1. Exploiting Sink Mobility for Maximizing Sensor Networks Lifetime Z. Maria Wang, Emanuel Melachrinoudis Department of Mechanical and Industrial Engineering Northeastern University Stefano Basagni Department of Electrical and Computer Engineering Northeastern University IEEE HICSS 2005

2. Outline Introduction System Model Mathematical Formulation Calculating power consumption Parameters and variables Calculating Linear programming formulation Simulation Conclusions

3. Introduction --- background A Sink Sensor B Sensor nodes that are closer to sink consume their energy rapidly  Network partition Sensor nodes that are closer to sink consume their energy rapidly  Network partition

4. Introduction --- motivation The joint problems of determining the movement of the sink the sojourn time at different point A fair balancing of the energy depletion among the network nodes

5. Introduction --- goal Network lifetime is maximized Network lifetime : the time till the first node dies

6. System model --- environment Mobile sink Sensor

7. System model --- assumption The traveling time of the sink between two nodes is considered negligible The distance between two adjacent nodes in the grid equals the node’s transmission range Each sensor generates data packet at a fixed data rate

8. System model --- assumption i Mobile sink Sensor Sensor nodes communicate with the sink by sending data via multiple hops along the shortest path

9. Mathematical Formulation --- overview

11. Mathematical Formulation --- calculating power consumption The first order radio model is used For receiving : p r = k 1 β For transmitting : p t = k 2 (α 1 +α 2 d p ) β ≒ α 1 +α 2 d p = e p r + p t = k 1 β+ k 2 (α 1 +α 2 d p ) ≒ e (k 1 + k 2 )

12. Mathematical Formulation --- parameters and variables Parameters e 0 : Initial energy e : Energy consumption coefficient for transmitting or receiving one bit r : Rate at which data packets are generate : Data transmission rate from node i to node j while the mobile sink stays at node k ij k

13. Mathematical Formulation --- parameters and variables : Power consumption of node i when the sink sojourns at node k Variables t k : Sojourn time of the sink at node k z : Network lifetime

14. Mathematical Formulation --- calculating Mobile sink is co-located with node i Mobile sink is not co-located with node i receiving data + data of the node receiving data transmitting data i j1j1 j2j2 j4j4 j3j3 = e ( 2(receiving data ) + data of the node)

15. Mathematical Formulation --- calculating 0 1 2 3 012 3 4 4 UR VAUL HR LR VB HL LL k i j2j2 j4j4 j1j1 j3j3 l1l1 l2l2 x y

16. Mathematical Formulation --- calculating 0 1 2 3 012 3 4 4 k i j2j2 j4j4 j1j1 j3j3 l1l1 l2l2 x y Node i retransmits the packets originated at nodes j 3 and l 2 to node j 2 and those originated at nodes j 1 and l 1 to node j 4

17. Mathematical Formulation --- calculating i j2j2 j4j4 j1j1 j3j3 l1l1 l2l2 Node i receives at a rate 2r and transmits at a rate 3r, having therefore power consumption = e(5r) r/2 k

18. Mathematical Formulation --- calculating 0 1 2 3 012 3 4 4 i x y =e( 2( receiving data) + node’s data) =e( 2(12 X r/2 + 2r ) + r ) = e(17r) r/2 r r

19. Mathematical Formulation --- calculating 0 1 2 3 012 3 4 4 k x y e(r) e(2r) e(3r) e(2r) e(3r) e(r) e(2r) e(3r) e(4r) e(5r) e(r)e(2r) e(3r)e(5r) e(r) e(5r) e(11r) e(17r)

20. Mathematical Formulation --- l inear programming formulation The Linear Programming model below determines the sojourn times t k of the sink The energy consumes at each node i should not exceed the initial energy of that node

21. Mathematical Formulation --- l inear programming formulation Sink sojourn times for 8 × 8 networks The sink sojourns mostly at the four comers (for most of the time ) and in the grid central area

22. Mathematical Formulation --- l inear programming formulation Sink sojourn times for 8 × 8 networksSink sojourn times for 14 × 14 networks x10 4 We observes that the higher the network size, the lower the sojourn times at the corners 18217 4000~5000

23. Simulation

24. Residual energy snapshot after episode E1 The location of the static sink The sojourn area of the mobile sink

25. Simulation Residual energy snapshot after episode E2 The location of the static sink The sojourn area of the mobile sink

26. Simulation Residual energy snapshot after episode E3 The location of the static sink The sojourn area of the mobile sink

27. Simulation Residual energy snapshot after episode E4 The location of the static sink The sojourn area of the mobile sink

28. Simulation Residual energy snapshot after episode E5 The location of the static sink The sojourn area of the mobile sink

29. Conclusions Our proposed method can effectively achieve Network energy is more balanced among the network nodes Data flow bottlenecks can be more effectively avoided