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An elementary proof of Sengupta's invariance relation and a remark on Miyazawa's conservation principle

Published online by Cambridge University Press:  14 July 2016

P. Brémaud
P. Brémaud*
Affiliation:
Laboratoire des Signaux et Systèmes, CNRS
*
∗ Postal address: Laboratoire des Signaux et Systèmes, CNRS-ESE, Plateau de Moulon, 91190 Gif-sur-Yvette, France.
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Abstract

In this short note we derive Sengupta's (1989) invariance relation using elementary arguments and we show that Miyazawa's (1983), (1985) conservation principle, on which Sengupta's proof is based, admits the Palm inversion formula as a consequence. This contrasts with Miyazawa's first proof based on the inversion formula. We also show that Neveu's (1976) cycle formula is a direct consequence of Miyazawa's principle.

Keywords

POINT PROCESSQUEUEING PROCESSPALM PROBABILITY

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 28 , Issue 4 , December 1991 , pp. 950 - 954
Copyright
Copyright © Applied Probability Trust 1991 

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References

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