Abstract
Arrivals in a queueing system are typically assumed to be independent and exponentially distributed. Our analysis of an online bookshop, however, shows that there is an autocorrelation structure. First, we adjust the inter-arrival times for diurnal and seasonal patterns. Second, we model adjusted inter-arrival times by the generalized autoregressive score (GAS) model based on the generalized gamma distribution in the spirit of the autoregressive conditional duration (ACD) models. Third, in a simulation study, we investigate the effects of the dynamic arrival model on the number of customers, the busy period, and the response time in queueing systems with single and multiple servers. We find that ignoring the autocorrelation structure leads to significantly underestimated performance measures and consequently suboptimal decisions. The proposed approach serves as a general methodology for the treatment of arrivals clustering in practice.
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Acknowledgements
We would like to thank the organizers and participants of the 7th International Conference on Management (Nový Smokovec, September 26–29, 2018), the 30th European Conference on Operational Research (Dublin, June 23–26, 2019), the 15th International Symposium on Operations Research in Slovenia (Bled, September 25–27, 2019) and the 3rd International Conference on Advances in Business and Law (Dubai, November 23–24, 2019) for fruitful discussions.
Funding
The work on this paper was supported by the Internal Grant Agency of the Prague University of Economics and Business under project F4/27/2020, the Czech Science Foundation under project 19-08985S, and the Institutional Support Funds for the long-term conceptual development of the Faculty of Informatics, Prague University of Economics and Business.
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Tomanová, P., Holý, V. Clustering of arrivals in queueing systems: autoregressive conditional duration approach. Cent Eur J Oper Res 29, 859–874 (2021). https://doi.org/10.1007/s10100-021-00744-7
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DOI: https://doi.org/10.1007/s10100-021-00744-7