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Clustering of arrivals in queueing systems: autoregressive conditional duration approach

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  • Petra Tomanová

    (Prague University of Economics and Business)

  • Vladimír Holý

    (Prague University of Economics and Business)

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.

Suggested Citation

  • Petra Tomanová & Vladimír Holý, 2021. "Clustering of arrivals in queueing systems: autoregressive conditional duration approach," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(3), pages 859-874, September.
    • Handle: RePEc:spr:cejnor:v:29:y:2021:i:3:d:10.1007_s10100-021-00744-7
    DOI: 10.1007/s10100-021-00744-7
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