Seminars

Modulated Branching Processes, Origins of Power Laws and Queuing Duality

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Date: 10-16-2007
Start Time: 1:00pm
End Time: 2:00pm
Speaker: Predrag Jelenkovic, Columbia University
Location: Mudd 303

ABSTRACT

We propose reflected modulated branching processes as generic models for many observations of power laws in proportional growth environments. Our main results show that the proposed mathematical models result in power law distributions under quite general polynomial Gartner-Ellis conditions. The generality of our results could explain the ubiquitous nature of power law distributions.
Furthermore, an informal interpretation of our main results suggests that alternating periods of expansion and reduction, e.g., economic booms and recessions, are primarily responsible for the appearance of power law distributions.

Our results also establish a general asymptotic equivalence between the reflected branching processes and the corresponding multiplicative processes. In addition, in the course of our analysis, we observe a duality between the reflected multiplicative processes and queueing theory. Essentially, this duality demonstrates that the power law distributions play an equivalent role for multiplicative processes with reflective/absorbing barriers as the exponential/geometric distributions do in queueing analysis.

Joint work with Jian Tan, the full paper is available here.

BIO

Predrag R. Jelenkovic received the Ph.D. degree from the Department of Electrical Engineering at Columbia University, New York, in 1996. From 1996-1998, he worked in the Mathematics of Networks and Systems Department at Bell Labs, Lucent Technologies, as a Member of Technical Staff. In 1998, he joined the Dept. of Electrical Engineering at Columbia University, where he currently works as an Associate Professor. His research focuses on mathematical foundations of information networks and systems. Prof. Jelenkovic is the recipient of a number of awards, including the first Best Student Paper Award at the International Teletraffic Congress in 1997, the NSF Presidential Early Career Award for Scientists and Engineers in 2000, co-author of the Best Student Paper Award at the International Teletraffic Congress in 2007 andthe IBM Pat Goldberg Memorial Best Paper Award in Computer Science, Electrical Engineering and Math in 2007.