Gated time-limited polling systems

Polling systems have found widespread application in the modeling of computer communication systems and protocols. As a consequence, a great deal of effort has been devoted to analyzing a variety of polling mechanisms. In particular, systems for which a limit on the length of time the server may spend while visiting a queue have recently been the subject of several studies. For example, protocols and multiplexing schemes for multimedia networks may employ a limit on the amount of time the shared channel is allocated to each type of traffic. However, such time-limited policies are difficult to analyze, and relatively few results about them have appeared in the literature. In this paper the previous methodology we developed to study the exhaustive service case with preemptive timeouts is extended and applied to the analysis of a system operating under the time-limited gated discipline and having either preemptive timeouts or nonpreemptive timeouts. Measures of interest that can be calculated include joint distributions at server arrivals, at server departures, and over all time. Additional measures of interest, such as expected waiting times and blocking probabilities for each customer class in the system, can also be computed.