Queues as Harris recurrent Markov chains (Q1107225)

We present a framework for representing a queue at arrival epochs as a Harris recurrent Markov chain (HRMC). The input to the queue is a marked point process governed by a HRMC and the queue dynamics are formulated by a general recursion. Such inputs include the cases of i.i.d., regenerative, Markov modulated, Markov renewal and the output from some queues as well. Since a HRMC is regenerative, the queue inherits the regenerative structure. As examples, we consider split \& match, tandem, G/G/c and more general skip forward networks. In the case of i.i.d. input, we show the existence of regeneration points for a Jackson type open network having general service and interarrival time distributions.