There is More than Mean and Variance on Waiting

Dominik Berbig

2023

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.

Paper Citation

in Harvard Style

Berbig D. (2023). There is More than Mean and Variance on Waiting. In Proceedings of the 13th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH; ISBN 978-989-758-668-2, SciTePress, pages 171-177. DOI: 10.5220/0011947400003546

in Bibtex Style

@conference{simultech23,
author={Dominik Berbig},
title={There is More than Mean and Variance on Waiting},
booktitle={Proceedings of the 13th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH},
year={2023},
pages={171-177},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0011947400003546},
isbn={978-989-758-668-2},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 13th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH
TI - There is More than Mean and Variance on Waiting
SN - 978-989-758-668-2
AU - Berbig D.
PY - 2023
SP - 171
EP - 177
DO - 10.5220/0011947400003546
PB - SciTePress