Probabilistic Coverage and Connectivity in Wireless Sensor Networks

1. Probabilistic Coverage and Connectivity in Wireless Sensor Networks Hossein Ahmadi hahmadi@cs.sfu.ca Simon Fraser University

2. Outline • Introduction • Probabilistic Coverage • Background • Probabilistic Coverage Protocol • Evaluation • Probabilistic Connectivity • Background • Probabilistic Connectivity Maintenance Protocol • Evaluation • Conclusion and Future Works Simon Fraser University

3. 1. Introduction • Every sensor can detect an event occurring within its sensing range, and communicate with sensor inside the communication range. • Objective: keep all points in the area coveredand every pair of sensors connected. In many of the previous works, sensing and communication ranges are assumed to be uniform disks: unrealistic Simon Fraser University

4. 1. Motivation • Using disk model may lead to: • Deploying unnecessary sensors -- incurring higher cost. • Activating redundant sensors -- increases interference, wastes energy. • Decreasing the lifetime of the sensor network. • Furthermore: • Current protocols may not function properly in real environments. • No assessment of the quality of communication between nodes. • Realistic models: • Difficult to analyze. • More complicated algorithms. Simon Fraser University

5. 1. Thesis Contributions • Distributed probabilistic coverageprotocol • Minimizes the number of activated nodes. • Consumes much less energy than the others. • Quantitative measure of communication quality between nodes • Analytically derive this quantity for common node deployment schemes. • Probabilistic connectivity maintenance protocol • Explicitly accounts for the probabilistic nature of communication links. • Achieves a given target communication quality. • Integrated coverage and connectivity maintenance protocol • Achieves a given target communication quality between nodes while maintaining the area covered. Simon Fraser University

6. 2.1 Disk Sensing Model and Coverage • Using the disk model, the area is covered if any arbitrary point in the area has a sensor within the sensing range. • The disk sensing makes coverage maintenance protocols less complicated to design and analyze. Covering an area with disks of same radius can optimally be done by placing disks on vertices of a triangular lattice. Simon Fraser University

7. 2.1 Previous Works • Several works conduct analytical analysis on coverage [KLB04, SSS05]. • Several distributed coverage protocols have been proposed : • OGDC [ZH05] • CCP [XWZ+05] • PEAS [YZC+03] • Ottawa [TG02] • Several studies have argued that probabilistic sensing models are more realistic. [AKJ05, CYA+03, LT04, ZC04, ZC05]. Simon Fraser University

8. 2.1 Probabilistic Sensing Models • Probabilistic sensing model has also been studied in literature • Several Models have been proposed [AKJ05, CYA+03, ZC05] • Distributed probabilistic coverage protocol : CCANS [ZC05] Simon Fraser University

9. 2.2 Probabilistic Coverage • Definition: An area A is probabilistically covered with threshold parameter θif for every point x. • pi(x) is the probability that sensor i detects an event occurring at x. Definition: A point x is called the least-covered point of Aif for all y in A. Simon Fraser University

10. 2.2 PCP: A Probabilistic Coverage Protocol • We propose Probabilistic Coverage Protocol (PCP): • Ensure that the least-covered point in the monitored area is covered by a probability of at least θ. • Main idea: Activate a subset of deployed sensors to construct an approximatetriangularlattice. • We divide the area into small triangles: • To implement the idea of the protocol with no global knowledge. • To work optimally under the disk sensing model as well as probabilistic models. • PCP is general and can use any deterministic or probabilistic sensing model. Simon Fraser University

11. 2.2 PCP: A Probabilistic Coverage Protocol • s is the maximum separation between any two active sensors. • Theorem: Under the exponential sensing model we have: Simon Fraser University

12. 2.2 PCP: A Probabilistic Coverage Protocol • We first assume: • Nodes know their location. • Nodes are time synchronized. • Single starting node. • PCP works in rounds of Rseconds each. • In the beginning of each round, all nodes start running PCP independent of each other. Simon Fraser University

13. 2.2 PCP: A Probabilistic Coverage Protocol • One node randomly enters active state. The node sends an activation message Closest nodes to vertices of the triangular mesh are activated. Activated nodes send activation messages. Simon Fraser University

14. 2.2 PCP: A Probabilistic Coverage Protocol • Every node receiving an activation message calculates an activation timer Taas a function of its closeness to the nearest vertex of the hexagon: Simon Fraser University

15. 2.2 PCP: A Probabilistic Coverage Protocol • Definition:δ-circle is the smallest circle drawn anywhere in the monitored area such that there is at least one node inside it. • Optimize the convergence time and saves the energy. • The diameter δ is computed for deployment with: • Grid distribution: • Uniform random distribution: Simon Fraser University

16. 2.2 PCP: A Probabilistic Coverage Protocol • Multiple Starting Nodes: • Faster protocol convergence. • Number of starting nodes is controlled by setting startup timer. • May increase total number of activated sensors. • Time Synchronization: • Protocol needs only coarse grained synchronization • Simple synchronization schemes suffice. Simon Fraser University

17. 2.3 Analysis : 3 Theorems • Correctness and Convergence Time: The PCP protocol converges in at most time units. • Convergence time only depends on the size of area. • Shows that PCP can scale. • Activated Nodes and Message Complexity: The number of nodes activated by the PCP protocol is at most • The same as the number of exchanged messages in a round. • Very few in comparison with total number of deployed sensors. • Network Connectivity: The nodes activated by PCP are connected if the communication range of nodes rc is greater than or equal to s. • Holds for most real sensors. Simon Fraser University

18. 2.4 Evaluation • We implemented PCP in NS-2 and in our own packet level simulator. • We deploy 20,000 nodes in a 1km x 1km area. • We verify correctness of our protocol and show it is robust against several parameters. • We also compare it against state-of-the-art protocols: • Probabilistic coverage protocol : CCANS • Deterministic coverage protocols : CCP, OGDC • We repeat each experiment 10 times and report the average, and minimum and maximum if they don’t clutter plots. Simon Fraser University

19. 2.4.1 Validation & Savings • Our analytical results are conservative. • PCP performs better in simulation. • Significant savings from probabilistic models. Simon Fraser University

20. 2.4.2 Robustness of PCP • PCP is robust against location inaccuracy and imperfect time synchronization. Simon Fraser University

21. 2.4.3 Comparison versus CCANS • PCP outperforms CCANS in terms of total energy consumed and network lifetime. Simon Fraser University

22. 2.4.4 Comparison versus OGDC, CCP • PCP outperforms both OGDC and CCP protocols in terms of energy consumption. Simon Fraser University

23. 3. Probabilistic Connectivity • Another fundamental problem in WSNs. • A network is connected if every pair of nodes can communicate with each other. • Deterministic Connectivity: Many previous works represent the network with an undirected unweighted graph. • There is an edge between two nodes if they are within the communication range of each other. • The communication range is typically assumed to be a disk. • Network connectivity is equivalent to graph connectivity. Simon Fraser University

24. 3.1 Probabilistic Communication Range • Communication ranges follow probabilistic models [ABB+04, KNE03]. • Two wireless nodes can not said to be ‘connected’ or ‘disconnected’. • It is neither sufficient nor precise to state that the network is simply connected. • A quantitative measure of the quality of communications in the network is needed. Simon Fraser University

25. 3.2 Connectivity under Probabilistic Model • Node-to-node packet delivery rate: the probability that vcorrectly receives a packet transmitted by u, without any retransmission by the MAC layer. • Definition: The network delivery rate,α,of a sensor network is the minimum packet delivery rate between any pair of nodes. Simon Fraser University

26. 3.2 Computing Network Delivery Rate • We derive lower bounds on the network delivery rate assuming: • All sensors use the same probabilistic communication model. • Links starting at the same sender node have independent delivery rates. • We only consider the delivery rates between immediate neighbors. Simon Fraser University

27. 3.2 Computing Network Delivery Rate • The network delivery rate, α,is lower bounded in: • Triangular mesh with link deliver rate of p by: • Square mesh with link deliver rate of p by: • Uniform random deployment by: Simon Fraser University

28. 3.3 Probabilistic Connectivity Maintenance Protocol • We propose a connectivity maintenance protocol (PCMP): • Explicitly accounts for the probabilistic nature of communication. • Goal: To activate a subset of deployed nodes with the network deliver rate of at least α. • PCMP activates nodes to form an approximate triangular mesh. • We choose triangular mesh for two reasons: • Activating nodes on the triangular mesh has been shown to be optimal, in case of deterministic connectivity. • Our analysis provide tighter lower bound for triangular mesh. Simon Fraser University

29. 3.3 Probabilistic Connectivity Maintenance Protocol • The spacing between activated nodes should be such that we have • p is the average delivery rate between two nodes and is given by (for the log-normal shadowing model): • PCMP works with the same activation mechanism as PCP. Simon Fraser University

30. 3.4 Integrated Coverage and Connectivity Protocol • We integrate our connectivity maintenance protocol with our coverage protocol. • dθ: The spacing required between nodes to guarantee θ coverage. • dα: The spacing required between nodes to guarantee α connectivity. • To achieve both probabilistic coverage and probabilistic connectivity at the same time, we activate nodes on an approximate triangular mesh with spacing min(dα, dθ). Simon Fraser University

31. 3.5 Evaluation of PCMP • We use the following experimental setup: • We use NS-2 simulator for all protocols. • We deploy 1,000 nodes in a 1km x 1km area. • We use MicaZ radio interface parameters. • We use Log-normal shadowing propagation model. • We validate the correctness of PCMP and our analysis. • We compare our PCMP against two state-of-the-art connectivity protocols SPAN and GAF. • Also, we compare it against an integrated coverage and connectivity protocol, CCP-SPAN. Simon Fraser University

32. 3.5.1 Validation of PCMP • Our lower bounds on network delivery rate are conservative. Simon Fraser University

33. 3.5.2 Validation of Integrated Protocol • Our PCMP protocol can provide both coverage and connectivity at the same time. Simon Fraser University

34. 3.5.3 Comparison versus SPAN, GAF • Our protocol outperforms SPAN and GAF in terms of total energy consumption and network lifetime. Simon Fraser University

35. 3.5.4 Comparison versus CCP-SPAN • Our integrated protocol outperforms CCP integrated with SPAN in terms of number of activated nodes and total energy consumption. Simon Fraser University

36. 4.1 Conclusions • Distributed probabilistic coverage protocol (PCP) • Energy efficient. • Increases the network lifetime. • Robust against several factors. • Quantitative measure of the quality of communication • Analysis on different deployment schemes. • Probabilistic connectivity maintenance protocol (PCMP) • Explicitly accounts for the probabilistic nature of communication links. • Outperforms others in literature. • Integrated coverage and connectivity maintenance protocol • Achieves a given target communication quality while keeping the area covered. • To the best of our knowledge, this is the only protocol that provides probabilistic coverage and probabilistic connectivity at the same time. Simon Fraser University

37. 4.2 Future Works • Variable Sensing and Communication Models. • Adaptive Sensing Models. • Adaptive Communication Models. • Network Delivery Rate under Realistic MAC Protocols. Simon Fraser University

38. Publications • M. Hefeeda and H. Ahmadi. A probabilistic coverage protocol for wireless sensor networks. In Proc. of IEEE International Conference on Network Protocols (ICNP'07), Beijing, China, October 2007. • M. Hefeeda and H. Ahmadi. Network connectivity under probabilistic communication models in sensor networks. In Proc. of IEEE International Conference on Mobile Ad-hoc and Sensor Systems (MASS'07), Pisa, Italy, October 2007. • M. Hefeeda and H. Ahmadi. Energy-Efficient Protocol for Deterministic and Probabilistic Coverage in Sensor Networks. Submitted to ACM/IEEE Transactions on Networking. Simon Fraser University