Gated time-limited polling systems

Abstract

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 timelimited 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 caD. be calculated include joint distributions at server arrivals, at server departures, and over all time. Additional measures of interest, such as expected wa.iting times and blocking probabilities for each customer class in the system, can also be computed. 'The work of E. de Souza e Silva and R. R.

Modeling, analysis, measurement and experimentation with the Tangram-II integrated environment

“…Then the transient analysis of certain submodels (depending on the particular problem) are used to calculate the transition probability matrix between the embedded points. Application examples include the analysis of: the GI/P H/1 queue [25]; schedule maintenance policies for computer systems [11]; polling models with timeouts [16,17]. In [15] a methodology was developed which addresses the solution of a broad class of non-Markovian models and associated measures.…”