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Comparing short and long-memory charts to monitor the traffic intensity of single server queues

Santos, M.; Morais, M. C. ; Pacheco, António

A publicar em Stochastics and Quality Control
https://doi.org/10.1515/eqc-2018-0026

The traffic intensity (rho) is a vital parameter of queueing systems because it is a measure of the average occupancy of a server. Consequently, it influences their operational performance, namely queue lengths and waiting times. Moreover, since many computer, production and transportation systems are frequently modelled as queueing systems, it is crucial to use control charts to detect changes in rho.
In this paper, we pay particular attention to control charts meant to detect increases in the traffic intensity, namely: a short-memory chart based on the waiting time of the n-th arriving customer; two long-memory charts with more sophisticated control statistics, and the two cumulative sum (CUSUM) charts proposed by Chen and Zhou (2015).
Taking advantage of Mathematica (Wolfram Research, Inc., 2016) and Mat- lab (MathWorks, 2016), we confront their performances in terms of some run length related performance metrics and under different out-of-control scenarios. Extensive results are provided to give the quality control practitioner a concrete idea about the performance of these charts.