  In Internet environment, traffic flow to a link is typically modeled by
superposition of ON/OFF based sources. During each ON-period for a particular
source, packets arrive according to a Poisson process and packet sizes (hence
service times) can be generally distributed. In this paper, we establish heavy
traffic limit theorems to provide suitable approximations for the system under
first-in first-out (FIFO) and work conserving service discipline, which state
that, when the lengths of both ON- and OFF-periods are lightly tailed, the
sequences of the scaled queue length and workload processes converge weakly to
short-range dependent reflecting Gaussian processes, and when the lengths of
ON- and/or OFF periods are heavily tailed with infinite variance, the sequences
converge weakly to either reflecting fractional Brownian motions (FBMs) or
certain type of long-range dependent reflecting Gaussian processes depending on
the choice of scaling as the number of superposed sources tends to infinity.
Moreover, the sequences exhibit a state space collapse-like property when the
number of sources is large enough, which is a kind of extension of the
well-known Little's law for M/M/1 queueing system. Theory to justify the
approximations is based on appropriate heavy traffic conditions which
essentially mean that the service rate closely approaches the arrival rate when
the number of input sources tends to infinity.
