  Arrivals in queueing systems are typically assumed to be independent and
exponentially distributed. Our analysis of an online bookshop, however, shows
that there is an autocorrelation structure present. 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.
