1. Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks Xiao Wang, Xinbing Wang, Jun Zhao Department of Electronic Engineering Shanghai Jiao Tong University, Shanghai, China

2. Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks 2 Outline  Introduction  Background  Related works  Motivations  System Model and Performance Measures  Main Results and Brief Explanation  The Impact of Mobility and Heterogeneity  Concluding Remarks

3. 3 Background  Coverage is a basic concern in designing and implemen- ting wireless sensor networks.  Security surveillance  Intrusion detection  Environment monitoring, etc  Efforts made for addressing coverage problems fall into three main categories.  Blanket coverage  Barrier coverage  Sweep coverage Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks

4. 4 Related Works--I  An unreliable wireless sensor grid network with n nodes:  The network remains covered if [1] [1]  A random network in which the locations of nodes can be modeled as a stationary 2-dimensional Poisson point process:  The area coverage of the sensor network is [2] [2] Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks [1] S. Shakkottai, R. Srikant and N. Shroff, “Unreliable Sensor Grid: Coverage, Connectivity and Diameter,” INFOCOM, 2003. Diameter,” INFOCOM, 2003. [2] B. Liu and D. Towsley, “A Study on the Coverage of Large-Scale Sensor Networks,” International Conference on Mobile Ad-hoc and Sensor Systems, 2004. Conference on Mobile Ad-hoc and Sensor Systems, 2004.

5. Related Works--II  K-coverage in a mostly sleeping wireless sensor networks:  For random uniform deployment, all points in the operational region are almost k-covered if for some.( goes to infinity as and ) [3] ) [3] [3] S. Kumar, T. H. Lai and J. Balogh, “On K-coverage in a Mostly Sleeping Sensor Networks,” [3] S. Kumar, T. H. Lai and J. Balogh, “On K-coverage in a Mostly Sleeping Sensor Networks,” MobiCom, 2008. MobiCom, 2008. Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks 5

6. Related Works--III  Dynamic coverage in mobile wireless sensor networks:  Consider a sensor network at time t=0, with sensors moving according to random mobility model: 1. At any time instant t, the fraction of area being covered is 2. The fraction of are that has been covered at least once during time interval [0, t) is [4] [4] [4] B. Liu, P. Brass, O. Dousse, P. Nain and D. Towsley, “Mobility Improves Coverage of Sensor [4] B. Liu, P. Brass, O. Dousse, P. Nain and D. Towsley, “Mobility Improves Coverage of Sensor Networks,” MobiHoc, 2005. Networks,” MobiHoc, 2005. Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks 6

7. 7 Motivation  WSNs can achieve better balance between cove- rage performance and the cost of sensors if opp- ortune degree of heterogeneity is incorporated in- to the network.  Many applied WSNs are inherently mobile. Mobil- ity is found to improve various aspects of network performance.  In previous works, usually the sufficient condition is obtained instead of the critical condition. Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks

8. 8 Outline Introduction System Models and Performance Measures  Deployment Scheme  Sensing Strategy  Mobility Pattern  Performance Measures Main Results and Brief Explanation The Impact of Mobility and Heterogeneity Concluding Remarks Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks

9. 9 Deployment Scheme  Let the operational region of the WSN be an unit square and the square is assumed to be a torus.  Uniform Deployment Model --- n sensors are randomly and unifor- mly deployed in the operational region, independent of each other.  Poisson Deployment Model --- the locations of sensors are model- ed as the 2-dimensional Poisson point process with density para- meter n. Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks

10. 10 Sensing Strategy  Basically, the binary disc sensing model is em- ployed in the study. Let r denote the sensing radius.  There are u groups in this heterog- eneous network, u is a positive number invariant of n. Group consists of sensors with sensing radius. Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks

11. 11 Mobility Pattern  I.I.D. Mobility Model  Reshuffle at the beginning of each time slot.  1-Dimensional Random Walk Mobility Model Mobility Model  Classified into H-nodes and V-nodes;  Travel distance D along its dimension, D is a random variable uniformly D is a random variable uniformly distributed from 0 to 1; distributed from 0 to 1;  2-Dimensional Random Walk Mobility Model  Randomly and independently choose a direction ;  Randomly and independently select a velocity. Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks

12. 12 Performance Measures -- I  Asymptotic Coverage  Equivalent Sensing Radius (ESR) under i.i.d. mobility model:  ESR under 1-dimensional random walk mobility model:  If then is the critical ESR under the i.i.d. model. Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks

13. 13 Performance Measures -- II  K-Coverage at an Instant  A point is said to be k-covered at an instant t if it is sensed by at least k sensors.  Let denote the fraction of the whole region that is k-covered at instant t.  K-Coverage over a Time Interval  A point is said to be k-covered over a time interval T if it has been sensed by more than k sensors at the end of that interval.  Let be the fraction of the whole region that is k-covered during time interval T. Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks

14. 14 Outline Introduction System Models and Performance Measures Main Results and Brief Explanation  Main results  Brief explanation The Impact of Mobility and Heterogeneity Concluding Remarks Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks

15. 15 Main Results  Under the uniform deployment scheme:  With i.i.d. mobility model, the critical ESR is  With 1-dimensional random walk mobility model, the critical ESR is  Under the Poisson deployment scheme with the 2-dimensional random walk mobility model: , is the upper incomplete gamma function, defined as gamma function, defined as , where denotes the expected area covered by a sensor. Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks

16. 16 Brief Explanation – Dense Grid  Dense grid: Transform the coverage of all points within the operational region to the coverage of certain set of points. Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks

17. 17 Brief Explanation – Necessary Part  Proposition 1: In the WSNs with i.i.d. mobility model, if and the density of the dense grid is and the density of the dense grid is, then, then where. proof:  Therefore, is necessary for the WSN to achieve full coverage of the dense grid. Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks

18. 18 Brief Explanation – Sufficient Part  If where, then  is sufficient to guarantee the full coverage of the dense grid. Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks

19. 19 Brief Explanation – Failure Pr  Under the 1-dimensional random walk mobility model: Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks

20. 20 Outline Introduction System Models and Performance Measures Main Results and Brief Explanation The Impact of Mobility and Heterogeneity  Impact of Mobility  Impact of Heterogeneity Concluding Remarks Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks

21. 21 Impact of Mobility  We use the sensing energy model as. The average energy consumption of the mobile heterogeneous WSN is.  Assume the network to be homogeneous and evaluate the impact of mobility:  Under i.i.d. mobility model or the network is stationary:  Under 1-dimensional random walk mobility model:  Impact Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks

22. 22 Impact of Heterogeneity  Sensing Energy Consumption  Under i.i.d. mobility model:  Under 1-dimensional random walk mobility model: (, ) (, ) Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks

23. 23 Outline Introduction System Models and Performance Measures Main Results and Brief Explanation The Impact of Mobility and Heterogeneity Concluding Remarks Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks

24. 24 Concluding Remarks  Asymptotic coverage under uniform deployment scheme with i.i.d. and 1-dimensional random walk mobility model.  Impact of mobility and heterogeneity on sensing energy consumption.  The k-coverage under Poisson deployment scheme with 2- dimensional random walk mobility model. Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks

25. Questions? Thanks for listening !