Topology Enhancement in Wireless Multihop Networks: A Top-down Approach

Transcription

1 Topology Enhancement in Wireless Multihop Networks: A Top-down Approach Symeon Papavassiliou (joint work with Eleni Stai and Vasileios Karyotis) National Technical University of Athens (NTUA) School of Electrical & Computer Engineering Network Management & Optimal Design Lab (NETMODE) December , IEEE Communications Society Lecture Series Technological University of America, Coconut Creek, FL, USA

2 Complex networks Network: A collection of (nodes, agents, components, objects, services ) that collaborate to accomplish actions, gains, that cannot be accomplished with out such collaboration It is all about Interactions that keep increasing and become more complex Trade-off: gain from collaboration vs. cost of collaboration Complex Networks (CNs): Describe wide range of systems of interacting entities Complex Network Analysis Models Properties/features Behavior

3 Complex Network Taxonomy Communication, infrastructure, technological networks Social and economical networks Biological networks Designed and/or engineered Human initiated, Spontaneous growth Spontaneous evolution

4 Evolutionary Design Loop - Motivation Physical networks, in which node associations correspond one-to-one in actual interactions among the entities and physical connectivity. Logical networks, involve logical associations and connectivity among peers. Such networks include, overlay and peerto-peer (p2p) networks. Social networks, involves more complex interactions, that take into account mainly unpredictable/hidden social associations (activities).

5 Control vs. Communications Many graphs as abstractions Collaboration graph or a model of what the system does (behavior) Communication graph or a model of what the system consist of (structure) Challenge 1: Given behavior, what structure (subject to constraints) gives best performance? Challenge 2: Given structure (and constraints) how well behavior can be executed? Topology modification topology formation/transformation

6 Objective Focus: on closing the loop between social and physical networking in the aforementioned design paradigm. Exploit:: how social knowledge and features of online social networks can be used in improving physical communication networks Demonstrate: infuse the desired properties of online social structure (small-world effect, power-law like degree distribution) into the core structure of a wireless multi-hop network. Use: Inverse Topology Control based techniques to modify topology in multi-hop networks (Edge Churn, Node Churn, Socially-aided Evolutionary Topology Modification (SETM)) Analyze: through a continuum-theory based framework Evaluate: Identify performance gains and tradeoffs

7 Random Geometric Graphs RGG/ Wireless Multi-hop Networks Constructed by allocating N points uniformly and randomly over a plane region and linking two points separated by a distance of at most r Realistic model for actual multi-hop networks where a node may be connected with one or more nodes in its vicinity/range. Characterized by: high clustering, long average path length. Idea: reducing average path length of wireless multi-hop networks, while not impacting clustering (its nature).

8 Average Path Length Path sequence of vertices traversed in a network Geodesic path shortest path (topology) shortest path through a network from a vertex to another Network diameter length of longest geodesic Definition: Un-weighted graph Total # nodes is n, d(v i,v j ) geodesic length of v i from v j The actual path length experienced on average by a user The lower l G is, the better it is in general Information dissemination Lower cost

9 Clustering Coefficient The clustering coefficient is a measure of direct connectivity between the neighbors of a node Quantifies how close its neighbors are to being a clique (complete graph) #triangles 1 #connected triples 5 #closed triples 3 C 3/5

10 Small-world Networks Obtained evolutionary from ordered lattices Start from an ordered lattice Randomly rewire each edge with prob. p excluding selfconnections and duplicate edges Arbitrary long-range edges maybe added Small average path length

11 Preferential Attachment Pref. Prob(x ) w = i x w i The probability that x participates in a process or takes a decision is proportional to a quantity w x characterizing x. Feature of social networks, w x is usually the node degree. "cumulative advantage", "the rich get richer Generates power law distributions. Small percentage of nodes with great degrees Majority of nodes with small degrees

12 Examples of Scale-free Networks

13 Applications of Scale-free Networks Internet/WWW Science collaboration graphs Hollywood co-starring graphs Citation networks road maps electric power grids voter networks social influence networks Human sexual contacts

14 Topology Control (TC)- Inverse TC Topology control is a technique used mainly in wireless ad hoc and sensor networks in order to modify the initial topology of the network to save energy and extend the lifetime of the network. TC tries to achieve the balance: Energy consumption Node interference Increase traffic carrying capacity Connectivity Cost at Delay, Path length itc: Aims at achieving QoS performance benefits without impacting the energy consumption significantly.

15 Proposed Mechanism and Assumptions We propose edge churn, node churn and combinations based on itc. Assumptions: Not arbitrary increment of the transmission radius of each node (limited available energy of each wireless node). Connected network at any time (addition probability higher than deletion). Links between nodes: directional or bidirectional. Connections determined at physical/logical layer. N nodes, in fixed locations. Homogeneous RGG initial network. Time t is slotted. Distributed operation of the mechanism.

16 Edge Churn description The transmission radius of selected nodes increases thus extending their neighborhood and becoming more popular in the network. Each node can vary its radius between R MIN and R MAX. Each time slot is characterized by two parameters R min and R max. R c (i) is the radius of node i at time step t. Initially we have a homogeneous RGG with transmission radius R f =R min =R max. At each time step R min (t)=r max (t-1) and R max (t)=r max (t-1)+a.

17 Link Addition

18 Link Rewiring

19 Link Deletion

20 Edge churn processes (1) Process p 1 : With probability p, 0 p<1, we add m 1, (m 1 <n) new links to m 1 selected nodes. First endpoint i: selected with probability Q 1 (k i ). Second endpoint j: a randomly chosen neighbor in the area of the annulus bounded by R min, R max radii values of node i. Link formed i j Process p 2 : With probability q, 0 q<1, we rewire m 2, (m 2 <n) links. First endpoint i: randomly and uniformly selected among new nodes. Deleted endpoint j: a randomly chosen neighbor of i. Link deleted i j Replacing endpoint s: selected with probability Q 2 (k s ). Link formed i s

21 Edge churn processes (2) Process p 3 : With probability r, 0 r<1, we delete m 3, (m 3 <n) links one from each of m 3 nodes selected with probability Q 3 (k i ). Link deleted i j Preferential attachment according to node degree Inverse preferential attachment according to node degree

22 Edge churn analysis via Continuum Theory Approximated 14 Approximation for average node degree Average node degree Simulation Analysis Step of the simulation

23 Node churn description- analysis Process p 4 : Node Addition: With prob. w, M a nodes of the network are randomly and uniformly selected and each one of them invites a new node to join the network, by an analogy to a social network. The new nodes have increased radius compared to the original nodes in the network. In social network terms, this means that the friendship of a new node is extended to the majority of the friends of the inviting node and also that such node is more open to new friendships. Process p 5 :Node Deletion: With prob. v, M d nodes are chosen, according to the inverse preferential attachment selection rule and deleted from the network. Process p 6 : No change in the network topology. Average node degree

24 Combined Mechanism-Demonstration Socially-aided Evolutionary Topology Modification p+q+r+w+u+prob(p6)=

25 Combined Mechanism Clustering Coefficient like RGG Path length improved Parameter Value N 750 L 2000 p, q, r, w, v 0.3,0.1,0.15,0. 3,0.15 Steps 30 R initial 150 Ma, Md 5,3 m1, m2, m3 10%N,10,6%N Average path length Average Path length Clustering coefficient Step of the simulation Clustering coefficient

26 Node degree distribution 0.12 Density of degree Initial Network Final Network Node degree

27 Performance benefits 60 % change Delay Throughput Path (hops) Parameter Value N 250 L 800 p, q, r, w, v 0.3,0.1,0.15,0.3,0.15 Steps 19 R initial 90 Ma, Md 5,3 m1, m2, m3 10%N,10,10%N NS2 simulator: 10 TCP connections for 10 randomly chosen pairs in initial and final topology and simulation of each topology for 300s. Average results over 5 different scenarios

28 Radius increase 300 Average node radius Initial network Node churn SETM Edge churn Mechanisms SETM leads to a mean radius less than Edge churn and higher than Node churn.

29 Energy consumed Initial network Induced network Network topologies Energy consumed per node (in e.u.)

30 Validation Open Issue Measurement-driven activity In the Internet, what we want to measure is often not what we can measure Critical role of data hygiene as a scientific pre-requisite The example of traceroute measurements Details matter Domain knowledge is critical Hub-like Internet core a myth Model validation Matching certain statistics of the data is insufficient Clean separation between data used for model selection vs data used for model validation

31 Virtualization+Federation: viable path to experimentation Network Virtualization: Allows multiple heterogeneous network architectures to cohabit on a shared physical substrate Provides a powerful way to run multiple virtual networks, each customized to a specific purpose, simultaneously over a shared substrate Provides flexibility, promotes diversity, promises manageability Testbed Federtation: Interconnection of independent testbeds/environments for enhanced experimentation under common management framework being part of single resource/environment Positive externality (benefits of both the users and providers of the individual testbeds) Heterogeneity and diversity (geographical, technological) Hybrid Testing: Large scale experimentation in combination with emulations

32 Conclusions We presented a socially inspired mechanism based on network churn aiming to improve the mean hop distance and as a result the performance metrics of a wireless multi hop network. The initial random geometric graph maintains its properties of clustering coefficient and approximated binomial distribution. The per node energy cost is affordable. By changing the process probabilities, it is possible to control the proposed mechanism at will. Future work: possibility of the SETM mechanism to achieve Topology Control. Validation - Experimentation

33 Questions? Thank you!