BUFFER OVERFLOW ASYMPTOTICS FOR A BUFFER HANDLING MANY TRAFFIC SOURCES

As a model for an ATM switch we consider the overflow frequency of a q ueue that is served at a constant rate and in which the arrival proces s is the superposition of N traffic streams We consider an asymptotic as N-->infinity in which the service rate Nc and buffer size Nb also i ncrease linearly in N. In this regime, the frequency of buffer overflo w is approximately exp(-NI(c, b)), where I(c, b) is given by the solut ion to an optimization problem posed in terms of time-dependent logari thmic moment generating functions. Experimental results for Gaussian a nd Markov modulated fluid source models show that this asymptotic prov ides a better estimate of the frequency of buffer overflow than ones b ased on large buffer asymptotics.