Abstract
A functional law of the iterated logarithm (LIL) and its corresponding LIL are established for an overloaded multiclass queueing model with preemptive priority service discipline. The functional LIL and the LIL limits quantify the magnitude of asymptotic stochastic fluctuations of the stochastic processes compensated by their deterministic fluid limits in two forms: the functional and numerical, respectively. We establish the functional LIL and LIL limits for five performance measures: queue length, workload, busy time, idle time and number of departures. By the primitive data of the first and second moments of the interarrival and service times, all the functional LILs are expressed into some compact sets of continuous functions and their corresponding LILs are some analytic functions. The proofs are based on the fluid approximation and the strong approximation of the queueing system, with the fluid approximation characterizing the expected values of the performance functions and the strong approximation approximating discrete performance processes with reflected Brownian motions.
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