GI/M/1 Priority Queue

We consider customers arriving at a service facility from a finite number of priority classes and being served according to a common negative exponential distribution with mean 1/μ. The priority discipline is preemptive, i.e., an arriving customer of higher priority than the customer currently being served displaces the latter and begins service himself. Taking the interarrival times to be independent, identically distributed, positive random variables with distribution function G(x), we consider the equilibrium queue-length distribution.