Queueing Networks with Gaussian Inputs

Abstract

This chapter analyzes queueing systems fed by Gaussian inputs. The analysis is of an asymptotic nature, in that the number of sources is assumed large, where link bandwidth and buffer space are scaled accordingly. Relying on powerful largedeviation techniques (in particular Schilder’s theorem), we identify the exponential decay rate of the overflow for the single queue. In addition we establish a number of appealing results (duality between decay rate and variance function; convexity of buffer/bandwidth trade-off curve). Then we extend the result to the tandem setting; a lower bound on the decay rate is found, which is proven to be ‘tight’ under specificconditions. Also approximations for the overflow probability are presented. The lastpart of the chapter is devoted to priority systems.