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Performance analysis of queue length monitoring of M/G/1 systems

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  • Nan Chen
  • Yuan Yuan
  • Shiyu Zhou

Abstract

This study investigates the statistical process control application for monitoring queue length data in M/G/1 systems. Specifically, we studied the average run length (ARL) characteristics of two different control charts for detecting changes in system utilization. First, the nL chart monitors the sums of successive queue length samples by subgrouping individual observations with sample size n. Next is the individual chart with a warning zone whose control scheme is specified by two pairs of parameters, (upper control limit, du) and (lower control limit, dl), as proposed by Bhat and Rao (Oper Res 20 (1972) 955–966). We will present approaches to calculate ARL for the two types of control charts using the Markov chain formulation and also investigate the effects of parameters of the control charts to provide useful design guidelines for better performance. Extensive numerical results are included for illustration. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:58:y:2011:i:8:p:782-794
    DOI: 10.1002/nav.20483
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    References listed on IDEAS

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    1. Don G. Wardell & Herbert Moskowitz & Robert D. Plante, 1992. "Control Charts in the Presence of Data Correlation," Management Science, INFORMS, vol. 38(8), pages 1084-1105, August.
    2. Kevin B. Hendricks & John O. McClain, 1993. "The Output Process of Serial Production Lines of General Machines with Finite Buffers," Management Science, INFORMS, vol. 39(10), pages 1194-1201, October.
    3. Papadopoulos, H. T. & Heavey, C., 1996. "Queueing theory in manufacturing systems analysis and design: A classification of models for production and transfer lines," European Journal of Operational Research, Elsevier, vol. 92(1), pages 1-27, July.
    4. 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.
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    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.

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