Exact buffer overflow calculations for queues via martingales
Let tau(n) be the first time a queueing process like the queue length or workload exceeds a level n. For the M/M/1 queue length process, the mean Etaun and the Laplace transform Ee(-staun) is derived in closed form using a martingale introduced in Kella and Whitt (1992). For workload processes and more general systems like MAP/PH/1, we use a Markov additive extension given in Asmussen and Kella (2