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Rare-event simulation for multi-server queues in the Halfin-Whitt regime

We consider a FCFS M/Hd/n queue which has a Poisson arrival process (M) and i.i.d. service times following a hyper-exponential distribution with d components (Hd). We develop rare-event simulation methodology to analyze large deviations for the queue length process in steady-state under the Halfin-Whitt regime. The key strategy consists of constructing two objects: I) a regenerative set A whose probability is bounded away from zero as n → ∞, and II) a free process for which the most likely path to overflow is easy to handle. In particular, the free process is coupled with the original system outside the set A and it is not sensitive to boundary behavior. The successful application of the algorithm takes crucial advantage of the simulation and evaluation of a time-inhomogeneous Markov chain that is defined in terms of matrix exponential functions.