MATRIX-GEOMETRIC DISTRIBUTIONS OF A QUEUE UNDER THE LCFS DISCIPLINE WITH INTERRUPTIONS AND DISTRIBUTIONS OF THE PHASE TYPE

A queueing system of the GI/GI/I/r type with distribution functions of the incoming stream and the service time of a phase type is considered. It is assumed that the incoming customer transfers the customer being served at the server into the queue and the interrupted customer is serviced anew later on. A matrix-geometric solution for the stationary distribution of the queue and recursive formulas for calculating the initial times of the sojourn of the customer in the system are presented.