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

Abstract

The traffic intensity (ρ) is a vital parameter of queueing systems because it is a measure of the average occupancy of a server. Consequently, it influences their operational performance, namely queue lengths and waiting times. Moreover, since many computer, production and transportation systems are frequently modelled as queueing systems, it is crucial to use control charts to detect changes in ρ. In this paper, we pay particular attention to control charts meant to detect increases in the traffic intensity, namely: a short-memory chart based on the waiting time of the n-th arriving customer; two long-memory charts with more sophisticated control statistics, and the two cumulative sum (CUSUM) charts proposed by Chen and Zhou (2015). We confront the performances of these charts in terms of some run length related performance metrics and under different out-of-control scenarios. Extensive results are provided to give the quality control practitioner a concrete idea about the performance of these charts.

Performance evaluation of DEWMA3 in phase-II for capturing changes in simple linear profiles based on run rule mechanism

“…If the computed CVRL value is greater than the threshold value, the production process is out-of-control, and corrective action may be necessary to bring it back into control. The CVRL values are categorized as in-control CVRL (CVRL 0 ) and out-of-control CVRL (CVRL 1 ) 48 – 50 .…”