1. Three-Dimensional Broadcasting with Optimized Transmission Efficiency in Dense Wireless Networks Presented by Prof. Jehn-Ruey Jiang National Central University, Taiwan

2. Outline  Introduction  Related Work  Our Solution: Hexagonal Prism Ring Pattern 3D Optimized Broadcasting Protocol (3DOBP)  Performance Comparisons  Conclusion 2

3. Outline  Introduction  Related Work  Our Solution: Hexagonal Prism Ring Pattern 3D Optimized Broadcasting Protocol (3DOBP)  Performance Comparisons  Conclusion 3

4.  3D wireless networks are deployed in Multi-storey building (or warehouse) Outer space (gravity-free factory) Ocean (underwater sensor network) (acoustic but not wireless)  We assume the network is dense; i.e., there are many nodes within a node’s wireless transmission area.  3D broadcasting A source node disseminates a broadcast message (e.g., control command or reprogramming code) to every node in the network. Broadcasting in 3D Wireless Networks 4

5.  We’d like to apply a certain structure as the underlay. 5 Let’s first examine some special structures!

6. Honeycomb – hexagonal lattice (grid) 6 Assume we’d like to use equal-radius circles to cover a plane. If the centers of circles are located at the centers of cells of a hexagonal grid, then we’ve got the minimum number of circles.

7. 7 As we are talking about 3D broadcasting, we focus on the 3D honeycomb (i.e., hexagonal grid with thickness), which consists of hexagonal prisms.

8. 8 Hexagonal Prism (8 faces) Cube (6 faces) Rhombic Dodecahedron (12 faces) Truncated Octahedron (14 faces)

9.  A simple protocol for broadcasting The source node sends out the broadcast message Every other node rebroadcasts the message once It is likely that every node gets the message  Drawbacks: Broadcast storm problem (too many collisions) Low transmission efficiency due to a lot of redundant rebroadcast spaceFlooding 9 Redundant rebroadcast space

10. Transmission Efficiency The theoretical upper bound of transmission efficiency is 0.61 for the 2D plane, and 0.84 for the 3D space. 10 COST BENEFIT

11.  Goal: Selecting as few as possible rebroadcast nodes to forward the message sent by the source node to fully span all nodes in the network (coverage) to keep all rebroadcast nodes connected (connectivity) to achieve the optimized transmission efficiency to save energy to reduce collision to prolong the network lifetime Optimized Transmission Efficiency 11 Selecting 4 (out of 8) nodes to rebroadcast can span all network nodes. Is this good enough?

12. 3D Connected Sphere Coverage Problem  Transmission range of a node is assumed as a sphere.  The problem can be modeled as the 3D Connected Sphere Coverage Problem in Geometry.  “How to place a minimum number of center-connected spheres to fully cover a 3D space” 12 Cube Hexagonal Prism Truncated Octahedron Rhombic Dodecahedron

13. Outline  Introduction  Related Work  Our Solution: Hexagonal Prism Ring Pattern 3D Optimized Broadcasting Protocol (3DOBP)  Performance Comparisons  Conclusion 13

14.  Most are Polyhedron Space-Filling Approaches: Transmission range of a node is reduced to a polyhedron Trying to cover (or fill) the given space with a regular arrangement of space-filling polyhedrons (and a node at the center of a polyhedron is a rebroadcast node). Existing Work in 3D broadcasting Sphere Cube Transmission Range to fill space is reduced to 14

15. 15 Space-Filling Polyhedron (1/5)  Polyhedron is a 3D shape consisting of a finite number of polygonal faces E.g., cube, hexagonal prism, …  Space-Filling Polyhedron is a polyhedron that can be used to fill a space without any overlap or gap

16. 16 Space-Filling Polyhedron (2/5)  Finding a space-filling polyhedron is difficult In 350 BC, Aristotle claimed that the tetrahedron is space-filling The claim was incorrect. The mistake remained unnoticed until the 16th century!

17.  In 1887, Lord Kelvin asked: “What is the optimal way to fill a 3D space with cells of equal volume, so that the surface area between cells is minimized?” Kelvin’s conjecture: 14-faced truncated octahedron is the best way  Kelvin’s conjecture has not been proven yet. (Weaire– Phelan structure has a surface area 0.3% less than that of the truncated octahedron. However, the structure contains two kinds of cells, irregular 12-faced dodecahedron and 14-faced tetrakaidecahedron.) 17 Space-Filling Polyhedron (3/5) Lord Kelvin Truncated Octahedron (8 hexagons + 6 squares)

18. Space-Filling Polyhedron (4/5)  What polyhedrons can be used to fill space ? Cubes, Hexagonal prisms, Rhombic dodecahedrons, and Truncated octahedrons 18 6-faced 8-faced Cube Hexagonal prism

19. Space-Filling Polyhedron (5/5)  What polyhedrons can be used to fill space ? Cubes, Hexagonal prisms, Rhombic dodecahedrons, and Truncated octahedrons Rhombic dodecahedrons Truncated octahedrons 19 14-faced 12-faced

20.  In polyhedron space-filling approaches, the transmission radius should be large enough to reach neighboring nodes, which leads to high redundancy and thus low transmission efficiency Observation A B transmission radius A B redundant overlap region Can we have better arrangement ? 20

21. Outline  Introduction  Related Work  Our Solution: Hexagonal Prism Ring Pattern 3D Optimized Broadcasting Protocol (3DOBP)  Performance Comparisons  Conclusion 21

22. OUR SOLUTION: 3DOBP USING HEXAGONAL PRISM RING PATTERN 22 S Top View Source node Center node Vertex node

23. Hexagonal Prism Ring Pattern (1/4)  The network space is divided into N layers, each of which is composed of hexagonal prisms  Layer 1 is covered by a set of rebroadcasting (forwarding) nodes … Layer N is covered by a set of rebroadcasting (forwarding) nodes Layer 2 Layer 1 Problem: How to activate (or choose) rebroadcasting (forwarding) nodes based on the hexagonal prism ring pattern to fully cover the space in a layer? 23

24. Hexagonal Prism Ring Pattern (2/4) Hexagonal Prism Ring Pattern (2/4)  Reducing spheres to hexagonal prisms The size of hexagonal prisms is determined by R:  Basic procedures to cover a layer of prisms: (1) Source node initially sends out the broadcast message (2) Nodes are activated to rebroadcast to form hexagonal prism rings to cover the entire space in a layer ● R: Transmission Radius Initial source (center) node 24 H L

25. Hexagonal Prism Ring Pattern (3/4) To activate nodes to rebroadcast ring by ring (in 2D top view) To activate all center nodes of hexagons via some vertex nodes of hexagons 25 S S S Source Node

26. Activation Target Mapping. The mapping is from one center node to an empty set or a set of two next-level nearest center nodes to be activated. q stands for the index of the 6 sectors, each of which spans 60 degrees. C k,i stands for the ith center node in the ring of level k. For example, C 0,0 is the source node. The source node activates 6 center nodes. Other center nodes activate 0 or 2 center nodes. But, a center node cannot reach a next-level center node. A vertex node located at the centroid of the three center nodes (1 Tx and 2 Rx) should help forward the message.

27. Geometric Mapping. The mapping is from one center node to a location relative to the source node s. (The source node is regarded as the origin.) Z k,q stands for the location relative to the source node of the hexagon center of the level-k hexagon ring on the starting axis of sector q. starting axis of sector 0 starting axis of sector 3

28. 3DOBP : Contention Control  (1) Contention Control Location-based contention control 28 Packet P 2 67 Sender: 1.Sends a packet with the destination of the rebroadcasting node Receiver: 1.Calculates distance from itself to destination 2.Set backoff-timer: Shorter distance  Shorter backoff 3.Wait for backoff-timer to expire to rebroadcast ***The nodes with the shortest distance will rebroadcast If all nodes exchange their location information periodically, then a node will certainly know that itself is the node closest to the destination and can thus rebroadcast the packet at once.

29. 3DOBP : Intralayer Activation  Intralayer activation at layer t 29 S S Packet P S V t,1,0 V t,1,1 V t,1,2 Packet P   

30. 3DOBP: Interlayer Activation Layer 1 Layer -1 Layer 0 Source node (or start node S 0 at layer 0) Interlayer n ode I 1 Start node S 1 at layer 1 Interlayer node I -1 Start node S -1 at layer -1 ◎  ◎  ◎ 30

31. Short Summary  3DOBP uses 3 major mechanisms to broadcast a message (packet) throughout the network (1) Contention Control (2) Intralayer Activation (3) Interlayer Activation 31 2 67

32. Outline  Introduction  Related Work  Our Solution: Hexagonal Prism Ring Pattern 3D Optimized Broadcasting Protocol (3DOBP)  Performance Comparisons  Conclusion 32

33. Transmission Efficiency  Cube circumsphere R: transmission radius L: cube length Rc: radius of circumsphere

34. Transmission Efficiency  Rhombic dodecahedron circumsphere A rhombic dodecahedron can be constructed by two cubes of the length L. Rc: radius of circumsphere The radius Rc of the circumsphere is L. The volume RDV of a rhombic dodecahedron is 2L 3. Transmision radius R=

35. Transmission Efficiency  Truncated octahedron circumsphere Rc: radius of circumsphere R: transmission radius L: length

36. Transmission Efficiency  Hexagonal prism circumsphere R: transmission radius L: length; H: height Rc: radius of circumsphere R

37. Transmission Efficiency  3DOBP circumsphere Rc: radius of circumsphere R: transmission radius We assume a hexagonal prism is with side length L and height H, and that the center of each hexagonal prism is located by a node with transmission radius R. N c : the number of center nodes N v : the number of vertex nodes L: length; H: height

38. Transmission Efficiency  3DOPB We consider a hexagonal prism ring patter of an infinite number of levels of rings (J  ), and we apply the L’Hospital Rule to derive the transmission efficiency TE.

39. Comparisons of Transmission Efficiency  Transmission Efficiency ApproachTransmission Efficiency Truncated Octahedron-based3/8π ≈ 0.119366 Hexagonal Prism-based3/( ) ≈ 0.168809 Rhombic Dodecahedron-based3/( ) ≈ 0.168809 Cube-based3/4π ≈ 0.238732 Hexagonal Prism Ring-based1/π ≈ 0.31831 39

40. Conclusion  We introduce the 3D Optimized Broadcast Protocol (3DOBP) using the Hexagonal Prism Ring Pattern (HPRP) to optimize the transmission efficiency of 3D broadcasting in dense wireless networks  The protocol is the best solution so far: 2D: 0.55/0.61 3D: 0.31/0.84  Future work: Derive better upper bounds Design better protocols 40

41. Related Publication  Jehn-Ruey Jiang and Tzu-Ming Sung, “Energy-Efficient Coverage and Connectivity Maintenance for Wireless Sensor Networks,” Journal of Networks, Vol. 4, No. 6, pp. 403-410, 2009.  Yung-Liang Lai and Jehn-Ruey Jiang, “Broadcasting with Optimized Transmission Efficiency in Wireless Networks,” in Proc. of Fifth International Conference on Wireless and Mobile Communications, 2009.  Yung-Liang Lai and Jehn-Ruey Jiang, “Broadcasting with Optimized Transmission Efficiency in 3-Dimensional Wireless Networks,” in Proc. of International Conference on Parallel and Distributed Systems (ICPADS 2009), 2009.  Jehn-Ruey Jiang and Yung-Liang Lai, “Wireless Broadcasting with Optimized Transmission Efficiency,” Journal of Information Science and Engineering (JISE), Vol28, No.3, pp. 479-502, 2012.  Yung-Liang Lai and Jehn-Ruey Jiang, “A 3-dimensional broadcast protocol with optimised transmission efficiency in wireless networks,” International Journal of Ad Hoc and Ubiquitous Computing (IJAHUC), Vol. 12, Issue 4, pp. 205-215, 2013. 41

42. Thank You! Jiang, Jehn-Ruey Professor, NCU, Taiwan ncujjr@gmail.com 42