SUBEXPONENTIAL INTERVAL GRAPHS GENERATED BY IMMIGRATION–DEATH PROCESSES

We propose a simple model of random interval graphs generated by immigration– death processes (also known asM/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 showthat 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.