Common-control queuing system with priority service

The paper presents a detailed study of a common-control delay system with non-pre-emptive priority service. The system considered in the paper has a single server and r priority classes of customers, each with a distinct independent Poisson input, but all customers have the same exponential service time. The operating time of the common control is assumed to have an exponential distribution. The stationary distribution of the number of customers or the state of the system and the Laplace transform of the waiting-time distribution are obtained.