1. Spatiotemporal Multicast in Sensor Networks Presenter: Lingxuan Hu Sep 22, 2003 Qingfeng Huang, Chenyang Lu and Gruia-Catalin Roman

2. Outline Problem Statement Background Parameter Analysis Optimization Discussion

3. Introduction  Methods of disseminating information:  Unicast  Broadcast  Multicast  Geocast  Mobicast

4. Scenario Thousands of sensor nodes communicating wirelessly to track a vehicle Sleeping nodes Awaken nodes

5. Scenario Wake up just in time Sleeping nodes Awaken nodes

6. Introduction (cont.) Examples

7. Introduction (cont.)  Geocasting GeocastRe-geocast L-W slack time

8. Introduction (cont.)

9.  Design Concerns Reliable delivery Make the initialization time as short as possible Reduce the slack time Reduce the retransmission overhead

10. Simple Mobicast Hold-and-forward strategy  In current delivery zone: deliver and forward  Will be in delivery zone soon: hold and forward at the time the delivery zone reaches the node  Other cases: Ignore the message Has minimal delivery overhead and has good slack time characteristics Not reliable In Current delivery zone Will be in delivery zone soon Other nodes

11. Problem of Simple Mobicast There is a hole between X and other nodes in the delivery zone. The protocol fails to deliver the mobicast message to node X To deliver reliably, some nodes that are not in the delivery zone have to participate in message forwarding. Delivery zone Hole How to determine who should participate?

12. Delivery ZoneFuture Delivery Zone Forwarding Zone Headway Distance Hold & Forward Zone Mobicast Framework

13. Two phases  Initialization phase:  Cruising phase:

14. What is the size and shape of forwarding zone? What is the headway distance? What is the initialization time? Undetermined Parameters

15. ∆-Compactness G(V, E): geometric graph d(i, j): Euclidean distance between node i and j M(i, j): Set of shortest hop network paths between node i and j đ(i, j): The minimum Euclidean length of all paths in M(i, j), also called S2 distance ∆-compactness of two nodes: δ(i, j) = d(i, j) / đ (i, j) ∆-compactness of network: δ = MIN i,j δ(i, j) ∆-dilation: The inverse of ∆-compactness ADEB, 3 hops d(A, B) ACB, 2 hopsđ(A, B) M(A, B)

16. Delivery Guarantee

17. An example ∆-compactness δ = MIN i,j d(i, j) / đ (i, j) For any two nodes A and B in the network, there must exist a shortest network path that is inside the ellipse which has A and B as its foci with eccentricity δ 10 6 8 5 5 5 d(A, B)=10, d(A, D)=8, d(B, C)=6, d(A, C)=d(C, D)= d(D, B)=5 δ(A,B)=10/15δ(A,D)=8/10δ(B,C)=6/10δ(A,C)=5/5δ(C,D)=5/5δ(D,B)=5/5 For A, B. c = 10/2 = 5, c/a = e = & = 0.6, so a=25/3, b=20/3 δ = MIN (10/15, 8/10, 6/10, 5/5, 5/5, 5/5) = 0.6 x 2 /(25/3) 2 + y 2 /(20/3) 2 = 1

18. Γ -Compactness If a network’s Γ-compactness value is γ, then any two nodes in the network separated by a distance d must have a shortest path no greater than d/γ hops h(i, j): The minimum number of network hops between nodes i and j d(i, j): The Euclidean distance between node i and j Γ-Compactness: γ = min d(i, j) / h(i, j) 10 6 8 5 5 5 d(A, B)=10, d(A, D)=8, d(B, C)=6, d(A, C)=d(C, D)= d(D, B)=5 γ(A,B)=10/3γ(A,D)=8/2γ(B,C)=6/2γ(A,C)=5/1γ(C,D)=5/1γ(D,B)=5/1 A, B has path no more than d/γ= 10/3 = 3.3 hopsγ = MIN (10/3, 8/2, 6/2, 5/1, 5/1, 5/1) = 3

19. Definition  Τ 1 : the max one-hop latency of the network  Sd: the diagonal length of a delivery zone  v: the traveling speed  γ: Γ-Compactness value. γ = min d(i, j) / h(i, j)  d s : headway distance Headway Distance d Diagonal length Sd v V d s = vΤ1[Sd/γ] Headway Distance

20. Simulation -Environment NS-2 simulator 800 sensor nodes 1000x400m area Circular delivery zone

21. Mobicast - Protocol  1. if ( ˜m ) is new and t < T  2. cache this message  3. if the value of the delta field is zero  4. use local delta value for computation  5. else  6. use the value in the packet for computation  7. end if  8. if (I am in current forwarding zone F[t])  9. broadcast ˜m immediately ;  // fast forward  10. if (I am in current delivery zone Z[t])  11. deliver data D to the application;  12. else  13. compute my td[in];  14.if td[in] exists and td[in] < T  15. schedule delivery of data D to the application layer at td[in];  16. end if  17. end if  18. else  19. compute my tf[in];  20. if tf [in] exists  21.if t0≤tf [in] ≤ t  22. broadcast ˜m immediately ;  // catch-up!  23. else if t < tf[in] < T  24. schedule a broadcast of ˜m at tf[in];  //hold and forward  25. end if  26. end if  27. end if  28. end if

22. Simulation result

23. Linear

24. Simulation Result (cont) The delivery ratio increases when node density or forwarding size increases The slack time of just-in-time delivery is much better than that of ASAP delivery Density Forwarding Zone Size

25. Conclusions  Propose a new and interesting application  The assumptions are expensive  The math result can’t be directly applied to real application  The adaptive mobicast need to be further explored