M/G/1 queues with Markov-generated server vacations

The focus here is a single-server first come first served queue with Poisson input and general service (i.e., M/G/1), where the server goes on vacation after each service time and after vacations where no customers are found waiting. The type of vacation taken by the server will depend on the immediately prior vacation type via a Markov chain, whether or not the vacations are separated by customer service times. Furthermore, service times will also depend on the immediately preceding vacation type. This model would seem to have potential use in numerous service situations, such as banks, where a teller may perform a manual accounting or computer task after each service or after busy periods, each of which takes its own random amount of time to do; in a manufacturing assembly line, where a machine may go for one of two types of maintenance after every task or busy period, each of which also takes a random amount of time to do; and in airline communications, where messages sent to a moving aircraft from fixed ground radar communication centers may be interrupted due to radar rotation, ‘silent’ zones, or interference.