Conceptual issues in scaling sensor networksMassimo Franceschetti,UC Berkeley

UCB Sensor Networks day, Jan 28, 2004 *

State of the art on scaling:PEG ~100 sensor nodes, 1 evader, 2 pursuersCory Sharp & Shawn SchaffertShankar Sastry group

UCB Sensor Networks day, Jan 28, 2004 *

Can we dramatically scale this?Practical problemsConceptual problems

UCB Sensor Networks day, Jan 28, 2004 *

Percolation theoryRandom graphsDistributed computingDistributed controlChannel physicsDistributed samplingNetwork information theoryNetwork codingConnectivityRoutingStorageFailuresPacket lossMalicious behaviorRemote operation

TheoryPractice

UCB Sensor Networks day, Jan 28, 2004 *

Some conceptual issues

LARGE SCALE CONNECTIVITYROUTINGCAPACITYCONTROL

UCB Sensor Networks day, Jan 28, 2004 *

Random connection modelSingle hop model

UCB Sensor Networks day, Jan 28, 2004 *

Multi-hop connectivity modelThere is a phase transition at a critical node density value

UCB Sensor Networks day, Jan 28, 2004 *

How does the critical density change with the shape of the connection function?

UCB Sensor Networks day, Jan 28, 2004 *

General Tendency When the selection mechanism with which nodes are connected to each other is sufficiently spread out, then few links (in the limit one on average) will suffice to obtain global connectivity.Balister, Bollobas, Walters (2003)Franceschetti, Booth, Cook, Bruck, Meester (2003)D. Dubhashi, O. Haggstrom, A. Panconesi (2003)R. Meester, M. Penrose, A. Sarkar (1997)M. Penrose (1993)

UCB Sensor Networks day, Jan 28, 2004 *

General TendencyIn contrast, when connections do not spreadout, few links are not enough for connectivity. Xue and P. R. Kumar (2003)O. Haggstrom and R. Meester (1996)

UCB Sensor Networks day, Jan 28, 2004 *

Spread out connections (1)

UCB Sensor Networks day, Jan 28, 2004 *

TheoremFor all connection functionslonger links are trading off for the unreliability of the connectionit is easier to reach connectivity in this model of unreliable networkFranceschetti, Booth, Cook, Bruck, Meester (2003)

UCB Sensor Networks day, Jan 28, 2004 *

Spread out connections (2)

UCB Sensor Networks day, Jan 28, 2004 *

Mixture of short and long linksTwo different spreading strategiesLinks are made all longer

UCB Sensor Networks day, Jan 28, 2004 *

TheoremConsider annuli shapes A(r) of inner radius r, unit area, and critical density For all , there exists a finite , such that A(r*) percolates, for all It is possible to decrease the connectivity threshold by taking a sufficiently large shift !Balister, Bollobas, Walters (2003)Franceschetti, Booth, Cook, Bruck, Meester (2003)

UCB Sensor Networks day, Jan 28, 2004 *

CNLWhat have we learnedCNL=average number of connections per node needed for connectivity

UCB Sensor Networks day, Jan 28, 2004 *

Navigation in the small worldNeed links at ALL scale lengths !What about routing?

UCB Sensor Networks day, Jan 28, 2004 *

ZIntuition: scale invariancer1 r2Model of neighbors density:

UCB Sensor Networks day, Jan 28, 2004 *

ZIntuition: scale invariancer1 r2Model of neighbors density:

UCB Sensor Networks day, Jan 28, 2004 *

ZIntuition: scale invariancer1 r2Model of neighbors density:

UCB Sensor Networks day, Jan 28, 2004 *

ZIntuition: scale invariancer1 r2Slow far from destinationSlow close to destination

UCB Sensor Networks day, Jan 28, 2004 *

TheoremeSTdFranceschetti & Meester (2003)

UCB Sensor Networks day, Jan 28, 2004 *

Bottom lineeSTdBuild routing trees that are scale invariant to route with few hops at all distance scalesWant to balance the number of short and long links

Need to exploit the hairy edge(D. Culler)

UCB Sensor Networks day, Jan 28, 2004 *

SummaryTowards a system theory of large scale networksConceptual issues at different levelsDesign for complexity strategyClose the gap between theory and practice