We consider a queue fed by a large number, say n,
on–off sources with generally distributed on- and off-times.
The queueing resources are scaled by n: The buffer
is B ≡ nb and the link rate is C
≡ nc. The model is versatile. It allows one to model
both long-range-dependent traffic (by using heavy-tailed
on-periods) and short-range-dependent traffic (by using
light-tailed on-periods). A crucial performance metric in this model
is the steady state buffer overflow probability.This probability decays exponentially in n. Therefore,
if n grows large, naive simulation is too time-consuming
and fast simulation techniques have to be used. Due to the exponential
decay (in n), importance sampling with an exponential change of
measure goes through, irrespective of the on-times being heavy or light
tailed. An asymptotically optimal change of measure is found by using
large deviations arguments. Notably, the change of measure is not
constant during the simulation run, which is different from
many other studies (usually relying on large buffer asymptotics).Numerical examples show that our procedure improves considerably
over naive simulation. We present accelerations, we discuss
the influence of the shape of the distributions on the overflow
probability, and we describe the limitations of our technique.
Fast simulation techniques based on large deviations theory
