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Spatiotemporal Multicast in Sensor Networks
Presenter: Lingxuan HuSep 22, 2003
Qingfeng Huang, Chenyang Lu and Gruia-Catalin Roman
OutlineOutline
Problem Statement BackgroundParameter AnalysisOptimizationDiscussion
ScenarioScenario
Thousands of sensor nodes communicating wirelessly to track a vehicle
Sleeping nodesAwaken nodes
ScenarioScenario
Wake up just in time
Sleeping nodesAwaken nodes
More examplesMore examples
Observations
The delivery zone is moving over time
Just-in-time delivery instead of ASAP delivery is preferred
Background: MulticastBackground: Multicast
IP multicast identifies the recipients by their subscription to a common multicast IP address.Geocast identifies the set of recipients by the geographical locations of the relevant parties.
Limitation of GeocastLimitation of Geocast
Geocast assume the information to be delivered as soon as possible
An early delivery of the wake-up call is likely to waste the precious power resources
Slack and Overhead Slack and Overhead
Rectangle A—C: Initial geocast areaB: The point of re-issuing requestL: The length of the geocast areaW: The distance between B and CVa: The speed of soldierVp: The speed of maximum message
propagation speed
The number of extra radio transmission per delivery Mw ~ W/(L-W)
The average earliness of the nodes receiving message ts = (L-W)(1/Va – 1/Vp)/2
Geocast has fundamental conflict in this application
GeocastRe-geocast
L-W
Mobicast ExamplesMobicast Examples
A mobicast session is specified by a tuple (m, Z(t), Ts, T)Figure (a) shows a rectangular delivery zone moving upwardFigure (b) shows a more general scenario where the delivery zone can change its direction, size and shape over time
How to decide the shape and direction of the delivery zone?
Design ConcernsDesign ConcernsReliable deliveryMake the initialization time as short as possible Reduce the slack time Reduce the retransmission overhead
Simple MobicastSimple 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 characteristicsNot reliable
In Current delivery zone
Will be in delivery zone
soon
Other nodes
Problem of Simple Mobicast
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?
Mobicast FrameworkMobicast Framework
Delivery zone: the area that message should be delivered
Forwarding zone: The area that message should be forwarded, which is some distance ahead of the delivery zone
Headway distance: The physical distance between the forwarding zone its delivery zone
Hold & Forward Zone: The area that receive the message before entering the forwarding zone
Delivery Zone
Future Delivery ZoneForwarding Zone
Headway Distance
Hold & Forward Zone
Mobicast FrameworkMobicast Framework
Two phases – Initialization phase: communicate the message in an ASAP fashion
to “catch-up” with the spatial and temporal demands of its specification
– Cruising phase: The forwarding zone moves at the same velocity as the delivery zone
Just-in-time – In forwarding zone: forward message immediately– Will be in forwarding zone: hold and forward at the time
becoming member of the forwarding zone– Other cases: Ignore the message
What is the size and shape of forwarding zone?What is the headway distance?What is the initialization time?
Undetermined Parameters
Undetermined Parameters
∆-Compactness∆-Compactness
G(V, E): geometric graphd(i, j): Euclidean distance between node i and jM(i, j): Set of shortest hop network paths between node i and jđ(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 = MINi,j δ(i, j) ∆-dilation: The inverse of ∆-compactness
ADEB, 3 hops
d(A, B)
ACB, 2 hops
đ(A, B)
M(A, B)
Delivery GuaranteeDelivery Guarantee• Math Concepts
x2/a2+y2/b2 = 1 c = sqrt(a2-b2) Eccentricity e = c/a
• Delivery guarantee– The ellipse that has A
and B as its foci and with eccentricity e = & (network ∆-compactness value) contains a shortest network path inside it.
Fociac b
An exampleAn example
∆-compactness δ = MINi,jd(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
10685
55
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)=10/15 δ(A,D)=8/10 δ(B,C)=6/10 δ(A,C)=5/5 δ(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
x2/(25/3)2 + y2/(20/3)2 = 1
Γ-CompactnessΓ-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)
10685
55
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)=10/3 γ(A,D)=8/2 γ(B,C)=6/2 γ(A,C)=5/1 γ(C,D)=5/1 γ(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
K-coverK-coverThe k-cover of a convex polygon P is defined as the locus of all points p in the plane such that there exists two points q and r in the polygon P that satisfy the constraints d(p, q) + d(p, r) ≤ kd(q, r)
K-cover of a line connecting two points i and j is exactly the ellipse of eccentricity 1/k with foci at i and j.
r
k*r
K-cover of a circle with radius r is a concentric circle of radius k*r
?
K-cover of arbitrary polygon is hard to compute
Headway DistanceHeadway Distance
Definition Τ1: 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) ds: headway distance
Headway Distance d
Diagonal length Sd vV
Result ds = vΤ1[Sd/γ]Discussion The longer transmission delay, the longer headway distance The larger delivery zone size, the longer headway distance The faster moving speed, the longer headway distance The smaller Γ-Compactness, the longer headway distance
Summary of Parameter Analysis
Summary of Parameter Analysis
Based on known network topology, we can compute the upper bound of forwarding zone and headway distance to ensure reliable deliveryThe forwarding zone is k-cover of the delivery zoneThe headway distance is also computable
Optimization—Real Application
Optimization—Real Application
The math result can ensure 100% delivery, however
Can the result be applied to real application?
Can we make a trade-off between delivery guarantee and communication overhead?
Can we use a local notion of compactness and the forwarding zone be adaptively adjusted to the local compactness values?
Pairwise Compactness Distribution
Pairwise Compactness Distribution
ObservationsThe value of ∆-compactness of the network is less than 0.290% of node pairs have ∆-compactness greater than 0.6200% of forward cost may be saved by sacrificing delivery guarantee to 90%
ApproachesDesign a sensor network with high compactness to support spatial temporal communicationUse a smaller forwarding zone than the one needed for an “absolute” delivery guaranteeUse a protocol that adapts to the local compactness conditions rather than the global one
∆-compactness of the network
More than 90% ∆-compactness value >= 0.6
(1/0.2-1/0.6)/(1/0.6)
Impact of Node Density
Impact of Node Density
The network dilation decreases as the node density increasesThere have a saturation point at a moderate densityThe occurrence of lower extreme compactness value is a rare event
Saturation Point
Lower bound of the top 99% δ
Optimistic Mobicast: Environment
Optimistic Mobicast: Environment
NS-2 simulator, 800 sensor nodes on a 1000x400m areaCircular delivery zonePacket Header
– Message type– delivery zone size (radius)– sender packet sequence number– delivery zone velocity (x and y components)– sender location (x and y coordinates)– delta factor– sending time– gamma factor– message lifetime
Optimistic Mobicast: Protocol
Optimistic 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
Simulation ResultSimulation Result
Metrics– Delivery ratio– Forwarding overhead– Forwarding zone factor
Results– The delivery ratio is 100% after forwarding zone factor reach 2.5– The forwarding overhead increases linearly as the forwarding zone
factor increases
Linear
Simulation Result (cont)
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
Den
sity
Forwarding Zone Size
Adaptive MobicastAdaptive Mobicast• Protocol
– The local compactness is computed for each node to a depth of five hops and within a 100 meter radius.
– A delivery zone node will replace the delta value in the packet by its local delta value before forwarding it.
– A non delivery zone node will not change the delta value in packet.
• Result– Appear to guarantee 100% delivery– Relatively high transmission overhead (because holes are common in
network)
Adaptive MobicastAdaptive Mobicast
Adaptive forwarding zone
Hole
Example of Adaptive Mobicast
Example of Adaptive Mobicast
The protocol adapts to the local topology, and achieves 100% delivery even in the presence of a large hole in its path
The radio transmission overhead is less than 1.2 transmissions per delivery (195 extra radio transmission for 164 deliveries)
DiscussionDiscussion
Mobicast enables applications to have control over the velocity of information dissemination across the space. However
The underlying routing protocol can be improved
The one-hop transmission latency may be unpredictable
The movement of delivery zone may be arbitrary
More CommentsMore Comments
Comments on assumptionsLocation awareness – May be expensive though reasonable– Can we track vehicles without location awareness?
Known network topology– Not applicable to large scale or mobile networks– Adaptive mobicast has advantages over mobicast with
weaker assumption
Conclusions and Future work
Conclusions and Future work
Conclusion– Propose a new and interesting application– Successfully change the problem to a mathematical
model– Analyze the upper bound of parameters for reliable
delivery– The assumptions are expensive– The math result can’t be directly applied to real
application– The adaptive mobicast need to be further explored
Future work– Adaptive mobicast– Other interesting real-time applications
ReferencesReferences
• J. C. Navas and T. Imielinski. Geocast – geographic addressing and routing. In Proceedings of MobiCom’97, pages 66-76, 1997
• Y. Ko and N. Vaidya. Geocasting in mobile ad hoc networks: Location-based multicast algorithms. TR 98-018, Texas A&M university, 1998.
• Q. Huang, C. Lu and G.-C. Roman. Spatiotemporal multicast in sensor networks. WUCSE 18, Washington University in Saint Louis, 2003.
• Q. Huang, C. Lu and G.-C. Roman. Design and analysis of spatiotemporal multicast protocols for wireless sensor networks. WUCS-03-45.
Related Work – RAPRelated Work – RAP
• RAP: A Real-Time Communication Architecture for Large-Scale Wireless Sensor Networks.
A
B
CE
HIGH
LOW
Related Work – LSRPRelated Work – LSRP
• LSRP: Local Stabilization in Shortest Path Routing
Containment Wave
Fault Propagation WaveInitiate a “Containment” action that moves faster than the “Fault Propagation” action.
Related Work – Trajectory
Related Work – Trajectory
Source
Destination
• Trajectory Based Forwarding and Its Applications
Trajectory
Related Work – SPEEDRelated Work – SPEED
23
5
9
10
7
DelayBoo
411
6
13
12Packet 1
Packet 1
Beacon
Packet 2
Packet 2
Packet 2
Packet 2
Packet 2
• SPEED: A Stateless Protocol for Real-Time Communication in Sensor Networks.
Related Work – MobicastRelated Work – Mobicast
• Spatiotemporal Multicast in Sensor Networks.
Just in Time Delivery
ComparisonComparison
Mobicast
SPEED
Trajectory
LSRP
RAP
N/A
N/A
Controlled
Shortest
N/A
Space
Controlled
Fastest
N/A
N/A
N/A
Time
N/A
N/A
N/A
N/A
Priority
Context