This paper considers a discrete time queuing system that models a communica
tion network multiplexer which is fed by a self-similar packet traffic. The
model has a finite buffer of size h, a number of servers with unit service
time, and an input traffic which is an aggregation of independent source-a
ctive periods having Pareto-distributed lengths and arriving as Poisson bat
ches. The new asymptotic upper and lower bounds to the buffer-overflow and
packet-loss probabilities P are obtained. The bounds give an exact asymptot
ic of log P/log h when h --> infinity. These bounds decay algebraically slo
w with buffer-size growth and exponentially fast with excess of channel cap
acity over traffic rate. Such behavior of the probabilities shows that one
can better combat traffic losses in communication networks by increasing ch
annel capacity rather than buffer size. A comparison of the obtained bounds
and the known upper and lower bounds is done.