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189. Standardized moments of waiting

Invited abstract in session WD-39: Analysis of Stochastic Models II, stream Stochastic Modelling.

Wednesday, 14:30-16:00
Room: 35 (building: 306)

Authors (first author is the speaker)

1. Dominik Berbig
Pforzheim University

Abstract

We all have to wait. Sometimes longer, sometimes shorter. Thanks to queuing theory, we know why this is the case. However, under the usual assumption of a continuous-time domain, we do not really know how long we have to wait. In the case where the Markov property does not hold for the inter-arrival-time distribution, only estimations for the waiting times exist. They are rather easy to calculate as they are solely based on the mean and variance of the distributions, everything else is neglected. But these estimates can be arbitrarily inaccurate and offer no guarantee of quality. One solution is to apply the discrete-time domain. Here, the entire distribution is known, exact parameters can be calculated. However, this approach is much more complex. Thus, an intermediate solution is required which is less complex but more precise. Therefore, the effect of other standardized moments must be analyzed and taken into consideration. First corresponding analyses especially regarding inter-arrival times have recently been carried out and have provided initial indications. In this paper, these results are reflected on and taken as basis. In addition, experiments specifically with regards to service-time distributions are presented and the results are compared. Corresponding findings and possible next steps are presented in this paper serving as a basis for discussion for future work as this is important to calculate correct buffer sizes.

Keywords

Status: accepted

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