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A Statistical Technique for the Control of Traffic Intensity in the Queuing Systems M / G /1 and GI / M /1

Author

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  • U. Narayan Bhat

    (Southern Methodist University, Dallas, Texas)

  • S. Subba Rao

    (Case Western Reserve University, Cleveland, Ohio)

Abstract

This paper presents a statistical technique for the control of the traffic intensity in single-server queuing systems with (i) Poisson arrivals and general service times and (ii) recurrent arrivals and exponential service times. The procedure is such that the system is readjusted only if the number of customers in the system either falls and stays beyond the upper control limit longer than a preassigned number of consecutive transitions or falls and stays below the lower control limit longer than a preassigned number of consecutive transitions. Methods are given to derive these two pairs of control limits using available transition probability tables, and tables of control limits have been provided for a selected number of parameter values in the queue with Poisson arrivals and general service times.

Suggested Citation

  • 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.
  • Handle: RePEc:inm:oropre:v:20:y:1972:i:5:p:955-966
    DOI: 10.1287/opre.20.5.955
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    Cited by:

    1. 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.
    2. Mandjes, M. & Ravner, L., 2021. "Hypothesis testing for a Lévy-driven storage system by Poisson sampling," Stochastic Processes and their Applications, Elsevier, vol. 133(C), pages 41-73.
    3. Lotfi Tadj & Gautam Choudhury, 2005. "Optimal design and control of queues," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 359-412, December.
    4. Tianhua Zhang & Juliang Zhang & Fu Zhao & Yihong Ru & John W. Sutherland, 2020. "Allocating resources for a restaurant that serves regular and group-buying customers," Electronic Commerce Research, Springer, vol. 20(4), pages 883-913, December.
    5. 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.
    6. 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.

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