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

Comparing Short-Memory Charts to Monitor the Traffic Intensity of Single Server Queues AbstractThis 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{M/G/1}, G⁢I/M/1{GI/M/1}and G⁢I/G/1{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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Economic Quality Control de Gruyter

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

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Publisher
de Gruyter
Copyright
© 2018 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1869-6147
eISSN
2367-2404
DOI
10.1515/eqc-2017-0030
Publisher site
See Article on Publisher Site

Abstract

AbstractThis 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{M/G/1}, G⁢I/M/1{GI/M/1}and G⁢I/G/1{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.

Journal

Economic Quality Controlde Gruyter

Published: Jun 1, 2018

References