Clustering of arrivals in queueing systems: autoregressive conditional duration approach

Petra Tomanová () and Vladimír Holý
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Petra Tomanová: Prague University of Economics and Business
Vladimír Holý: Prague University of Economics and Business

Central European Journal of Operations Research, 2021, vol. 29, issue 3, No 6, 859-874

Abstract: 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.

Keywords: Inter-Arrival Times; Queueing Theory; Autoregressive Conditional Duration Model; Generalized Autoregressive Score Model; Retail Business (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10100-021-00744-7

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