This paper considers a discrete time queueing system that models a communication 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-active periods having Pareto-distributed lengths and arriving as Poisson batches. The new asymptotic upper and lower bounds to the buffer-overflow and packet-loss probabilities P are obtained. The bounds give an exact asymptotic of log P/log h when h approaches infinity. These bounds decay algebraically slowly with buffer-size growth and exponentially fast with excess of channel capacity over traffic rate. Such behaviour of the probabilities shows that one can better combat traffic losses in communication networks by increasing channel capacity rather than buffer size. A comparison of the obtained bounds and the known upper and lower bounds is done.
