Overflow and losses in a network queue with a self-similar input

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.