Fishing in poisson streams: Focusing on the whales, ignoring the minnows

Maxim Raginsky, Sina Jafarpour, Rebecca Willett, Robert Calderbank

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper describes a low-complexity approach for reconstructing average packet arrival rates and instantaneous packet counts at a router in a communication network, where the arrivals of packets in each flow follow a Poisson process. Assuming that the rate vector of this Poisson process is sparse or approximately sparse, the goal is to maintain a compressed summary of the process sample paths using a small number of counters, such that at any time it is possible to reconstruct both the total number of packets in each flow and the underlying rate vector. We show that these tasks can be accomplished efficiently and accurately using compressed sensing with expander graphs. In particular, the compressive counts are a linear transformation of the underlying counting process by the adjacency matrix of an unbalanced expander. Such a matrix is binary and sparse, which allows for efficient incrementing when new packets arrive. We describe, analyze, and compare two methods that can be used to estimate both the current vector of total packet counts and the underlying vector of arrival rates.

Original languageEnglish (US)
Title of host publication2010 44th Annual Conference on Information Sciences and Systems, CISS 2010
DOIs
StatePublished - 2010
Externally publishedYes
Event44th Annual Conference on Information Sciences and Systems, CISS 2010 - Princeton, NJ, United States
Duration: Mar 17 2010Mar 19 2010

Publication series

Name2010 44th Annual Conference on Information Sciences and Systems, CISS 2010

Other

Other44th Annual Conference on Information Sciences and Systems, CISS 2010
CountryUnited States
CityPrinceton, NJ
Period3/17/103/19/10

ASJC Scopus subject areas

  • Information Systems
  • Information Systems and Management

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