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

Author

Listed:
  • Santos Marta

    (Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001Lisboa, Portugal)

  • Morais Manuel Cabral

    (Department of Mathematics & CEMAT (Center for Computational and Stochastic Mathematics), Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001Lisboa, Portugal)

  • Pacheco António

    (Department of Mathematics & CEMAT (Center for Computational and Stochastic Mathematics), Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001Lisboa, Portugal)

Abstract

The traffic intensity (ρ) 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 ρ. 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). We confront the performances of these charts 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.

Suggested Citation

  • Santos Marta & Morais Manuel Cabral & Pacheco António, 2019. "Comparing Short and Long-Memory Charts to Monitor the Traffic Intensity of Single Server Queues," Stochastics and Quality Control, De Gruyter, vol. 34(1), pages 9-18, June.
    • Handle: RePEc:bpj:ecqcon:v:34:y:2019:i:1:p:9-18:n:2
    DOI: 10.1515/eqc-2018-0026
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    References listed on IDEAS

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    1. U. Narayan Bhat & S. Subba Rao, 1972. "A Statistical Technique for the Control of Traffic Intensity in the Queuing Systems M / G /1 and GI / M /1," Operations Research, INFORMS, vol. 20(5), pages 955-966, October.
    2. Nan Chen & Yuan Yuan & Shiyu Zhou, 2011. "Performance analysis of queue length monitoring of M/G/1 systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(8), pages 782-794, December.
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