Control charts for the queue length in a G/G/S system

Statistical-process-control-based monitoring of performance measures of queuing systems has so far eluded mainstream practices within the quality engineering discipline. There are two reasons for this. First, most measures have highly skewed distributions, and, secondly, no general theoretical formulae exist that may provide a platform to calculate control limits for the general G/G/S queue. In this paper, Shewhart-like general control charts for attributes, recently introduced, are combined with existent highly accurate approximations for the steady-state probabilities of the G/G/S queue, to develop control charts for the queue size in a G/G/S system. The effectiveness of this approach is discussed and demonstrated by applying the proposed control charts to a sample of queues with various inter-arrival time and service time distributions.