STANFORD UNIVERSITY
PROBABILITY & STOCHASTIC PROCESSES SEMINAR

4:15 p.m., Monday, May 12, 2003
Sequoia Hall, Room 200
Cookies at 4:00 p.m., 1st Floor Lounge

Balaji Prabhakar
Electrical Engineering Department
Stanford 


Connections between information and queueing theories 


Abstract 

A collection of theorems in point process theory assert that the
Poisson process results as the limit of repeatedly performing certain
operations on an arbitrary initial (input) process.  Since the Poisson 
process has the highest entropy rate of all processes at a given rate, 
one is naturally lead to the question: Do these operations increase the 
entropy of the input process?

In this talk we show that certain queueing systems indeed increase 
the entropy.  Some useful by-products are discrete-time versions of: 
(i) a proof of the celebrated Burke's theorem, (ii) a proof of the 
uniqueness, amongst renewal inputs, of the Poisson process as a fixed 
point for exponential server queues, (iii) Papangelou's theorem relating 
time and arrival (or Palm) entropy rates.  We will also investigate the
ability of "logically reversible" queues to sort numbers.


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The Department of Statistics is in Sequoia Hall, at the intersection of
Serra Mall and Lomita Mall, near the Math. corner of the Main Quadrangle.

Titles of Probability and Stochastic Processes seminars can be accessed
on the web from http://www-stat.stanford.edu/seminars/
and from        http://math.stanford.edu/html/seminars.html