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Three-Dimensional Broadcasting with Optimized Transmission Efficiency in Dense Wireless Networks

Three-Dimensional Broadcasting with Optimized Transmission Efficiency in Dense Wireless Networks. Presented by Prof. Jehn-Ruey Jiang National Central University, Taiwan. Outline. Introduction Related Work Our Solution: Hexagonal Prism Ring Pattern

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Three-Dimensional Broadcasting with Optimized Transmission Efficiency in Dense Wireless Networks

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  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

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

  4. Broadcasting in 3D Wireless Networks • 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 anode’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.

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

  6. Honeycomb – hexagonal lattice (grid) 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. 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. Cube (6 faces) Rhombic Dodecahedron (12 faces) Hexagonal Prism (8 faces) Truncated Octahedron (14 faces)

  9. Flooding • 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 efficiencydue to a lot of redundant rebroadcast space 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. BENEFIT COST

  11. Optimized Transmission Efficiency • 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 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 assumedas 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” Rhombic Dodecahedron Hexagonal Prism Truncated Octahedron Cube

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

  14. Existing Work in 3D broadcasting • 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). is reduced to to fill space Transmission Range Cube Sphere

  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. Space-Filling Polyhedron (2/5) • Finding a space-filling polyhedronis 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. Space-Filling Polyhedron (3/5) • In 1887, Lord Kelvin asked: • “What is the optimal way to fill a 3D spacewith 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.) Lord Kelvin Truncated Octahedron(8 hexagons + 6 squares)

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

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

  20. Observation • 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 transmission radius A B A B redundant overlap region Can we have better arrangement ?

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

  22. Center node Source node Vertex node Our solution:3DOBP usingHexagonal Prism Ring Pattern S Top View

  23. Hexagonal Prism Ring Pattern (1/4) Problem: How to activate (or choose) rebroadcasting (forwarding) nodes based on the hexagonal prism ring pattern to fully cover the space in a layer? Layer 2 Layer 1 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

  24. Hexagonal Prism Ring Pattern (2/4) R: Transmission Radius H ● L Initial source(center) node • 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 ringsto cover the entire space in a layer

  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 S S Source Node S

  26. Sector 1 C3,5 C3,4 C3,6 C3,3 Sector 2 Sector 0 C2,2 C3,7 C2,4 C3,2 C2,3 C3,8 C1,2 C1,1 C2,1 C3,1 C2,5 C0,0 C3,9 A0 A3 S C2,6 C1,0 C2,0 C3,0 C1,3 C2,11 C1,5 C1,4 C3,10 C3,17 C2,7 Sector 3 C2,8 C3,11 C2,9 C2,10 Sector 5 C3,16 C3,15 C3,12 C3,13 C3,14 A4 Sector 4 A5 Activation Target Mapping . • q stands for the index of the 6 sectors, each of which spans 60 degrees. • Ck,i stands for the ith center node in the ring of level k. For example, C0,0 is the source node. • The mapping is from one center node to an empty set or a set of two next-level nearest center nodes to be activated. • 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 locationrelative to the source node s. (The source node is regarded as the origin.) starting axis of sector 0 starting axis of sector 3 • Zk,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.

  28. 3DOBP : Contention Control • (1) Contention Control • Location-based contention control Packet P < destination> Sender: Sends a packet with the destinationof the rebroadcasting node Receiver: Calculates distance from itself to destination Set backoff-timer: Shorter distance Shorter backoff Wait for backoff-timer to expire to rebroadcast ***The nodes with the shortest distance will rebroadcast 2 6 7 • 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 Packet P <Vt,1,0, Vt,1,1, Vt,1,2> • Intralayer activation at layer t  S  Packet P <Ct,1,2, Ct,1,3>  Packet P <Ct,1,0, Ct,1,1> S Vt,1,1 Vt,1,0 S • Vt,1,2 Packet P <Ct,1,4, Ct,1,5>

  30. 3DOBP: Interlayer Activation ◎ • Start node S1 at layer 1 Layer 1  Interlayer node I1 Layer 0 ◎ • Source node (or start node S0 at layer 0)  • Interlayer node I-1 Layer -1 • Start node S-1 at layer -1 ◎

  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 2 6 7

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

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

  34. Transmission Efficiency circumsphere • Rhombic dodecahedron Rc: radius of circumsphere A rhombic dodecahedron can be constructed by two cubes of the length L. The radius Rc of the circumsphere is L. The volume RDV of a rhombic dodecahedron is 2L3. Transmision radius R=

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

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

  37. Transmission Efficiency circumsphere • 3DOBP R: transmission radius Rc: radius of circumsphere 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. L: length; H: height Nc: the number of center nodes Nv: the number of vertex nodes

  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

  40. Conclusion • We introduce the 3D Optimized Broadcast Protocol (3DOBP) using the Hexagonal Prism Ring Pattern (HPRP) to optimize the transmission efficiencyof 3D broadcasting in dense wireless networks • The protocol is the best solution so far:2D: 0.55/0.613D: 0.31/0.84 • Future work: • Derive better upper bounds • Design better protocols

  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.

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

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