Utilization, Standardized Moments and Their Effect on Waiting

Tempus fugit—a well-known Latin proverb. Normally, time “flees” continuously. However, processes in material flow, i.e. queuing systems, are discrete in time. Currently, the major focus of research is on time-continuous modelling. Unfortunately, for G/G/m-queues—which often have to be used in material flow systems—the parameters relevant to the analysis like waiting times can only be estimated, since there are only approximations based on the first two central moments of the inter-arrival and service time distribution. These can be arbitrarily wrong. In discrete-time approach, on the other hand, these parameters can be derived exactly. This leads to the assumption that other standardized moments of the according distributions have a non-negligible influence e.g. on waiting times. In this paper, therefore, the influence of other parameters, such as the skewness of service time distributions, on the expected waiting times for customers in the queue is investigated, also considering the utilization rate. For this purpose, the discrete-time approach is applied and the resulting waiting times within the queuing system are calculated based on service time distributions with equal mean and variance. More than 200 according experiments are conducted, utilization rates are additionally considered, and first results as well as assumptions from previous work are cross-checked.