Randomized Algorithms for Data Propagation in Wireless Sensor Networks

1. Randomized Algorithms for Data Propagation in Wireless Sensor Networks Sotiris Nikoletseas University of Patras (UoP) and (CTI), Greece. (visiting University of Geneva, Switzerland) COST/DYNAMO/GRAAL Meeting, Maribor, Slovenia, 2007

2. Overview of the talk • models / assumptions • twoproblems: data propagation and energy balance • three representativeprotocols: • local optimization (LTP) • probabilistic redundance (PFR) • energy balance (EBP) • performance evaluation: • analysis • simulation • conclusions / more problems /future directions

3. Work presented in this talk • I. Chatzigiannakis, S. Nikoletseas and P. Spirakis, “Efficient and Robust Protocols forLocal Detection and Propagation in Smart Dust Networks”, in the Journal of MobileNetworks (MONET), 2005. • I. Chatzigiannakis, T. Dimitriou, S. Nikoletseas, and P. Spirakis, “A ProbabilisticAlgorithm for Efficient and Robust Data Propagation in Smart Dust Networks”, in theJournal of Ad-Hoc Networks, 2006. - C. Efthymiou, S. Nikoletseas and J. Rolim, “Energy Balanced Data Propagation inWireless Sensor Networks”, in the Wireless Networks (WINET) Journal, 2005.

4. A Wireless Sensor Network • very large number of tiny “smart” sensors • severe limitations • densely / randomly deployed in an area • self-organization • co-operation • locality an “ad-hoc” wireless network for: • sensing crucial events • data propagation

5. Unique characteristics - Hugenumbers, increased complexity, dense interactions - High dynamics / rapid evolution - Autonomic character (open/self-organizing) - Cooperation under severe constraints - Locality / lack of knowledge

6. New Challenges (I) - Scalability: how does protocol performance/correctness scale with size? - Efficiency: mainly energy, time - Fault-tolerance: can the network tolerate faults? To what extent?

7. New Challenges (II) • Inherent trade-offs (e.g. energy vs time, fault-tolerance) • Competing goals / various aspects: - minimizing total energy spent in the network - maximising the number of “alive” sensors over time - combining energy efficiency and fault-tolerance - balancing the energy dissipation • Application dependence thus • variety of protocols needed / hybrid combinations • adaptive protocols, locality • simplicity, randomization, distributedness

8. Limitations of Previous Work • Directed Diffusion: maintains a set of paths (e.g. a tree) to get data and reinforces best paths (it is suitable for low dynamics) • LEACH: sensors create clusters and elect cluster-heads that collect/aggregate/compress data and transmitdirectly to the control center (it is suitable for small area networks)

9. A smart dust “cloud” model (a set of “particles” is spread in the plane) Definitions: Let d the density of particles in the area. Let R be the transmission range of each particle. A receiving wall W is an infinite line in the plane. The wall represents the authorities (the fixed control center). Alternatively, W may be a single point (the “sink” S). Each particle is aware of the location of W.

10. The Problem of Local Detection and Propagation • A particle p detects a local crucial event ε • “How can particle p, via cooperation with the rest of the cloud, propagate information about event εto the receiving wall W” • - Efficiency measures: • - propagation time (time for data to reach the control center) • - number of particle to particle transmissions(“hops”), which also characterizes energy consumption - fault-tolerance

11. Our Local Target Protocol (LTP) • Let d(pi , pj )the (vertical) distance of pi , pj • and d(pi , W) the (vertical) distance of pifrom W. • Each p’ receiving data does the following: • Search Phase:It tries to discover a particle closer to W, • i.e. a p’’ where d(p’’, W) < d(p’, W). • Direct Transmission Phase:If found, then, p’ sends data to p’’ • Backtrack Phase: If repetitions of the search phase fail, • then p’ sends data back to the particle it received data from.

12. The search phase Example of a transmission

13. Efficiency (number of hops) Definitions: Let hopt the (optimal) number of “hops” (vertical to Wtransmissions) needed to reach W, if particles always exist in distances R towards W. Let h the actual number of hops (transmissions) taken to reach W. The “hops” efficiency of the protocol is: where

14. Simplifying Assumptions for a Rigorous Analysis • The position of p′′ is random uniform in the arc of angle 2α. • Each target selection is stochastically independent of the others.

15. Theorem: The expected “hops” efficiency of the protocol in the α-uniform case is Also Proof: A sequence of points is generated, p0 = p, p1, p2, …, ph-1, ph where ph-1is within W’s range and ph is beyond W. Let αithe angle of pi w.r.t. pi-1’s vertical line to W. It is: The vertical progress towards W is

16. We get: From Wald’s equation then since Assuming large values for hopt and since for it is we get the result.

17. Summary evaluation of LTP • local, simple, greedy protocol • no global structure (set of paths) maintained • good for dense networks • performance drops in sparse / faulty networks

18. Our Probabilistic Forwarding Protocol (PFR) - a protocol that avoids flooding by probabilistically favouring certain (“close to optimal”) data transmissions. -Data is broadcast with probability Pfwd = φ/π while it is not propagated with probability 1- Pfwd. - our protocol is very simple, uses only local information and assumes no co-ordination between sensors.

19. The Correctness of PFR • Lemma: PFR always succeeds in sending information from E to S when the network is operational In the proof, we use geometry (i.e. we cover the network area by unit squares and show that there are always particles “close enough” to the optimal line that always broadcast)

20. The Energy Efficiency of PFR (I) • We consider particles that propagate data as far as possible from ES line • We approximate ω by the following random walk:

21. The Energy Efficiency of PFR (II) By using stochastic dominance by a continuous time “discouraged arrivals” birth and death process, we prove: Theorem: The ratio of activated particles in PFR protocol is Θ((n0/n)2), where n0 = |ES| and n2 = N is the number of particles in the network. For n0 = o(n) this o(1).

22. The Robustness of PFR -We study the case when some of these particles are not operating - We consider particles very near the ES line Lemma: PFR manages to propagate the information across lines parallel to ES, and of constant distance, with fixed nonzero probability.

23. Experimental evaluation • - Implementation of protocols: • - software simulation (in ns2 + our extensions) • - real devices (Berkeley mica-1 motes) • more realistic (technical details) • large scale (thousands of sensors simulated) • visualization of protocol evolution • LTP/PFR comparison findings: • LTP is best is dense networks, • while PFR is best in sparse networks.

24. Our Energy Balance Protocol (EBP) - Motivation • Most protocols tend to “strain” some specific nodes in the network: - In a hop-by-hop scheme the nodes closer to the sink tend to be overused. - In a direct transmission scheme the distant nodes tend to be overused. • “How can we achieve equal energy dissipation per node in order to prolongthe network lifetime by avoiding early network disconnection?”

25. The Protocol • Data Propagation:Each node in sector i propagates messages as follows: - Propagate the message to sector i−1 with probabilty pi. - Propagate the message directly to the sink with probability 1−pi. • The choice of pi is made such as the average per sensor energy dissipation isthe same for all sensors in the network.

26. Computation of pi (message handling) • Let hithe number of messages that handles sector i. • Let fi the number of messages that were forwarded to sector i. • Let githe number of messages that were generated in sector i. • Clearly:hi = fi + gi • By linearity of expectation: E[hi] = E[fi] + E[gi]

27. A recurrence relation for pi

28. A closed form for pi

29. Dynamic aspects/Heterogeneity • Two groups of nodes: - “usual” energy nodes - super-nodes (twice as much energy) • Same total energy as in the homogeneous case (for fairness of comparison) • Various heterogeneity degrees (20%-80% of total energy in super nodes) • One more heterogeneity aspect: super-nodes deployed in a non-uniform way (more nodes closer to the sink).

30. Dynamic aspects/Redeployment • We use the same number of nodes andseparate them in g groups g0, g1, …. The group g0 is deployedat t = 0sec and each gi (for 0 < i < g) is deployedat t = i x 200sec. • We also examine the effect of non-uniform redeployment for the nodes of groups g1, g2, … while the nodes of group g0 are always deployed uniformly.

31. Adaptive/local exploration protocols • The Adaptive Power Conservation Protocol (APCP) that locally and implicitly monitors the network conditions (density, energy) and accordingly adjusts towards good/optimal operation choices, in networks with node redeployment/heterogeneous sensors. • (I. Chatzigiannakis, A. Kinalis and S. Nikoletseas, in the Theory of Computing Systems (TOCS) Journal, 2007.) • Fault-tolerant and Efficient Data Propagation using Limited, Local, Additional Network Information, • (I. Chatzigiannakis, A. Kinalis and S. Nikoletseas, in the Journal of Parallel and Distributed Computing (JPDC), 2007)

32. Dynamic aspects/Mobility • Many, mobile sinks • We propose several sink mobility strategies for data collection that reduce energy a lot (I. Chatzigiannakis, A. Kinalis and S. Nikoletseas, ACM MOBIWAC 06)

33. Hybrid Worlds: A NanoPeers paradigm • several similarities and differences of the two “worlds”… • NanoPeers: a network of sensors • acting as lightweight peers in a P2P overlay • Hydrid layered models: several layers eg milli-peers coordinate micro-peers, micro-peers coordinate nano-peers, etc in the sense that higher order peers act as sinks for lower layers. • an example application scenario: parcel delivery • sensors (nano-peers) put on parcels • micro-peers put on boxes carrying several parcels • milli-peers put on (interconnected)warehouses • Goal: on-the-fly tracking of parcels

34. Thank you!