Power Efficient Monitoring Management In Sensor Networks Zelikovsky Georgia State Joint work with P. Berman Pennstate G. Calinescu Illinois IT Y. L i Georgia State C. Shah Georgia State

Outline Sensor Network Model Maximum Sensor Network Lifetime Problem Centralized Algorithms Distributed Algorithms Result Conclusion

The set of sensors largely exceeds the necessary amount to monitor R Sensor Network Model All sensor nodes have the same sensing range r. Each sensor monitor a disc region Ri Each sensor has a battery life bi The set of sensors largely exceeds the necessary amount to monitor R

Data Structure Grid Data Structure: A set of grid points (gg) to discretize R. Partition all grid points into ‘fields’. A field is defined as a subset of grid points covered by the same set of sensors. New Data Structure: Face: points covered by same set of sensors forms the equivalence class, called face. Number of Intersection points are at most n(n-1) Number of the faces o(n2) Any face can not be covered partially. face 1 face 8 face 7 face 6 face 11 face 2 face 3 face 4 face 5 face 10 face 9 face 12 face 13

Sensor Cover Problem And Sensor Lifetime Problem Sensor cover - A set of sensors C covering monitored area R. Generalized q-Cover q[0,1] problem, e.g. q = 0.9, 90% monitored area covered by sensors. For given constant q[0,1], the monitored region R with area M, and a set of sensors Find subset {p1, p2, … , pt} of sensors. such that  w (pi ) min with the constraint Partial q-Coverage problem is equivalent to the weighted set q-cover problem. Sensor lifetime problem is a packing LP problem LP formulation Maximize: Subject to: CMij = 1 if sensor j covers face i 0 if sensor j doesn’t cover face j { bi = lifetime of sensor i tj a time variable for each cover cj. Packing LP is defined as: max{cTx| Ax ≤ b, x ≥ 0 } — where A , b and c have positive entries; — the dimensions of A as mn.

Maximizing the Sensor Network Lifetime Problem (SNLP) Multiple sensor covers are found during the life time of the sensor networks Disjoint set covers: If any sensor in sensor-cover is died then new sensor cover is found Every sensor participate in only one sensor cover It gives life time of 2 unit for the scenario in fig. Non-Disjoint set covers: A sensor can participate in more than one sensor cover. Time ti is given to sensor cover i schedule ({p1, p2}, 1), ({p1 p3}, 1), ({p3, p2}), 1) gives the life time of 3 units P3 monitored region R P2 P1 Each Sensor has 2 battery unit

Centralized Algorithmic solution for SNLP (Garg-Könemann / Tight / CPLEX ) Garg-Könemann finds the life time for each sensor cover and divides it by constant number based on epsilon and number of iteration Tight solution is obtained using the finding the tightest energy constraint from Garg-Könemann solution CPLEX After Garg-Könemann finds the all the sensor-covers, the best time schedule for each sensor covers can be obtained using CPLEX Constraints: satisfying the battery requirements Objective: Maximizing the life time Garg-Könemann is primal dual algorithm to solve the packing LP. It finds the solution using iterations, which can be controlled by epsilon

Test Result (Life Time) Number of Nodes Sensing Range Life Time GK Tight CPLEX 100 18.11 19.48 20.00 150 21.22 22.49 23.61 18.28 19.60 29.35 31.04 32.86 200 20.32 21.52 23.28 37.46 39.40 40.00 250 19.68 20.62 21.58 63.23 67.58 71.67 300 21.44 22.53 23.89 74.32 80.31 87.44 350 25.01 26.25 27.78 95.55 103.70 113.61 400 28.61 29.75 30.00 108.45 117.31 123.08

Test Result (Run Time) Number of Nodes Sensing Range Run Time GK Tight CPLEX 100 3.55 5.06 12.39 150 5.75 7.58 17.87 6.86 9.63 23.09 17.55 21.52 43.31 200 13.26 17.10 42.26 45.83 53.00 90.98 250 20.74 25.81 57.03 120.21 135.88 228.48 300 34.11 40.70 81.49 220.28 242.91 382.78 350 53.37 62.60 118.40 459.39 495.52 765.16 400 79.40 91.67 161.27 795.01 841.47 1165.14

Distributed Algorithms and State Diagram Vulnerable sensors change it state into --Active when there is a face which is not covered by any other active or vulnerable sensor -- Idle state if all its faces are covered by one of two types of sensors: active or vulnerable sensors with a larger energy supply Active/Idle sensors change its state into vulnerable state if any neighboring sensor becomes vulnerable. G Permanent Terminated If there is a face not covered by any other active or vulnerable sensor If all its faces are covered by active or vulnerable sensors with a larger energy supply D or upon reaching the reshuffle-triggering threshold value When neighbor node goes into vulnerable state If current sensor is the only sensor covers one or more faces F&G When sensor nodes exhausts all its batteries Vulnerable E F A B Active Idle C D

Correctness of distributed algorithm Theorem: The distributed algorithm always finds the minimal sensor cover. Lemma: The distributed algorithm is deadlock-free. Among vulnerable sensors there is always one that either should become active or idle On the contrary, assume that each vulnerable sensor covers at least one face non-covered by active sensor and does not have an individual face Then there is always vulnerable sensor which is not a champion for any of its faces: Sensor 1 should be a champion for face say a, but a is not individual so there should be a sensor 2 covering face a and having less batteries than 1. Similar, 2 is a champion for a face say b which is also covered by 3 who has less batteries than 2, and so on. Since all the sensors 1,2, … have different battery supply, they all are different Resulted active set is minimal since any active sensor has individual face Resulted active set covers all faces since a sensor cannot go to idle state if it has individual face Sensors 1 2 3 4 … n Faces a b c d e

Reshuffle-Triggering Threshold Value Number of Nodes Sensing Range Reshuffle-Triggering Threshold Value 1 2 3 5 10 100 19.33 18.67 18.33 15.00 10.00 150 21.67 21.33 20.00 18.00 17.67 16.67 31.33 30.00 28.33 25.00 23.33 200 20.33 39.33 38.67 37.33 35.00 33.33 250 19.67 13.33 67.67 64.67 63.33 60.00 50.00 300 81.67 78.00 75.33 70.00 350 26.67 25.33 108.33 104.00 100.33 93.33 80.00 400 29.33 28.67 118.00 114.00 112.00 106.67

New distributed algorithms Consider the following case: ... … …. Sensor with life time of 100 Face Sensor with life time of 1 Optimum life time: 100 + 100 = 200 Life time by previous distributed algorithms: Less than 102 Updated Algorithms: (Modified transition rules A and B in state diagram) If it’s the only sensor cover the face If not A and has the smallest battery energy among those which also cover the sink

Test Result Conclusion For Maximizing the Sensor Network Lifetime Problem (MSNLP), centralized and distributed algorithms are proposed and has been compared in simulated environment Centralized algorithms have trade-off between life time and run time Distributed algorithms have trade-off between life time and communication overhead