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A Distributed Algorithm for Joint Sensing and Routing in Wireless Networks with Non-Steerable Directional Antennas

Chun Zhang*, Jim Kurose+, Yong Liu~, Don Towsley+, Michael Zink+

* IBM T.J. Watson Research Center+ Dept of Computer Science, University of Massachusetts at Amherst~ Dept of Electrical & Computer Engineering, Polytechnic University

Nov 14, 2006 ICNP

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Outline

motivation

problem formulation

distributed algorithm

result

summary

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Multi-hop wireless sensor networks

sensor nodes directional-antenna links

link capacity constraints

• 802.11 protocol: 2/5.5/11Mbps

energy constraints energy supplied by solar panel

sink A

sink B

applications: weather monitoring

performance metric amount of information delivered to sinks

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Interesting problem ?

limited energy

link capacities

communication energysensing energy

sensing rate (information)

radio layerapplication layer

demand generator capacity generator

more demand ? or more capacity?routing solution ?

network layer

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Our contribution

joint optimization problem formulation for energy allocation (between sensing, data transmission, and data reception), and routing

distributed algorithm to solve the joint optimization problem, with its convergence proved

simulation to demonstrate the energy balance achieved in a network of X-band radars, connected via point-to-point 802.11 links with non-steerable directional antennas

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Related work

[Lin,Shroff@CDC04] [Eryilmaz,Srikant@ISC06] joint rate control, resource allocation, and routing in

wireless networks

our work further considers energy consumption for data sensing data reception

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Outline

motivation

problem formulation

distributed algorithm

result

summary

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Resource model

power resource three power usages: data sensing, data transmitting,

data reception power is a convex and increasing function of data rate constraint: consumption rate ≤ harvest rate

link capacity resource constraint: link data rate ≤ link capacity

resource constraints satisfied by penalty functions

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Goal : information maximization

information modeled by utility function

: node i sensed and delivered data rate node i collected information

assumption: is a concave and increasing function

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Optimization problem formulation

s: sensing rates; X: data routes

routes X deliver sensing rates s to data sink

Joint sensing and routing problem

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Transforming joint sensing/routing problem to routing problem with fixed

demands

i

i’

wireless sensor network

sensing link difference link

sensing power ->reception power

idea: treat data sensing as data reception through sensing link

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Transformed problem

fixed demand: maximum sensing rates; X: data routes

routes X deliver maximum sensing rates to data sink

Routing problem with fixed traffic demand

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Outline

motivation

problem formulation

distributed algorithm

result

summary

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Distributed algorithm: generalize [Gallager77] wired network algorithm

wired network link-level resource constraint

wireless network node-level resource constraint

How to generalize from link-level to node-level?

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Generalized distributed algorithm

generalize algorithm from wired network (link-level) to wireless network (node-level)

repeat, until all traffic loaded on optimal path each link locally compute gradient information gradient information propagated from downstream to upstream in

accumulative manner routing fractions adjustment from non-optimal path to optimal

path

for generalized gradient-based algorithm: • prove convergence • provide step-size for routing fraction adjustment

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Outline

motivation

problem formulation

distributed algorithm

result

summary

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Simulation scenario

From CASA student testbed

energy harvest rate: 7-13W

X-band radar-on power: 34W radar-on rate 1.5Mbps

link-on trans power: 1.98W link-on receive power: 1.39W link-on goodput rate: as

shown

Utility function

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1Mb

2Mb

5.5Mb

2Mb

1Mb

goodput rate

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Optimization results for different energy harvest rates

As power budget increases • utility and sensing power increase• communication power first increases, then decreases and flats out

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Node level energy balance for different energy harvest rates

power budget = 9W power budget = 13W

power rich network: max-min fair (single-sink) : sensing rates not affected by choice of utility functions

power constrained network: close to sink nodes spend less energy on sensing

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Summary: a distributed algorithm for joint sensing and routing in wireless

networks

Goal : a distributed algorithm for joint sensing and routing

Approach : 1. mapping joint problem to routing problem2. proposed a distributed algorithm with convergence

proof and step size

Simulation to demonstrate energy balance for different energy harvest rates:

1. energy rich: proven max-min fairness (for single sink)2. energy constrained: close-to-sink nodes spend more

energy on communication, and thus less energy on sensing

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Thanks !Questions ?