M/M/1 queue with impatient customers of higher priority

We introduce a simple approach for the analysis of the M/M/c queues with a single class of customers and constant impatience time by finding simple Markov processes, and then by applying this approach we analyze the M/M/1 queues with two classes of customers in which class 1 customers have impatience of constant duration, and class 2 customers have no impatience and lower priority than class 1 customers.