Time dependence of queues with semi-Markovian services

A single server queueing system with Poisson input is considered. There are a finite number of types of customers and the service time of the n th customers depends on the types of the nth and the ( n – l)th customers. The time dependence of the queue size process will be studied, (it will be clear how the methods of the paper can be applied to other processes of interest,) and limiting as well as transient results will be given.