Weighted likelihood ratio chart for statistical monitoring of queueing systems

Abstract

In recent years, effective monitoring of queueing systems has increasingly attracted attention of researchers in the area of statistical process control. Most existing works in the literature, however, did not consider the data autocorrelation, nor rigorously evaluate the performance. In this paper, considering the data autocorrelation, a control chart based on the weighted likelihood ratio test (WLRT) is proposed to efficiently monitor the utilization of queueing systems, particularly the M/M/1 queueing system. Our approach can be readily extended to other general queueing systems if the likelihood function can be obtained. Numerical results and illustrative example show that the performance of the proposed WLRT chart is quite satisfactory.

Keywords:

• Average run length
• queueing systems
• statistical process control
• weighted likelihood ratio statistics

Acknowledgements

The authors would like to thank Dr. Nan Chen of National University of Singapore for discussions. The authors would also like to thank the Editor and two Referees for their insightful comments.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Natural Science Foundation of China [grant number 11431006], [grant number 11371202], [grant number 11131002], [grant number 11201246], [grant number 11101306], [grant number 11271205], [grant number 11101198], [grant number 11401573], [grant number 11571191]; RFDP of China [grant number 20110031110002].