Clustering of arrivals in queueing systems: autoregressive conditional duration approach

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-arrival times for diurnal seasonal patterns. Second, model adjusted by generalized autoregressive score (GAS) based on gamma distribution spirit conditional duration (ACD) models. Third, a simulation study, investigate effects dynamic arrival number customers, busy period, response time with single multiple servers. We find ignoring leads significantly underestimated performance measures consequently suboptimal decisions. The proposed approach serves as general methodology treatment arrivals clustering practice.