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The Worst-Case Capacity of Wireless Networks

The Worst-Case Capacity of Wireless Networks . TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A A A A. Disclaimer…. Work is about wireless networking in general Presentation focusing on wireless sensor networks Joint Work

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The Worst-Case Capacity of Wireless Networks

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  1. The Worst-Case Capacity of Wireless Networks TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA

  2. Disclaimer… • Work is about wireless networking in general • Presentation focusing on wireless sensor networks • Joint Work • Thomas Moscibroda (thanks for some slides) • Olga Goussevskaia • Yvonne Anne Oswald • Yves Weber

  3. Today, we look much cuter! And we’re usually carefully deployed Power Radio Processor Sensors Memory

  4. Periodic data gathering in sensor networks • All nodes produce relevant information about their vicinity periodically. • Data is conveyed to an information sink for further processing. • Data may or may not be aggregated. • Variations • Sense event (e.g. fire, burglar) • SQL-like queries (e.g. TinyDB)

  5. Data gathering & aggregation Classicapplication of sensornetworks Sensor nodesperiodically sense environment Relevant informationneeds to betransmitted to sink FunctionalCapacity of Sensor Networks Sink peridicallywants to compute a functionfn of sensordata At whatratecanthisfunctionbecomputed? Data Gathering in Wireless Sensor Networks (1) (2) (3) ,fn fn ,fn sink

  6. Data Gathering in Wireless Sensor Networks Example: simple round-robin scheme  Each sensor reports its results directly to the root one after another sink Simple Round-Robin Scheme: • Sink can compute one function per n rounds  Achieves arate of 1/n x1=7 x3=4 x2=6 x4=3 (3) (2) (1) (4) fn fn fn fn x8=5 x7=9 t x5=1 x6=4 x9=2

  7. Data Gathering in Wireless Sensor Networks There are better schemes using • Multi-hop relaying • In-network processing • Spatial Reuse • Pipelining sink (1) (2) (3) (4) fn fn fn fn t

  8. Capacity in Wireless Sensor Networks (1) (1/log n) (1/n) (1/√n) Only perfectly compressible functions (max, min, avg,…) Answer depends on: • Function to be computed • Coding techniques • Network topology • Wireless communication model No fancy coding techniques At what ratecan sensors transmit data to the sink? Scaling-laws  how does rate decrease as n increases…?

  9. “Classic” Capacity… The Capacity of Wireless Networks Gupta, Kumar, 2000 [Arpacioglu et al, IPSN’04] [Giridhar et al, JSAC’05] [Barrenechea et al, IPSN’04] [Grossglauser et al, INFOCOM’01] [Liu et al, INFOCOM’03] [Gamal et al, INFOCOM’04] [Toumpis, TWC’03] [Kyasanur et al, MOBICOM’05] [Kodialam et al, MOBICOM’05] [Gastpar et al, INFOCOM’02] [Zhang et al, INFOCOM’05] [Mitra et al, IPSN’04] [Li et al, MOBICOM’01] [Dousse et al, INFOCOM’04] [Bansal et al, INFOCOM’03] etc… [Yi et al, MOBIHOC’03] [Perevalov et al, INFOCOM’03]

  10. Capacity studies so far make strong assumptions on node deployment, topologies randomly, uniformly distributed nodes nodes placed on a grid etc... Worst-Case Capacity What if a network looks differently…?

  11. Like this?

  12. Or rather like this?

  13. Worst-Case Capacity • Capacity studies so far have made very strong assumptions on node deployment, topologies • randomly, uniformly distributed nodes • nodes placed on a grid • etc... What if a network looks differently…? We assume arbitrary node distribution worst-case topologies Worst-Case Capacity Classic Capacity How much information can be Transmitted in any network How much information can be transmitted in nice, well-behaving networks

  14. Two standard models in wireless networking Models Protocol Model (graph-based, simpler) Physical Model (SINR-based, more realistic)

  15. Protocol Model • Based on graph-basednotion of interference • Transmission range and interferencerange Algorithmic work on worst-case topologies usually in protocol models (unit disk graph,…) (1+)ry (1+)rx y rx ry R(y) x R(x) • R(x) is in interference range of y • R(x) and R(y) cannot simultaneously receive!

  16. Physical Model Based on signal-to-noise-plus-interference (SINR) Simplest case:  packets can be decoded if SINR is larger than  at receiver Received signal power from sender Power level of sender u Path-loss exponent Minimum signal-to-interference ratio Noise Distance between two nodes Received signal power from all other nodes (=interference)

  17. Twostandardmodels of wirelesscommunication Algorithms typicallydesigned and analyzed in protocolmodel Justification: Capacityresultsaretypically (almost) thesame in bothmodels (e.g., Gupta, Kumar, etc...) Models Protocol Model (graph-based, simpler) Physical Model (SINR-based, more realistic) Premise: Results obtained in protocol model do not divert too much from more realistic model!

  18. Example: Protocol vs. Physical Model Assume a single frequency (and no fancy decoding techniques!) Let =3, =3, and N=10nW Transmission powers: PB= -15 dBm and PA= 1 dBm SINR of A at D: SINR of B at C: A sends to D, B sends to C C D B A 4m 1m 2m NO Protocol Model Is spatial reuse possible? YES Physical Model In Reality!

  19. This works in practice! • Wedidmeasurementsusingstandardmica2nodes! • Replacedstandard MAC protocolby a (tailor-made) „SINR-MAC“ • Measuredforinstancethefollowingdeployment... u1 u2 u3 u4 u5 u6 • Time forsuccessfullytransmitting 20‘000 packets: [Moscibroda, Wattenhofer, Weber, Hotnets’06] Speed-up is almost a factor 3

  20. Upper Bound Protocol Model • Therearenetworks, in which at mostonenodecantransmit!  likeround-robin • Consider exponential nodechain • Assumenodescanchoosearbitrarytransmission power • Whenever a node transmits to another node  All nodes to its left are in its interference range!  Network behaves like a single-hop network sink xi d(sink,xi) = (1+1/)i-1 In the protocol model, the achievable rate is (1/n).

  21. Muchbetterbounds in SINR-basedphysicalmodelarepossible (exponential gap) Paper presents a schedulingalgorithmthatachieves a rate of (1/log3n) Algorithm is centralized, highly complex  not practical But it shows that high rates are possible even in worst-case networks Basic idea: Enable spatial reuse by exploiting SINR effects. Lower Bound Physical Model In the physical model, the achievable rate is (1/polylogn).

  22. High-level idea is simple Construct a hierarchical tree T(X) that has desirable properties 1) Initially, each node is active 2) Each node connects to closestactive node 3) Break cycles  yields forest 4) Only root of each tree remains active Scheduling Algorithm – High Level Procedure Can be adjusted if transmission power limited loop until no active nodes Phase Scheduler: How to schedule T(X)? The resulting structure has some nice properties  If each link of T(X) can be scheduled at least once in L(X) time-slots  Then, a rate of 1/L(X) can be achieved

  23. Scheduling Algorithm – Phase Scheduler • How to schedule T(X) efficiently • Weneed to schedule links of different magnitudesimultaneously! • Onlypossibility: senders of small links mustoverpowertheirreceiver! R(x) x d If we want to schedule both links… … R(x) must be overpowered  Must transmit at power more than ~d 1) Subtle balance is needed! If senders of small links overpower their receiver… … their “safety radius” increases (spatial reuse smaller) 2)

  24. Scheduling Algorithm – Phase Scheduler • Partition links intosets of similarlength • Group sets such that links a and b in twosets in thesamegroup have at least da¸ ()(a-b)¢db  Each link gets a ijvalue Small links have large ij and viceversa  Schedule links in thesesets in oneouter-loopiteration  Intuition: Schedule links of similarlengthorvery different length • Schedule links in a group Consider in order of decreasinglength(I will not showdetailsbecause of time constraints.) small large Factor 2 between two sets =1 =2 =3 Together with structure of T(x)  (1/log3 n) bound

  25. Worst-Case Capacity in Wireless Networks Worst-Case Capacity Traditional Capacity Max. rate in random, uniform deployment Max. rate in arbitrary, worst-case deployment Networks Model (1/log n) (1/n) Protocol Model [Giridhar, Kumar, 2005] (1/log n) (1/log3n) Physical Model The Price of Worst-Case Node Placement • Exponential in protocol model • Polylogarithmicin physical model (almost no worst-case penalty!) Exponential gap between protocol and physical model!

  26. Possible Applications – Improved “Channel Capacity” • Consider a channelconsisting of wirelesssensornodes • Whatisthethroughput-capacity of thischannel...? time Channel capacity is 1/3

  27. Possible Applications – Improved “Channel Capacity” • A betterstrategy... • Assumenodecanreach 3-hop neighbor Channel capacity is 3/7 time

  28. Possible Applications – Improved “Channel Capacity” • All such (graph-based) strategieshavecapacitystrictlylessthan 1/2! • For certain and , thefollowingstrategyisbetter! time Channel capacity is 1/2

  29. Possible Application – Hotspots in WLAN • Traditionally: clients assigned to (more or less) closest access point •  far-terminal problem  hotspots have less throughput Y X Z

  30. Possible Application – Hotspots in WLAN • Potentially better: create hotspots with very high throughput • Every client outside a hotspot is served by one base station •  Better overall throughput – increase in capacity! Y X Z

  31. Possible Applications – Data Gathering • Neighboring nodes must communicate periodically (for time synchronisation, neighborhood detection, etc…) • Sending data to base station may be time critical  use long links • Employing clever power control may reduce delay & reduce coordination overhead! • From theory (scheduling) to practice (protocol design)…?

  32. Summary • Introduceworst-casecapacity of sensornetworks  Howmuchdatacanperiodicallybesent to data sink • Complementsexistingcapacitystudies • Manynovelinsights 1) Possibilities and limitations of wireless communication 2) Fundamentals of wireless communication models 3) How to devise efficient scheduling algorithms, protocols Protocol Model Poor! Exponential gap between protocol and physical model! Sensor Networks Scale! Efficient data gathering is possible in every (even worst-case) network! Efficient Protocols! Must use SINR-effects and power control to achieve high rate!

  33. Remaining Questions…? • My talk so far was based on the paper Moscibroda & W, The Complexity of Connectivity in Wireless Networks, Infocom 2006 • The paper was more general than my presentation • It was not about data gathering rate, but rather… • Given an arbitrary network • Connect the nodes in a meaningful way by links • Schedule the links such that the network becomes strongly connected • Question: Given n communication requests, assign a color (time slot) to each request, such that all requests sharing the same color can be handled correctly, i.e., the SINR condition is met at all destinations (the source powers areconstant). The goal is to minimize the number of colors. Is this a difficult problem?

  34. C D F B A E G Scheduling Wireless Links: How hard is it? Too much interference?

  35. Scheduling: Problem Definition • P: constant power level • L: set of communication requests • S: schedule S = {S1, S2,…,ST} • Interference Model: SINR • A: path-loss matrix, defined for every pair of nodes • Problem statement: Min. SINR threshold Received signal power from sender Ambient noise Received signal power from all other nodes (Interference!) Find a minimum-length schedule S, s.t. every link in L is scheduled in at least one time slot t, 1≤t ≤T, and all concurrently scheduled receivers in Stsatisfy the SINR constraints.

  36. C D F B A What if interference is determined by mutual distances (Geometric Model)? Is it harder? Or easier?? E “Scheduling as hard as coloring” … not really! “The Wall Model”: Now only adjacent links interfere! (Has been shown to be as hard as coloring [Bjoerklund 2003]) G Analogy: Euclidean Traveling Salesperson Problem

  37. Partition problem (NP-Complete [Karp 1972]): - Given a set of integers I, find two subsets of integers I1, I2, s.t.: Decision version of Scheduling: T≤2: - Consider a set of integers I, whose elements sum up to σ: Signal Interference Signal Scheduling: Reduction from Partition Schedule with timeT ≤ 2↔ Partition

  38. SINR Models • Abstract SINR • Arbitrary path loss matrix • No notion of triangle inequality • If an algorithm works here, it works everywhere! • Best model for upper bounds • Geometric SINR • Nodes are points in plane • Path loss is function of distance • If an impossibility result holds here, it holds everywhere! • Best model for lower bounds too optimistic too pessimistic • Reality is here • Path loss roughly follows geometric constraints, but there are exceptions • Open field networks are closer to Geometric SINR • With more walls, you get more and more Abstract SINR

  39. Models can be put in relation • Try to proof correctness in an as “high” as possible model • For efficiency, a more optimistic (“lower”) model might be fine • Lower bounds are best proved in “low” models

  40. Overview of results so far • Moscibroda, W, Infocom 2006 • First paper in thisarea, O(log3n) boundforconnectivity, and more • Moscibroda, W, Weber, HotNets 2006 • Practicalexperiments, ideasforcapacity-improvingprotocol • Goussevskaia, Oswald, W, MobiHoc 2007 • Hardnessresults & constantapproximationforconstant power • Moscibroda, W, Zollinger, MobiHoc 2006 • First resultsbeyondconnectivity, namely in thetopologycontroldomain • Moscibroda, Oswald, W, Infocom 2007 • Generalizion of Infocom 2006, proofthatknownalgorithmsperformpoorly • Chafekar, Kumar, Marathe, Parthasarathy, Srinivasan, MobiHoc 2007 • Cross layeranalysisforscheduling and routing • Moscibroda, IPSN 2007 • Connection to datagathering, improvedO(log2n) result • Goussevskaia, W, FOWANC 2008 • Hardnessresultsfor analog networkcoding • Locher, von Rickenbach, W, ICDCN 2008 • Still some major open problems

  41. Main open question in this area • Most papers so far deal with special cases, essentially scheduling a number of links with special properties. The general problem is still wide open: • A communication request consists of a source and a destination, which are arbitrary points in the Euclidean plane. Given n communication requests, assign a color (time slot) to each request. For all requests sharing the same color specify power levels such that each request can be handled correctly, i.e., the SINR condition is met at all destinations. The goal is to minimize the number of colors. • E.g., for arbitrary power levels not even hardness is known…

  42. Thank You!Questions & Comments? TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA

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