SenMetrics 20051 Towards Efficient Routing in Wireless Sensor Networks Bhaskar Krishnamachari Autonomous Networks Research Group Department of Electrical.

SenMetrics 2005 1

Towards Efficient Routing in Wireless Sensor Networks

Bhaskar Krishnamachari

Autonomous Networks Research Group

Department of Electrical Engineering-Systems

USC Viterbi School of Engineering

http://ceng.usc.edu/~anrg

2

Talk Overview

We will examine the modeling and analysis of three different aspects of information routing that are of particular concern to wireless sensor networks:

1. Joint routing and in-network compression - minimize total number of bits transmitted

2. Low latency routing with sleep schedules– minimize end to end latency, given duty cycle

3. Robust geographic routing over real wireless links– maximize delivery ratio and energy efficiency

This work has been supported in part by the National Science Foundation under grants CNS-0435505, CNS-0347621, CNS-0325875, and CCF-0430061

3

1. Impact of Spatial Correlation on Routing with Compression

Pattem, Krishnamachari, Govindan, “Impact of Spatial Correlation on Routing with Compression in Wireless Sensor Networks,” IPSN 2004. [Best Student Paper Award]

Minimizing the total number of bit transmissions

4

Spatial Correlation Model

Inter-nodespacing d

Correlationlevel c

Number ofnodes n

Entropy of single source H1

A parameterized expression for the joint entropy of n linearly placed equally spaced nodes

5

Comparison of Basic Strategies

• Routing Driven Compression: route along shortest paths to sink, compress wherever paths happen to overlap

• Compression Driven Routing: Route to maximize compression, though this may incur longer paths

• Distributed Source Coding (ideal): perform distributed compression at sources, and route along shortest paths. If we ignore costs of learning correlation, this provides an idealized lower bound.

6

Comparison of Basic Strategies

7

Analysis

• Consider a linear set of sources, in a 2D grid. Data from s nodes is compressed first before routing to the sink.

• We can derive expressions for the energy cost as a function of the cluster size s:

• We can even derive an expression for the optimal cluster size as a function of the network size and correlation level:

8

Cluster-based routing + compression

Suggests the existence of a near-optimal cluster (about 15) that is insensitive to correlation level!

9

Near-Optimal Clustering

• Can formalize the notion of near-optimality using a maximum difference metric:

• We can then derive an expression for the near-optimal cluster size:

• This is independent of the correlation level, but does depend on the network size, number of sources, and location of the sink. For the above scenario, it turns out sno = 14 (which explains the results shown).

10

Near-Optimal Clustering

11

Summary

• These results (further extended to 2D scenarios in recent work) indicate that a simple, non-adaptive, cluster-based routing and compression strategy is robust and efficient.

12

2. Low Latency Routing with Sleep

Lu, Sadagopan, Krishnamachari, Goel “Delay Efficient Sleep Scheduling in Wireless Sensor Networks,” IEEE Infocom 2005.

Minimizing end to end latency, given duty cycle

13

Sleep Latency

• Largest source of energy consumption is keeping the radio on (even if idle). Particularly wasteful in low-data-rate applications.

• Solution: regular duty-cycled sleep-wakeup cycles. E.g. S-MAC

• Another Problem: increased latency

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

time

14

Special Case Solution: D-MAC

Gang Lu, Bhaskar Krishnamachari and Cauligi Raghavendra, "An Adaptive Energy-Efficient and Low-Latency MAC for Data Gathering in Sensor Networks," IEEE WMAN 2004.

Staggered sleep wake cycles minimize latency for one-way data gathering.

15

General Problem Formulation

• Each node is assigned one slot out of k to be an active reception slot which is advertised to all neighbors that may have to transmit to it.

• Nodes sleep on all other slots unless they have a packet to transmit.

• Assume low traffic so that only sleep latency is dominant and there is low interference/contention.

• The per-hop sleep delay is the difference between reception slots of neighboring nodes

• Data between any pair of nodes is routed on lowest-delay path between them (arbitrary communication patterns possible)

• Goal: assign slots to nodes to minimize the worst case end to end delay (delay diameter)

16

DESS Problem Formulation

Given a graph G, assign one of k reception slots to each node to minimize the maximum (shortest-cost-path) delay between any two points in the network

17

NP-Hardness

18

• Although problem is NP-hard in general, can derive optimal solutions for some special cases with structure

• Tree: alternate between 0 and k/2. Gives worst delay diameter of dk/2

• Ring: sequential slot assignment has best possible delay diameter of (1 - 1/k)*n

• A constant factor approximation can be obtained in case of the square grid by using the solution for the ring as a building block

Special Cases: Tree, Ring

0

1

2

012

2

0

1

19

Special Case: Grid

• A solution for the grid is to use an arrangement of concentric rings

• Can prove that this provides a constant factor approximation

20

Comparison of Heuristics

21

Multi-Schedule Solutions

• If each node is allowed to adopt multiple schedules, then can find much more efficient solutions:

• Grid: delay diameter of at most d + 8k (create four cascading schedules at each node, one for each direction)

• Tree: delay diameter of at most d+4k (create two schedules at each node, one for each direction)

• On general graphs can obtain a O( (d + k)log n) approximation for the delay diameter

22

Summary

• Sleep schedules should be intelligently designed to enable low-latency routing

• Ongoing work looks at adaptively assigning these schedules depending on current flows in the network (rather than worst-case over all possible flows)

23

3. Geographic Routing on Real Wireless Links

• Seada, Zuniga, Helmy, Krishnamachari, Energy-Efficient Forwarding Strategies for Geographic Routing in Lossy Wireless Sensor Networks, ACM Sensys 2004.• Li, Hsu, Krishnamachari, Helmy, A Local Metric for Geographic Routing with Power Control in Wireless Networks, IEEE SECON 2005, to appear.

• Zuniga, Krishnamachari, “Analyzing the Transitional Region in Low-Power Wireless Links,” IEEE SECON 2004.

Maximizing delivery ratio and energy efficiency

24

Recent Empirical Observations

• Ganesan et al. [TR ’02], Zhao [SenSys ’03], Woo [Sensys ’03], Cerpa [TR ’04].

• Wireless Links show three regions : connected, transitional, and disconnected.

• Transitional region is characterized by – Asymmetric links. – High variance space/time. – High sensitivity to HW

25

Channel & Radio Models• Exponential path loss with log-

normal variation due to multi-path fading.

• PRR(SNR) depends on modulation, encoding and packet size.

26

Explanation of Observation

distance (m)

rece

ive

d p

ow

er

(dB

m)

Observations

• σ ↑ → TR ↑

• η ↑ → TR ↓

27

Empirical EvaluationIndoor Environment: aisle of building (3.0, 3.8)

empirical

model

med pw high pw

Realistic wireless topology generators available at http://ceng.usc.edu/~anrg/

28

Empirical EvaluationOutdoor Environment: football field (4.7, 4.6)

med pw high pw

empirical

model

Realistic wireless topology generators available at http://ceng.usc.edu/~anrg/

29

Implications for Geographic Routing

30

Two Extremes

1. Forward to best-distance improvement neighbor– Pro: fewer total hops– Con: each long hop likely to have low packet reception rate (PRR), hence, may

need many retries to get packet across each hop.

2. Forward to nearby neighbor in direction of destination– Pro: each hop is likely to be high PRR, hence energy-efficient – Con: Requires more total hops, since only a short distance is traveled at each

step

31

The PRR*D metric

The product of link reception rate and distance improvement provides a local metric that balances the two concerns.

32

Evaluation of PRR*d

33

Summary

• For robust performance, routing approaches suitable for sensor networks must carefully take into account realistic wireless link conditions.

• Newer work (to appear in SECON ‘05) looks at extending results to the case of robust geographic routing with power control with a slightly modified local metric: PRR*d/(power) , with power level and PRR selected at each hop to optimize energy efficiency.

34

Conclusions

• We examined how to make wireless sensor network routing techniques more efficient, in three different contexts:

– when performing in-network compression while gathering correlated information to save energy

– when minimizing the latency induced by radio sleep schedules

– when routing using local geographic information, over real wireless links with loss

• A major research goal for the future is to determine whether these and other such optimizations can be unified under a single routing architecture that would be suitable for a sufficiently large set of applications