A Unified Approximate Evaluation of Congestion Functions for Smooth and Peaky Traffics

Abstract

In teletraffic engineering the predictive value of Pascal and Bernoulli distributions has often been noted in relation to the problem of approximating busy-idle state probabilities in lost-call-cleared systems. Because of the parametric similarities between these two sets of distributions and of their limiting relationship to Poisson and Gaussian distributions, it is then possible to design a unified procedure to approximate the main congestion functions associated with peaky and smooth traffic. Moreover, suitably truncated productform combinations of these distributions can also be used to estimate the different levels of blocking experienced by two streams of traffic with different peakedness factors offered to the same trunk group. The main purpose of this paper is to describe the procedure, illustrate its effectiveness, and also discuss some of its limitations.