponds to service discipline LCFS PRR (Last Come First Served Preemtive Resume Repetition). Thus, the service discipline assumes the reversed order of serving claims with interruption and repetition of service of interrupted claim with the same distribution. The stochastic behaviour of queuing system is described by homogeneous Markovian process over some set of states. The matrix-geometric form for queue stationary distribution is obtained. The recurrent relations for the moments of staying time of the claim in the system are derived. The numerical analysis are given. Particularly, these results enable to calculate the dependencies of probability of losses and mean number of claims on the capacity.