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Superposition of renewal processes

Published online by Cambridge University Press:  01 July 2016

C. Y. Teresalam  and
John P. Lehoczky
C. Y. Teresalam*
Affiliation:
University of Michigan, Ann Arbor
John P. Lehoczky*
Affiliation:
Carnegie-Mellon University
*
∗Postal address: Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI 48109, USA.
∗∗Postal address: Department of Statistics, Carnegie-Mellon University, Pittsburgh, PA 15213, USA.
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Abstract

This paper extends the asymptotic results for ordinary renewal processes to the superposition of independent renewal processes. In particular, the ordinary renewal functions, renewal equations, and the key renewal theorem are extended to the superposition of independent renewal processes. We fix the number of renewal processes, p, and study the asymptotic behavior of the superposition process when time, t, is large. The key superposition renewal theorem is applied to the study of queueing systems.

Keywords

S-RENEWAL FUNCTIONSS-RENEWAL EQUATIONSKEY SUPERPOSITION RENEWAL THEOREMQUEUEING SYSTEMS
Type
Research Article
Information
Advances in Applied Probability , Volume 23 , Issue 1 , March 1991 , pp. 64 - 85
Copyright
Copyright © Applied Probability Trust 1991 

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Footnotes

Research of both authors supported in part by a grant from the National Science Foundation DMS-87-02537.

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