Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-23T22:59:13.128Z Has data issue: false hasContentIssue false
  • English
  • Français

A generalization of Rapp's formula

Published online by Cambridge University Press:  17 February 2009

C. E. M. Pearce
C. E. M. Pearce
Affiliation:
Department of Applied Mathematics, University of Adelaide, Adelaide, South Australia 5000
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The Rapp formula of teletraffic dimensioning is generalized to admit an arbitrary renewal stream of offered traffic. The derivation proceeds from a heavy traffic approximation and provides also an estimate of the order of error involved in the Rapp formula. In principle, the method could be used to seek convenient higher order approximations.

Our equations give an incidental theoretical substantiation of an empirical result relating to marginal occupancy found recently by Potter.

Type
Research Article
Information
The ANZIAM Journal , Volume 23 , Issue 3 , January 1982 , pp. 291 - 296
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]Cohen, J. W., “The full availability group of trunks with an arbitrary distribution of the inter-arrival time and the negative exponential holding time distribution”, Simon Stevin Wis-en Natuurkundig Tijdschrift 26 (1957), 169–181.Google Scholar
[2]Pearce, C. E. M. and Potter, R. M., “Some formulae old and new for overflow traffic in telephony”, 8th int. Teletraffic Congress, Melbourne (1976), 421.1–6 (also with addenda in Aust. Telecom. Res. (1977), 92–97).Google Scholar
[3]Potter, R. M., “The equivalent non-random method and restrictions imposed on renewal overflow systems by the specification of a finite number of overflow traffic moments”, 9th Int. Teletraffic Congress, Torremolinos, Spain (1979), 1–6.Google Scholar
[4]Rapp, Y., “Planning of junction network in a multi-exchange area”, Ericsson Technics 20 (1964), 77–130.Google Scholar
[5]Takács, L., Introduction to the theory of queues (Oxford University Press, 1962), Chapters 3,4.Google Scholar
[6]Wilkinson, R. I., “Theories for toll traffic engineering in the U.S.A.’, Bell System Tech. J. 35 (1956), 421–514.CrossRefGoogle Scholar