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

Santos Marta (), Morais Manuel Cabral () and Pacheco António ()
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Santos Marta: Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal
Morais Manuel Cabral: Department of Mathematics & CEMAT (Center for Computational and Stochastic Mathematics), Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal
Pacheco António: Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal

Stochastics and Quality Control, 2018, vol. 33, issue 1, 1-21

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{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.

Keywords: Phase-Type Distributions; Queues; Run Length; Statistical Process Control; Traffic Intensity (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1515/eqc-2017-0030

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