Asymptotic variability analysis for multi-server generalized Jackson network in overloaded

The asymptotic variability analysis is studied for multi-server generalized Jackson network. It is characterized by law of the iterated logarithm (LIL), which quantifies the magnitude of asymptotic stochastic fluctuations of the stochastic processes compensated by their deterministic fluid limits. In the overloaded (OL) case, the asymptotic variability is studied for five performance measures: queue length, workload, busy time, idle time and number of departures. The proof is based on strong approximations, which approximate discrete performance processes with (reflected) Brownian motions. We conduct numerical examples to provide insights on these LIL results.