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Maximizing Network Lifetime Online by Localized Probabilistic Load-Balancing

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Maximizing Network Lifetime Online by  Localized Probabilistic Load-Balancing Powered By Docstoc
					Yongcai Wang1, Yuexuan Wang1, Haisheng Tan2, Francis. C.M. Lau2

  1. Institute for Interdisciplinary Information Science, Tsinghua
                           University, China

            2. Hongkong University, Hongkong, China
     How to maximize the running lifetime of a sensor
      network after it is deployed for data collection?
     
•An example of sensor network for farmland Information monitoring
    •The network is hoped to work for several years.
    •The network can be very large in size.
    •The nodes, links, data flows maybe dynamic and unpredictable.
    •Centralized, offline routing policies are not satisfactory for recalculation cost.
    •Distributed, online, adaptive method for network lifetime maximization is
    needed.




                       Yongcai Wang, IIIS, Tsinghua University                       2
             Sink
                                  Data Collection Network
             Sink
                                    Every node captures one unit data in each
                      3              period and transmits data towards the sink.
     3        4
                                    The intermediate nodes transmit its own
                      2
                                     data and forward data for their children.
     2        3
                                    Routes are selected in minimum hop
                                     manner for energy efficiency and collision
                          1
 1       1        1                  avoidance.
                                  Lifetime optimization problem
Routing tree optimization           The lifetime of the network is defined as
                                     work duration before the first node dies.
Load-balancing
                                    Construction of an optimal routing tree is
Network lifetime                     NP-Complete [Liang2007, 2007]
optimization                         [Buragohain2005].
                              Yongcai Wang, IIIS, Tsinghua University             3
                                                                    Sink 1
• Probabilistic Routing
  • Route data to parent candidates with                  p2,1
                                                                       p3,1 p4,1
    some probabilities, forming weighted
                                                              2          3          4
    graph.
                                                       p5,2       p5,3 p6,3 p6,4
• Characters
  1. Better:Providing better network                               5            6
     lifetime than the tree-based routing.
                                                                  Sink
  2. Easier: It can be transformed to the
     maximum flow problem, which can be
     solved in polynomial time by linear
     programming [Buragohain2005].
  3. More reliable: because of multiple-path
     routing.
                                                                         Probabilistic
  4. Meet the real scenarios: Traffic system,                            Routing
                         networks.
     internet, sensorWang, IIIS, Tsinghua University
                 Yongcai                                                            4
   But, real applications require.                                               Sink 1
     Scalability
                                                                         p2,1
     Self-Adapting to nodes movement;                                               p3,1 p4,1
      join/Leave; Link, flow dynamics                                        2        3          4
     Localized communication and localized
                                                                      p5,2       p5,3 p6,3 p6,4
      decision
                                                                                 5          6
   Distributed Probabilistic Routing
     Make local decisions based on local
      information.

   Challenged by:                                             General challenges
     Load Oscillation (Instability)                             in distributed
     Local Optimum                                                algorithms


                     Yongcai Wang, IIIS, Tsinghua University                                         5
1.   We investigate the reason of instability and local optimum.

2.   Localwiser, a localized probabilistic routing algorithm for
     online maximizing the network’s lifetime is proposed.

3.   Proofs to the convergence and optimality properties of
     Localwiser are presented .

4.   The convergence speed, scalability, and self-adapting
     performances of Localwiser in static and dynamic networks
     are evaluated by simulation.

5.   A demo system was developed.

                 Yongcai Wang, IIIS, Tsinghua University           6
• Local Info of a sensor i:                     Node 3’s local information in round t
    • Li(t) : current load of itself;
    •       : children set.                          L1(t) 1            2 L2(t)
    •       : parent candidate set.                       P31(t)      P32(t)
    • {Pi,j(t)}: Transmission probabilities among
                                                            L3(t) 3
      one-hop neighbors
    • {Lj(t)}: Loads of one-hop neighbors               P43(t)      P53(t) P63(t)
•The amount of data i transmits in round t:                          4                 6
                                                                            5
                                                                    L4(t)   L5(t)          L6(t)
                                                      Load
                                                      accumulation
•Suppose the network can converge quickly, the expected lifetime of node i:
                           Li(s) is stable load of i.

• The goal of network lifetime maximization:
                                                                Minimize the maximum
                      Yongcai Wang, IIIS, Tsinghua University
                                                                load/energy ratio              7
              l1t         l2t
                                                        Uncontrollable Loads
                                                               x1 = l1t - p1t * lt
              p1t        p2t                                   x2 = l2t - p2t * lt
       x1                              x2
                    lt
                                                        Balance Parent candidate’s loads
                                                        in greedy manner
Load Oscillation Problem:
                                                         if ( x1  x2 )  l t   p21  1, p1t 1  0
                                                                                 t




                                                        if ( x2  x1 )  l t    p1t 1  1, p21  0
                                                                                             t



                                                                                             n
                                                         if |x2  x1 | l                    x
                                                                            t
                                                                                                    j    nxi
                                                                                        1    j 1
                                                                                pit 1  
                                                                                        n           n

Sensor is unaware of other siblings’ concurrent operations. The total force of
the sensors’ greedy reactions causes the load oscillation.
                         Yongcai Wang, IIIS, Tsinghua University                                                8
      Probabilistic Dynamic Load Balance [Yan 2005]:

                   l1        l2
                   t         t                            The proposed a heuristic that
                                                          the forwarding probability is
                 p1t         p2t                          inversely
                                                          proportional to the parent
 Local Optimum Problem:                                   candidate’s loads:

                                                                        t 1            1
                                                                      pi               n
                                                                                           1
                                                             DLBT:                 l  t
                                                                                   i
                                                                                    t

                                                                                      j 1 l j


• Phenomenon: converge to some stable status, but the status is not optimal.
The algorithm cannot proceed towards load-balance any more.
•Reason: unawareness to the expected balanced load of its parents; the
algorithms converge to some local optimum without enough knowledge.
                        Yongcai Wang, IIIS, Tsinghua University                                  9
   Propose a local cost function (LCNL) as sensor’s metric about
    network lifetime




      • LCNL is calculated recursively.                                                                  Sink 1
                                                                                    Example
      • LCNL of a sensor is affected by the                                                    p2,1
        loads of all ancestors and the link                                                                  p3,1 p4,1
        probabilities.                                                                             l2         l3         l4
        C 2 ( t )  L2 ( t ) / e2 ; C 3 ( t )  L3 ( t ) / e3 ; C 4 ( t )  L4 ( t ) / e4   p5,2        p5,3 p6,3 p6,4
        C5 ( t )  P52 ( t )C 2 ( t )  P53 ( t )C 3 ( t )
        C6 ( t )  P63 ( t )C 3 ( t )  P64 ( t )C 4 ( t )                                              l5          l6




                           Yongcai Wang, IIIS, Tsinghua University                                                  10
   Instability and local optimum are still challenging.
   we propose a virtual guidance E(C), i.e., LCNL of sensors when
    all LCNLs of sensors are equal. Although it is unknown, we use
    it to derive formulas.
   Based on the virtual guidance, a distributed LocalWiser
    algorithm was proposed.
                                                            E(C) is unknown


   Where Mi(t) is the normalize to keep the sum of transmission
    probabilities equal to one:


   Then, we have:
                                                                 E(C) disappears.

                  Yongcai Wang, IIIS, Tsinghua University                           11
Yongcai Wang, IIIS, Tsinghua University   12
Yongcai Wang, IIIS, Tsinghua University   13
   We prove:
    1. LocalWiser must be stable.
    2. The stable status of Localwiser provides
       optimal lifetime of the network.

   The convergence speed, adapting
    performances are evaluated by simulations.




                Yongcai Wang, IIIS, Tsinghua University,   Adhoc Now2011   14
Yongcai Wang, IIIS, Tsinghua University   15
So, MCN’s parent candidates with positive links are all MCNs.




               Yongcai Wang, IIIS, Tsinghua University          16
1. The network is composed of K isolated sets, where nodes in
   each isolated set have equal LCNL.
2. The transmission probabilities among nodes in different sets
   are zero.
3. Each isolated set contains first level nodes, and the first level
   nodes are fully covered by the K isolated sets.




                   Yongcai Wang, IIIS, Tsinghua University             17
   A Chebyshev’s Sum Inequality based metric
    [Dai,2003] is used to measure the load-balancing
    performance of the first level sensors:




Theorem 3 (Optimality). When the network has reached stable
status, any modification to the probability assignments at any
node can only make the load balancing performance of the first
level nodes worse.

    Proved by Rearrangement Inequality.
               Yongcai Wang, IIIS, Tsinghua University       18
   Evaluate:                       the minimum energy/load ratio
   Compared with:
    1. Centralized algorithm using global information and Linear
       Programming (LP), which is the global optimal result;
    2. Greedy algorithm for local load-balancing (Greedy);
    3. Dynamic Load-Balanced routing Tree(DLBT);
    4. Level-based load balancing algorithm (Level-based
       Balancing).
   Evaluation in:
    1. Static networks
    2. Dynamic networks
      ▪   Network topology is dynamic
      ▪   Flow dynamic

                   Yongcai Wang, IIIS, Tsinghua University          19
                                          Quick
                                          convergence
                                          and optimality




Yongcai Wang, IIIS, Tsinghua University               20
                                          Quick
                                          convergence
                                          and optimality




Yongcai Wang, IIIS, Tsinghua University               21
                                          Quick
                                          adaptation to
                                          topology
                                          dynamics.




Yongcai Wang, IIIS, Tsinghua University               22
                                          Quick
                                          adaptation to
                                          flow dynamics.




Yongcai Wang, IIIS, Tsinghua University                23
   http://project.iiis.tsinghua.edu.cn/balance




              Yongcai Wang, IIIS, Tsinghua University,   Adhoc Now2011   24
   Mapping the network lifetime maximization problem to
    a localized cost-balancing problem.
   LocalWiser:
    1.   computing locally and distributedly;
    2.   stable;
    3.   optimal;
    4.   fast self-adapting to the network dynamics;
    5.   easily implemented
   Future work:
        Jointly optimize the transmission power and the link
         probability.
        Mobility of the sensors can improve the performance of
         LocalWiser
        The convergence speed of LocalWiser
                   Yongcai Wang, IIIS, Tsinghua University        25
       Thanks. Q&A




Yongcai Wang, IIIS, Tsinghua University   26

				
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posted:11/2/2011
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