Probabilistic-based Message Dissemination in Ad-Hoc and Sensor Networks using Directional Antennas

1. Probabilistic-based Message Dissemination in Ad-Hoc and Sensor Networks using Directional Antennas Xueli An and RaminHekmat Delft University of Technology The Netherlands (IEEE-MASS 2009) • Presented by Binh Tran • 02/22/2010

2. Outline • Introduction • Preliminaries: • Percolation Theory and Phase Transition Phenomenon • Graph Types: random graph, lattice graph, and random geometric graph • Antenna Modes: Omni-directional and directional antenna. • Multiple directional gossiping mechanisms on random graph, lattice graph, and random geometric graph. • The gossiping performance by using different combinations of transceiver antenna mode and variant antenna beam-width. • The gossiping extension schemes based on directional antennas. • Conclusion

3. Introduction • By using gossiping approach, each node in the network forwards packet with pre-specified probability p, named gossiping probability. • GOSSIP further uses two forwarding probabilities p1 and p2, instead of a single probability p, where p2>p1. A packet is forwarded with p2 if the number of its neighbor is below certain threshold. Otherwise, it forwarded with p1. • All the work mentioned above is based on Omni-directional antennas • By concentrating energy on a certain direction, directional antennas could efficiently use power for transmission, and meanwhile avoid interference from other directions. • However, using directional antennas for broadcasting is not a trivial issue. • Solutions: • Only the farthest neighbor in a certain direction forwards broadcasting packets • Others investigated directional routing protocols in ad hoc networks. To reduce routing overhead by avoiding forwarding route request in the direction where the channel is busy. • Probabilistic-based message dissemination in ad hoc and sensor network using directional antennas.

4. Choosing the right antenna • Omni-directional antennas – The Ultimate Solution?

5. Preliminaries: Percolation Theory and Phase Transition Phenomenon • Percolation theory is used to model the behavior of random medium (number of nodes in a network) • Define percolation probability : the probability that a given node belongs to an infinite cluster. There exists a critical threshold for gossiping probability p. If the gossiping probability is larger than , it is almost sure to guarantee the dissemination of information in the entire network, such that • This phenomenon is termed as bimodal or phase transition • This phenomenon is observed from gossip-based protocols. • If the network is sufficiently large, the gossiping probability p of omni-directional and directional broadcasts over a network are the same as the percolation threshold of site percolation.

6. Percolation example Does an infinite open cluster exist? That is, is there a path of connected points of inifite length “through” the network? Theory: For any given p, the prob that an infinite cluster exists is either 0 or 1 Since this prob is an increasing function of p, there must be a critical p below which the probability is always 0 and above which the prob is always 1

7. Preliminaries: Graph types A random geometric graph is a variation of the random graph, in which a link exists according to a variable probability We define a node i have probability 1 to connect to neighbors within its transmission range d. Where : the Euclidean distance between node i and j. Each node links with all the other nodes within its transmission range Random geometric graph is a good model for ad-hoc wireless networks. A random graph consists of N nodes, in which each link between 2 nodes is chosen independently and with probability The mean node degree in random graph T1: Random graph T2: Lattice graph T3: Random geometric graph

8. Preliminaries: Antenna Mode • Two operating modes for transmitting and receiving: omni-directional mode and directional mode • Directional Mode (beam mode): antenna radiates greater power in one or more directions allowing for increased performance on transmit and receive and reduced interference from unwanted sources • Omni-directional Mode: antenna system which radiates power in one plane with a directive pattern shape in a perpendicular plane. • Several neighbor-hood relationships: O-O neighbor, D-O (or O-D) neighbor and D-D neighbor

9. Performance Metrics • Giant component size (GCS): indicates the connectivity of a network. GCS is the fraction of nodes in the network, in single-hop or multi hop fashion, that are connected to each other. • Overhead: the total number of generated packets in one run of simulation (the amount of overhead indicates the efficiency of a gossiping protocol) • Path length: the hop count of the longest path in the network = latency of the gossiping process • Delivery ratio( ): the probability that all the nodes within the network are informed when the path length is L. (Delivery ratio could be considered as the percolation probability in a network with finite size)

10. Assumptions • To achieve a homogeneous gossiping environment, the source is at the center of the network when random geometric graph and lattice graph are used. All nodes in random graph and random geometric graph are uniformly distributed within the network. • During the gossiping process, a node only reacts to the first received packet, and simply discards all other packets after the first one received. • All the constructed networks are completely connected. At first, a node has no information about its surrounding neighbors. • All the distances are normalized value. • All the simulation results are averaged based on 1000 iterations.

11. Gossipping Using Directional Antennas • The original gossiping protocol defines that after a node receives a packet, it has a probability p to forwards the packet. • By using directional antennas, the azimuth plane of a node is divided into beam sectors • Two basic Directional Gossiping (DG) mechanisms: • Per-sector based DG (DG1): after a node receives a packet, it generates a probability for each beam sector, where . A packet is forwarded from beam sector i, if • Per-node based DG(DG2): after a node receives a packet, it only generates one probability . If , it forwards a packet in each beam sector. Otherwise, it does not forward it at all.

12. Performance comparison between DG1 and DG2 • Simulation: • Random geometric graph • Nodes use directional antennas for transmitting and omni-directional antenna for receiving or listening • Network density = 10.5 • Total number of nodes = 25 to 225 In general, DG1 exhibits a higher GCS than DG2, i.e. DG1 can inform more nodes in one execution of gossiping process. Thus, DG1 is more reliable than DG2

13. Network Graph Influence • To evaluate the directional gossiping performance (DG1) in several network graphs • Node degree = number of direct neighbors of that node in the network. • In a large scale network, the mean node degree can be simply approximated as where :the normalized transmission range by using directional antenna with beamwidth N : the total number of nodes in the network R : the normalized radius of the circular network. • When the network radius R is not large enough, the border effect should be taken into consideration. The mean node degree is approximately as where f(x) : the position probability density functions of the node, and : the proportion of the effective coverage area of a node at the network border area, and we have • In a lattice graph, if the distances between adjacent nodes are set to1., when using directional antennas, the mean node degree is 10.68 for lattice graph • In random geometric graph, the network radius = 8.36

14. Network graph influence on directional gossiping performance Fig 3a. Compare the GCS using DG1 in different network graphs with 90 degrees directional antenna Fig 3b. Set the gossiping prob to 1 and vary the antenna beam-width to get path length performance DG1 algo in random graph (T1) exhibits the highest GCS and the shortest path length. Thus, the message dissemination speed is faster in random graph(T1) than in random geometric graph (T3) T1: Random graph T2: Lattice graph T3: Random geometric graph

15. Transceiver Antenna Mode Influence Using different transceiver antenna mode (D-O and D-D) D-O and D-D induce similar amount of overhead in the gossiping progress, but using D-D mode achieves higher GCS compared to D-O mode, especially when the gossiping prob is low DG1-DD is better

16. Transceiver Antenna Mode Influence (con’t):gossiping probability influence When the gossiping probability is lower than 0.3, the network cannot be totally covered at all, which verifies the bimodal behavior of the directional gossiping process. Fig 5a,b. Using D-D mode for directional gossiping results shorter path length Fig 4. Using D-D mode could achieve higher GCS than using D-O mode, especially at low prob Thus, compared to D-O mode, using D-D mode has faster message dissemination speed and fair message coverage capability.

17. Antenna Beamwidth Influence • Simulation: • DG1-T3(Random geometric graph) using D-O and D-D mode • Fixed the gossiping prob = 0.5 • Two transceiver antenna modes behave in a piecewise manner When antenna beam-width is narrow (<20), D-O mode exhibits higher GCS than D-D mode, and also higher overhead. When between 20 and 60, using D-O and D-D modes achieve similar connectivity and over head When antenna beam-width is bigger, using D-D mode obtains better connectivity and both mode have similar overhead Thus, using D-D mode is not suitable for small antenna beam-width. When antenna beamwidth is within a moderate range, using D-D mode is better than D-O mode, because they can use the similar amount of overhead to achieve the same connectivity, but D-D mode results shorter path length

18. Directional Gossiping Extensions • Two gossiping extension mechanisms based on DG1: distance and angle based optimization and k-hop based gossiping algorithm • Distance and Angle based Optimization (DG3) Previous works: • After receiving a packet, the distance between transmitter and receiver can be estimated based on the received signal strength. In a distance-based broadcasting optimization scheme, if the estimated distance is smaller than a threshold, the received packet will not be broadcasted from the receiver. • An extension of the above node that covers a bigger range has a higher probability of forwarding. In a forwarding probability calculation method, it depends on the source-destination distance and the packet forwarding direction. • DG3: combine this distance and angle based optimization schemes with gossiping protocol. Each node could have different gossiping probability which depends on the distance and relative direction between a node and its previous transmitter.

19. DG3 (cons’t) • When a node receives a packet from beam sector , based on the received signal strength, the node estimates the distance D between the transmitter and itself. This node computes a gossiping prob for each beam sector, which is a product between the basic gossiping prob and a weighting factor where is the beam sector difference between the receiving sector and the forwarding sector is the normalized transmission range The forwarding probability is calculated as

20. Simplified Distance and Angle based Optimization (DG4) • DG4 is a simplified version of DG3 • Based on the estimated distance, a node estimate a threshold angle where • If the packet forwarding direction is bigger than , the weighting factor is 1, otherwise 0 where The forwarding probability is calculated as

21. DG1, DG3, and DG4 in random geometric graph(T3) using D-O mode DG4 achieves slightly lower GCS than DG1, but it significantly reduces the amount of overhead. Compared to DG1 and DG4, DG3 has the worst performance in terms of GCS At this point, DG1 and DG4 are better

22. DG4 Combined with ‘k-hop’ • Problem: • The source node is located in the center of the network, and the other nodes are uniformly distributed within the network. • If the source has a smaller number of neighbors, the gossiping process could probably die very fast. • To avoid this phenomenon, k-hop gossiping protocol. • Set the gossiping probability to be 1 for the first k hops from the source, and then the gossiping process continues with probability p since the k+1 hop. • Combine this mechanism with DG1 and denoted it as and combine it with DG4 and denoted it as

23. Comparison the DG4 k-hop with the original DG1 Compared to DG1, the k-hop scheme enhances the message delivery ratio but also increases the amount of overhead. The optimization scheme DG could effectively reduce the overhead, but it also reduces the message delivery ratio. The combination of the k-hop scheme and DG4 together could achieve the similar delivery ratio, but lower overhead. Also, using D-D mode with the optimization scheme has better performance than using D-O mode

24. Conclusion • A comprehensive investigation on the gossiping protocols using directional antennas. • Two directional gossiping DG mechanism: per-sector based DG (better network connectivity) and per-node based DG. • The per-sector based DG mechanism in various network graphs, messages are disseminated fastest in random graph. • The gossiping protocols according to different transceiver modes. • Two gossiping extension mechanisms- distance and angle based optimization, and k-hop based optimization. The combination of these two optimization schemes can inherit the benefits of both sides

28. What is network coding? Network coding for cost

29. Network coding for cost

30. Network coding for cost Cost of trees = 26

31. Network coding for cost Cost of network coding = 23

32. Randomized linear network coding

33. Motivation: Why to study the impact of network topology on the power of network coding? • Some Pioneering works have proved that NC • Can achieve multicast capacity in directed networks • Can speed up downloads over random block selection by 2-3 times (BitTorrent-like P2P content distribution) • However, others have showed that the rarest first algorithm of BitTorrent guarantees close-to-ideal diversity of blocks among peers, and using NC in such systems cannot be justified. CONFUSION due to the lack of theoretical understanding of NC’s benefit in P2P network, which are better modeled by gossip-based overlay broadcast Previous works show in the time-synchronized model that NC • Achieves the optimal delay performance for any transmission schedules in P2P networks • Achieves shorter broadcast delay of k blocks in complete graphs On the other hand, some works propose a decentralized block exchange algorithm based on push and pull that has a close-to-optimal performance

34. Motivation (con’t) • QUESTIONS • Does randomized network coding achieve the optimal broadcast delayas a block selection protocol? • Even if network coding achieves the optimal delay, how much benefit can it bring over reasonably good non-coding protocols? • Are there any factors that critically affect the marginal benefit of network coding, so much so that such benefit is only substantial under certain circumstances? • This paper proves • The optimality of NC in continuous-time gossiping model. • The marginal benefits of NC over reasonably good non-coding block selection policies. • And claims that topological dynamics serve as a critical factor that impacts the marginal benefits of NC in P2P network : • Clustering (traffic locality) topology • Time-varying topology

35. Gossip-like algorithms • The Gossip Algorithms conform to the following rules • For each node , at rate , it • Randomly chooses one of its neighbors to serve, and • Transmits one or a linear combination (in Galois field) of blocks it has obtained

36. Problem formulation • P2P network: , where nodes, and : the edge set that may change over time. • : an average upload bandwidth of node i • To accommodate random transmission delays, the time to take for node i to transmit a block follows a certain distribution with mean • An edge between 2 peers = data connection between them • A node maintain connections with a subset of all other peers = neighborhood • Inspired by gossip-based overlay broadcast systems, delivering k data blocks • The broadcast delay : the time needed to disseminate all k blocks to all the nodes in • The €-broadcast delay : 1- € of all the peers finish downloading.

37. Continuous-time model • A continuous-time trellis • If a block is sent from node u at time and is received by node v at time , we introduce vertices : and • A directed edge of capacity 1 from to • “Transmission edges” are determined by transmission schedules According to the well-known theorem on multicast in acyclic graphs, those nodes with can receive all k blocks Given a transmission schedule, the minimum possible time it takes a node v to receive all k block is

38. On the optimality of network coding • Proposition 1: Randomized Network Coding achieves the minimum possible broadcast delay for any topology and any transmission schedule with high probability. • Proposition 2: the author derive a theoretical lower bound on the broadcast delay of any “gossip algorithm” in complete graphs

39. Claims • Show that both coding and non-coding protocols can achieve performance close to the theoretical limits in complete and random graphs. • Performance of different algorithms • Random Usefull Block (RUB): among the blocks needed by the target peer, the sender transmits a random block • Local Rarest First (LRF): among the blocks need by the target peer, the sender transmits a random block with the smallest number of copies in the neighborhood • Global Rarest First (GRF): among the blocks needed by the target peer, the sender transmits a random block with the smallest number of copies in the network • Randomized Network Coding (NC): the sender linearly encodes all the coded blocks it has obtained using random coefficients in Galois field GF and uploads the encoded block to the target peer. • These block selection and encoding algorithms are implemented with SSE2 SIMD vector instruction

40. Performance of Different algorithms

41. Performance of Different algorithms (con’t) Network coding is not necessarily needed to achieve close-to-optimal broadcast delay in complete and random graphs. This means the marginal benefit of NC is trivial in these graph

42. Clustered and time-varying topologies • Network model: • : graph of size N= mn, m clusters of peers: • Each peer p in also maintain global links with The links from peer p are changing periodically with cycle Each peer uploads to a random global neighbor at the points of a Poison process

43. Clustered and time-varying topologies Proposition 3: Implications: NC automatically makes better choices of blocks when transmitting across clusters.

44. Experimental studies: broadcast delay The performance of NC, GRF, RUB are not affected by the sparsity Varying can hardly affect the performance of RUB, NC, and GRF, with RUB being cosntantly inferior

45. Experimental studies: broadcast delay (con’t)

46. Experimental studies: broadcast delay (con’t) The benefits of NC only increase dramatically when <= 1 The benefit of NC becomes to drop again if is too small

47. Experimental studies: broadcast delay (con’t)

48. Experimental studies: broadcast delay (con’t)

49. Experimental studies: broadcast delay (con’t)

50. Experimental studies: broadcast delay (con’t)