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Comparing Short-Memory Charts to Monitor the Traffic Intensity of Single Server Queues

  • Marta Santos , Manuel Cabral Morais EMAIL logo and António Pacheco
Published/Copyright: March 28, 2018
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Abstract

This paper describes the application of simple quality control charts to monitor the traffic intensity of single server queues, a still uncommon use of what is arguably the most successful statistical process control tool. These charts play a vital role in the detection of increases in the traffic intensity of single server queueing systems such as the M/G/1, GI/M/1 and GI/G/1 queues. The corresponding control statistics refer solely to a customer-arrival/departure epoch as opposed to several such epochs, thus they are termed short-memory charts. We compare the RL performance of those charts under three out-of-control scenarios referring to increases in the traffic intensity due to: a decrease in the service rate while the arrival rate remains unchanged; an increase in the arrival rate while the service rate is constant; an increase in the arrival rate accompanied by a proportional decrease in the service rate. These comparisons refer to a broad set of interarrival and service time distributions, namely exponential, Erlang, hyper-exponential, and hypo-exponential. Extensive results and striking illustrations are provided to give the quality control practitioner an idea of how these charts perform in practice.

MSC 2010: 62P30; 60K20

Award Identifier / Grant number: UID/Multi/04621/2013

Funding statement: This work was partially supported by FCT (Fundação para a Ciência e a Tecnologia) through project UID/Multi/04621/2013.

Acknowledgements

The second author would like to express his sincere thanks to Professor Dr. Sven Knoth for all the support given during the preparation of the final draft of this article, while visiting the Institute of Mathematics and Statistics at the Helmut Schmidt University, Hamburg, Germany. The authors wish to acknowledge the time and attention the reviewers selflessly devoted to carefully examine the original manuscript.

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Received: 2017-11-27
Accepted: 2018-3-5
Published Online: 2018-3-28
Published in Print: 2018-6-1

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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