QUEUING AT LARGE RESOURCES DRIVEN BY LONG-TAILED M G/INFINITY-MODULATED PROCESSES/

We analyze the queue at a buffer with input comprising sessions whose arrival is Poissonian, whose duration is long-tailed, and for which in dividual session detail is modeled as a stochastic fluid process. We o btain a large deviation result for the buffer occupation in an asympto tic regime in which the arrival rate nr, service rate ns, and buffer l evel nb are scaled to infinity with a parameter n. This can be used to approximate resources which multiplex many sources, each of which onl y uses a small proportion of the whole capacity, albeit for long-taile d durations. We show that the probability of overflow in such systems is exponentially small in n, although the decay in b is slower, reflec ting the long tailed session durations. The requirements on the sessio n detail process are, roughly speaking, that it self-averages faster t han the cumulative session duration. This does not preclude the possib ility that the session detail itself has a long-range dependent behavi or, such as fractional Brownian motion, or another long-tailed M/G/inf inity process. We show how the method can be used to determine the mul tiplexing gain available under the constraint of small delays (and hen ce short buffers) for multiplexers of large aggregates, and to compare the differential performance impact of increased buffering as opposed to load reduction.