The paper deals with a service system In which the arriving calls belong to several pre-emptive priority classes. The service process involved can be described by means of the following three characteristics:
(1) Structure of the System - a queueing system is dealt with having n parallel service units and one waiting line with s waiting places;
(2) Service Discipline - a pre-emptive priority discipline is applied; a pre-empted call is relegated to the queue where it awaits completion of service;
(3) Arrival and Service Process - the offered traffic Is originated by POISSON sources; both a finite and an infinite number of sources are dealt with. The service time is negatively exponentially distributed.