Loss behavior of an Internet router with self-similar input traffic via Fractal point process

2013 ◽  
Author(s):  
Rajaiah Dasari ◽  
Malla Reddy Perati
Keyword(s):  
Point Process ◽  
Self Similar ◽  
Internet Router

scholarly journals A class of self-similar random measure

2005 ◽  
Vol 37 (04) ◽  
pp. 908-914 ◽  
Author(s):  
David Vere-Jones
Keyword(s):  
Point Process ◽  
Marked Point ◽  
Random Measure ◽  
Aftershock Sequence ◽  
Marked Point Process ◽  
Stable Processes ◽  
Epidemic Type Aftershock Sequence ◽  
Self Similar ◽  
The Masses ◽  
Invariance Relation

We describe a class of self-similar random measure that generalizes the class of stable, completely random measure, or, in one dimension, the class of processes with stable independent increments. As with the stable processes, the realizations are purely atomic, but the masses of the atoms are not necessarily independent, but rather characterized by self-similar dependence relations. Indeed, the class can be described most effectively in terms of the point process on the product space for the locations and sizes (‘marksȉ) of the atoms. Then self-similarity reduces to an invariance relation (‘biscale invariance’) on the distribution of this marked point process. The condition can be satisfied when the marked point process is compound Poisson, corresponding to the nonnegative stable processes, but is by no means restricted to this case. An example is given which modifies and extends Ogata's epidemic-type aftershock sequence model for earthquake occurrence.

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