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

L. E. N. Delbrouck

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Advanced Queuing Theory Analysis Network Traffic and Congestion Control Wireless Communication Networks Research

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.

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References

1993An introduction to queueing theory 1973Introduction to Queueing Theory 1973The Interrupted Poisson Process As An Overflow Process 1962Introduction to Congestion Theory in Telephone Systems.1961Introduction to Congestion Theory in Telephone Systems.

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1995An inversion algorithm to compute blocking probabilities in loss networks with state-dependent rates 1995Efficiently Providing Multiple Grades of Service with Protection Against Overloads in Shared Resources 1983An Approximate Formula for Individual Call Losses in Overflow Systems 1990Overflow analysis for finite waiting room systems 1995Approximating the heterogeneous fluid queue with a birth-death fluid queue 1983The Uses of Kosten's Systems in the Provisioning of Alternate Trunk Groups Carrying Heterogeneous Traffic

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