Author:
Dominik Berbig
Affiliation:
Pforzheim University, Business School, BW/Purchasing and Logistics, Tiefenbronner Str. 65, 75175 Pforzheim, Germany
Keyword(s):
Queuing Theory, Discrete-Time Modelling, Waiting Times, Skewness, Kurtosis.
Abstract:
Processes in material flow systems, which can be regarded as queuing systems, are discrete in time. Nevertheless, the main research work considering queuing theory focuses on time-continuous modelling. However, for G/G/m-queues in continuous time, analysis relevant parameters can only be estimated and not exactly calculated anymore. These approximations are based on the first two central moments of the inter-arrival and service time distribution only and can be arbitrarily wrong. Considering discrete-time approach, the parameters can be calculated exactly. This means that also other central moments of according distributions may have an effect that is not to be neglected. Thus, in this paper we investigate the effect of skewness and kurtosis of service time distributions on the expected waiting times for queuing customers. In order to do so, we modelled queuing systems in a discrete-time manner and calculated resulting waiting times for distributions having the same mean and variance
. In continuous time approximation, the result is always the same. Exact calculations following a discrete-time approach show differences of more than 15 %. Afterwards, we investigated on the effect the skewness and kurtosis of the according distributions have. First findings and need for further research are presented in this position paper.
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