A MAP/SM/1 queue with service times depending on the arrival process

We study a MAN/SM/1 queue with Markov arrival process input and semi-Markov service. Service times may depend on the arrival phase states, that is, there are many types of arrivals which have different service time distributions. At first, we derive the joint distribution of the numbers of different types of customers at departures. The distributions of the virtual and actual waiting times as well as the queue length distributions at an arbitrary time, arrivals, and departures are derived.