abstract
- We propose an approach to modelling maximum queue sizes for heavy-tail interarrivals and service times. We derive models for high percentiles of queue length based on the principle that for subexponential distributions, large deviations of cumulative workload are dominated by single extreme observation. This allows the distribution of aggregate workload to be approximated through the distribution of the maximum service time, leading to tractable models for extreme queue length quantiles. We derive parametric models that require fewer fitted parameters than extreme value methods, including generalized extreme value (GEV), generalized Pareto (POT), and power-law tail models. Event-driven Monte Carlo simulations of heavy-tailed single-server queue are used to evaluate and compare proposed models. We show that the model called Par Sum Exp gives best results.