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

Author

Listed:
  • Santos Marta
  • Pacheco António

    (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)

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 & Pacheco António & Morais Manuel Cabral, 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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