A Note On Queues with M/G/inf Input

We consider a fluid queue fed by sessions, arriving according to a Poisson process; a session has a heavy-tailed duration, during which traffic is send at a constant rate. We scale Poisson input rate lambda, buffer space B, and link rate C by n, such that we get n lambda, nb, and nc, respectively. Then we let n grow large. In this regime, the overflow probability decays exponentially in the number of sources n; we examine the specific situation in which also b is large.