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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Santos Marta & Morais Manuel Cabral & Pacheco António, 2018. "Comparing Short-Memory Charts to Monitor the Traffic Intensity of Single Server Queues," Stochastics and Quality Control, De Gruyter, vol. 33(1), pages 1-21, June.
    • Handle: RePEc:bpj:ecqcon:v:33:y:2018:i:1:p:1-21:n:4
    DOI: 10.1515/eqc-2017-0030
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    References listed on IDEAS

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    1. Ying‐Chao Hung & George Michailidis & Shih‐Chung Chuang, 2014. "Estimation and monitoring of traffic intensities with application to control of stochastic systems," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 30(2), pages 200-217, March.
    2. M C Testik & J K Cochran & G C Runger, 2004. "Adaptive server staffing in the presence of time-varying arrivals: a feed-forward control approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(3), pages 233-239, March.
    3. 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.
    4. Sudha Jain, 2000. "An autoregressive process and its application to queueing model," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1-2), pages 131-138.
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