Workloads and waiting times in single-server systems with multiple customer classes

One of the most fundamental properties that single-server multi-class service systems may possess is the property of work conservation. Under certain restrictions, the work conservation property gives rise to a conservation law for mean waiting times, i.e., a linear relation between the mean waiting times of the various classes of customers. This paper is devoted to single-server multi-class service systems in which work conservation is violated in the sense that the server's activities may be interrupted although work is still present. For a large class of such systems with interruptions, a decomposition of the amount of work into two independent components is obtained; one of these components is the amount of work in the corresponding systemwithout interruptions. The work decomposition gives rise to a (pseudo)conservation law for mean waiting times, just as work conservation did for the system without interruptions

The general distributional Little's law and its applications

"March 1991."Includes bibliographical references (p. 31-32).Research supported by the Leaders for Manufacturing Program at MIT and Draper Laboratory.Dimitris Bertsimas, Daisuke Nakazato

The general distributional Little's law and its applications

"March 1991."Includes bibliographical references (p. 31-32).Research supported by the Leaders for Manufacturing Program at MIT and Draper Laboratory.Dimitris Bertsimas, Daisuke Nakazato

On a queueing model with service interruptions

Single-server queues in which the server takes vacations arise naturally as models for a wide range of computer-, communication- and production systems. In almost all studies on vacation models, the vacation lengths are assumed to be independent of the arrival, service, workload and queue length processes. In the present study we allow the length of a vacation to depend on the length of the previous active period, viz., the period since the previous vacation. Under rather general assumptions regarding the offered work during active periods and vacations, we determine the steady-state workload distribution. We conclude by discussing several special cases including polling models, and relate our findings to results obtained earlier

On some queueing systems with server vacations, extended vacations, breakdowns, delayed repairs and stand-bys

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This research investigates a batch arrival queueing system with a Bernoulli scheduled vacation and random system breakdowns. It is assumed that the repair process does not start immediately after the breakdown. Consequently there maybe a delay in starting repairs. After every service completion the server may go on an optional vacation. When the original vacation is completed the server has the option to go on an extended vacation. It is assumed that the system is equipped with a stand-by server to serve the customers during the vacation period of the main server as well as during the repair process. The service times, vacation times, repair times, delay times and extended vacation times are assumed to follow different general distributions while the breakdown times and the service times of the stand-by server follow an exponential distribution. By introducing a supplementary variable we are able to obtain steady state results in an explicit closed form in terms of the probability generating functions. Some important performance measures including; the average length of the queue, the average number of customers in the system, the mean response time, and the value of the traffic intensity are presented. The professional MathCad 2001 software has been used to illustrate the numerical results in this study