The Poissonian-spectrum method for treating a loss system serving nonPoissonian multi-bit-rate traffic

Abstract

A two-component simplification of the powerful Poissonian-spectrum method of analyzing a loss system serving a mixture of a nonPoissonian multi-bit-rate traffic system is proposed. The spectrum concept is implicit in L.E.N. Delbrouck's (1981) recursions for homogeneous and heterogeneous traffic and has its roots in Hayward's rather simplistic, yet accurate, method for treating homogeneous peaked traffic. The Poissonian-spectrum representation is not unique. To determine the sensitivity of the method to the spectrum shape, a study is made of three distinctly different representations. With appropriate selection of the spectrum shape, the method reduces to simple recursions. A layman's approach is used to derive these recursions as a natural extension of the Roberts-Kaufman recursion. The case of smooth traffic requires careful considerations, which are discussed.<>