Comparing short memory charts to monitor the traffic intensity of single server queues

Stochastics and Quality Control, 33 (2018), 1-21
https://doi.org/10.1515/eqc-2017-0030

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, GI/M/1 and GI/G/1 queues. The corresponding control statistics refer solely to a customer-arrival/departure epoch as opposed to several such epochs.
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.