The Markov-Modulated Single Server Queue

We consider a single server queueing system whose customers belong to certain types indexed by j ∈ ε (a countable space), the switching mechanism between different types of customers being governed by a Markov chain J = {J _n , n ≥ 0} with the state space ε. Customers of each type have their own interarrival time and service time distributions determined by the state of J at the epoch of arrival. We assume that J is irreducible and persistent nonnull. The queue discipline is first come, first served.