We consider a fluid queue where the input process consists of N identical
sources that turn on and off
at exponential waiting times. The server works at the constant
rate c and an on source generates fluid at unit rate.
This model was first formulated and analyzed by Anick et
al. (1982). We obtain an alternate representation of the joint
steady-state distribution of
the buffer content and the number of on sources. This is
given as a contour integral that we then analyze in the limit
N→∞. We give detailed asymptotic results for the
joint distribution as well as the associated marginal and
conditional distributions. In particular, simple conditional
limits laws are obtained. These show how the buffer content
behaves conditioned on the number of active sources and vice
versa. Numerical comparisons show that our asymptotic results are
very accurate even for N=20.