A law of iterated logarithm for multiclass queues with preemptive priority service discipline

A law of iterated logarithm (LIL) is established for a multiclass queueing model, having a preemptive priority service discipline, one server and customer classes, with each class characterized by a renewal arrival process and i.i.d. service times. The LIL limits quantify the magnitude of asymptotic stochastic fluctuations of the stochastic processes compensated by their deterministic fluid limits. The LIL is established in three cases: underloaded, critically loaded, and overloaded, for five performance measures: queue length, workload, busy time, idle time, and number of departures. The proof of the LIL is based on a strong approximation approach, which approximates discrete performance processes with reflected Brownian motions. We conduct numerical examples to provide insights on these LIL results.