Clustering of Arrivals in Queueing Systems: Autoregressive Conditional Duration Approach
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Arrivals in queueing systems are typically assumed to be independent and exponentially distributed. Our analysis of an online bookshop, however, shows that there is autocorrelation structure present. First, we adjust the inter-arrivals times (i.e. durations) for diurnal and seasonal patterns. Second, we model adjusted durations by the autoregressive conditional duration (ACD) model based on the generalized gamma distribution with the generalized autoregressive score (GAS) dynamics. 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 treatment of arrivals clustering in practice.
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