INTERDISCIPLINARY STOCHASTIC PROCESSES COLLOQUIUM

Tuesday January 20, room 60 Evans, 4.10 - 5.00pm

Speaker: Balaji Prabhakar (EECS, Stanford University)

Title: 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 led 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) connections with the timing
capacity of queues, and (iv) Papangelou's theorem relating time and
arrival (or Palm) entropy rates.

     Joint work with Robert Gallager, Chandra Nair and Devavrat Shah.