Large deviations and importance sampling for a tandem network with slow-down

摘要

We consider a variant of the two-node tandem Jackson network where the upstream server reduces its service rate when the downstream queue exceeds some pre-specified threshold. The rare event of interest is the overflow of the downstream queue. Based on a game/subsolution approach, we rigorously identify the exponential decay rate of the rare event probabilities and construct asymptotically optimal importance sampling schemes.