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SUBEXPONENTIAL INTERVAL GRAPHS GENERATED BY IMMIGRATION–DEATH PROCESSES

Published online by Cambridge University Press:  18 March 2010

Naoto Miyoshi ,
Mariko Ogura ,
Takeya Shigezumi  and
Ryuhei Uehara
Naoto Miyoshi
Affiliation:
Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo, Japan E-mail: miyoshi@is.titech.ac.jp
Mariko Ogura
Affiliation:
Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo, Japan E-mail: miyoshi@is.titech.ac.jp
Takeya Shigezumi
Affiliation:
Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo, Japan E-mail: miyoshi@is.titech.ac.jp
Ryuhei Uehara
Affiliation:
School of Information Science, Japan Advanced Institute of Science and Technology, Tokyo, Japan
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Abstract

We propose a simple model of random interval graphs generated by immigration–death processes (also known as M/G/∞ queuing processes), where the length of each interval follows a subexponential distribution, and provide a condition under which the stationary degree distribution is also subexponential. Furthermore, we consider the conditional expectation of the cluster coefficient of a vertex given the degree and show that it vanishes in the limit as the degree goes to infinity under the same condition as that for obtaining the tail asymptotics of the stationary degree distribution.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 24 , Issue 2 , April 2010 , pp. 289 - 301
Copyright
Copyright © Cambridge University Press 2010

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