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Maximizing Path Durations in Mobile Ad-Hoc Networks. Yijie Han and Richard J. La Department of ECE & ISR University of Maryland, College Park CISS, Princeton University March 22nd, 2006. Outline. Background Basic Model Setup Distributional convergence Proposed algorithm

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maximizing path durations in mobile ad hoc networks

Maximizing Path Durations in Mobile Ad-Hoc Networks

Yijie Han and Richard J. La

Department of ECE & ISR

University of Maryland, College Park

CISS, Princeton University

March 22nd, 2006

outline
Outline
  • Background
  • Basic Model
  • Setup
  • Distributional convergence
  • Proposed algorithm
    • Maximizing expected path durations
  • NS-2 simulation results
    • Parameter update
  • Conclusion & Future Directions
background
Background
  • Ad hoc network routing protocols
    • Table-driven routing protocols (proactive)
      • Attempt to maintain consistent, up-to-date routing information from each node to every other node in the network.
        • Each node maintains one or more tables to store routing information.
      • Example: DSDV(Destination-Sequenced Distance-Vector), WRP (Wireless Routing Protocol), etc
    • On-demand routing protocol (reactive)
      • Attempt to minimize the number of required broadcasts by providing a path only when requested
      • Require path/route discovery phase/mechanism
      • Examples: AODV( Ad-hoc On-demand Distance Vector), DSR (Dynamic Source Routing)
motivation
Motivation
  • On-demand routing protocols in ad-hoc networks
    • Path recovery procedure initiated when an existing path is broken
      • Disruption in network service to applications
    • Performance and overhead shaped by the distribution of link and path durations
      • Suggests that (expected) path duration should be taken into account when selecting a path
        • Reduce overhead
        • Provide more reliable network service to applications
    • Requires understanding of statistical properties of path duration
existing protocols
Existing protocols
  • Ad-hoc On-demand Distance Vector (AODV)
    • Selects the first discovered route
  • Dynamic Source Routing (DSR)
    • Selects the min-hop route
  • Associativity Based Routing (ABR)
    • Each node maintains “associativity” for each neighbor from beacons
      • Higher beacon counts = more stable links
    • Destination selects the path with the highest average associativity
slide6

Outline

  • Background
  • Basic Model
  • Setup
  • Distributional convergence
  • Proposed algorithm
  • NS-2 simulation results
    • Parameter update
  • Conclusion & Future Directions
basic model for studying statistical properties of path duration

Connectivity between nodes

    • {0, 1}-valued reachability process

between two nodes

      • xij(t) = 1 – if the link (i,j) is up
      • xij(t) = 0 – if the link (i,j) is down
      • xij(t) = xji(t) – symmetric links
Basic Model (for studying statistical properties of path duration)
  • V = {1, …, I} - set of mobile nodes moving across a domain D of R2 or R3
    • - location/trajectory of node i
slide8

Basic Model

Basic Model

  • Link durations
    • {Uij(k), k = 1, 2, ,…} and {Dij(k), k = 1, 2, …}
      • Uij(k) (resp. Dij(k)) – duration ofk-thup (resp. down) time
  • Time-varying graph (V, E(t))

t

basic model
Basic Model
  • Path discovery phase
    • Path available between s and d if a set of links provides

connectivity

      • May not be unique
      • Routing algorithm selects one
    • Denote the set of links along the selected path byLsd(t)

n4

n1

n2

s

d

n3

excess life and path duration
Excess Life and Path Duration
  • For each link
    • - time to live or excess life after time t
  • Time to live or duration of a path
    • Path available till one of the links goes down
    • Path duration = amount of time that elapses till one of the links in breaks down
slide11
Question:What does the distribution of look like?
    • In particular, when the hop counter is large
      • In a large scale MANET, the number of hops is expected to be large
slide12

Outline

  • Background
  • Basic Model
  • Setup – Parametric Scenario and Difficulties
  • Distributional convergence
  • Proposed algorithm
  • NS-2 simulation results
    • Parameter update
  • Conclusion & Future Directions
slide13

Parametric Scenario

  • Scaling: For each fixed n = 1, 2, …,
    • -- set of mobile nodes
    • -- domain across which nodes move
  • Stationarity:Reachability processes jointly stationary
    • constitutes a stationary sequence with generic marginals
    • - CDF of
  • A pair of source and destination nodes selected at time t = 0 for each n
slide14

Parametric Scenario (cont’d)

  • Define
    • Excess or residual life of a link
      • Distribution of forward recurrence time
      • Follows from elementary renewal theory
slide15

Parametric Scenario (cont’d)

  • Path duration -
  • Explore the distributional properties of the rvs

as

sources of difficulty
Sources of Difficulty
  • - random set that depends on
    • Assume is a deterministic sequence with for convenience

Example:

  • Fix the domain, and randomly select the locations of the source and destination
  • Randomly place n2 – 2 other nodes in the domain
  • Transmission range decreases as 1/n
  • Number of hops along the shortest path increases with n
slide17

Sources of Difficulty (cont’d)

  • Dependence of reachability processes
    • Introduces dependence in link excess lives
    • Asymptotic independence – dependence in link excess lives goes away asymptotically as hop distance increases
      • Mixing conditions
slide18

Outline

  • Background
  • Basic Model
  • Setup
  • Distributional convergence
  • Proposed algorithm
  • NS-2 simulation results
    • Parameter update
  • Conclusion & Future Directions
slide19

Assumptions

  • Assumption 1: (scaling) There exists such that

where

    • Scaling introduced for defining limit distribution parameter
  • Assumption 2: For every and any given

there exists an integer such that

  • Interpretation:probability that a link duration is strictly
  • positive is one
definitions
Definitions
  • Array of -valued rvs
  • for notational convenience
definitions1
Definitions
  • Let be a sequence of real numbers
    • Usually increases with n
slide22

Definitions

  • Sufficient condition:
slide23

Assumptions

  • Define
    • A sufficient condition is that there exists an arbitrarily small constant e > 0 such that for all and
slide26

Distributional convergence

  • Implications: For sufficiently large hop count, the expected path duration can be approximated by
slide27

Outline

  • Background
  • Basic Model
  • Setup
  • Distributional convergence
  • Proposed algorithm
  • NS-2 simulation results
    • Parameter update
  • Conclusion & Future Directions
proposed algorithm
Proposed algorithm
  • Link durations seen by a node likely to depend on its own type and the types of neighbors
    • Different nodes with different speeds and capabilities
    • Each node maintains average link durations
    • Can maintain a separate average for each type of neighbors
    • Average link duration used as estimate of expected link durations (during path discovery)
slide29

Outline

  • Background
  • Basic Model
  • Setup
  • Distributional convergence
  • Proposed algorithm
  • NS-2 simulation results - AODV
    • Parameter update
  • Conclusion & Future Directions
ns 2 simulation setup
NS-2 simulation - Setup
  • Modified AODV routing protocol
  • 200 nodes in 2 km x 2 km rectangular region
  • Transmission range = 250 m
  • Two classes of nodes
    • Nodes with different speed (e.g., soldiers vs. jeeps or tanks)
    • Class 1 node speed ~ [1, 5] m/s
    • Class 2 node speed ~ [10, 30] m/s
  • Varying mixture
    • Class1:Class2 = 140:60, 160:40, and 180:20
slide34

Outline

  • Background
  • Basic Model
  • Setup
  • Distributional convergence
  • Proposed algorithm
  • NS-2 simulation results
    • Parameter update
  • Conclusion & Future Directions
estimation of expected path duration
Estimation of expected path duration
  • Recall: For sufficiently large hop count, the expected path duration can be approximated by
  • Question: For finite hop counts, how good is this approximation?
    • For back-up paths
    • Local recovery after a link failure
threshold update local recovery
Threshold update – local recovery
  • Select a back-up path only if the estimated probability of being available exceeds a certain threshold
    • Probability of being available estimated to be
    • Not accurate due to discrepancy in exp. parameter and collected IPD value (sum of inverses of expected link durations)
      • Target probability
      • Update the threshold as follows

where is the threshold after n back-up path tries and is the indicator function of a back-up path being available

Amount of time since last update

threshold update
Threshold update
  • Define to be the indicator function of the event that a selected backup path is available when the threshold value is
  • and - unknown distribution of and its mean, respectively
    • Assume (i) is strictly increasing in , and (ii) there exists

such that

slide38

Outline

  • Background
  • Basic Model
  • Setup
  • Distributional convergence
  • Proposed algorithm
  • NS-2 simulation results
    • Parameter update
  • Conclusion & Future Directions
conclusions future directions
Conclusions & Future Directions
  • Studied the statistical properties of path durations in MANETS
    • Showed distributional convergence with increasing hop count
    • Relationship between link durations and path duration
  • Proposed an algorithm for maximizing expected durations of selected paths
    • Stochastic approximation based algorithm for handling the discrepancy between IPD values and exponential parameters
  • Plan to implement with other on-demand routing protocols
    • Validation of assumptions
    • Convergence speed
proposed algorithm in aodv
Proposed algorithm in AODV
  • Each node maintains a route entry from each known dest node
    • Up to k paths (instead of a single path in AODV)
    • (i) dest seq. number, (ii) next hop, (iii) hop count, and (iv) Inverse Path Duration (IPD)
      • IPD = sum of the inverses of average link durations reported in a path reply message
    • Paths ranked based on (i) seq. number, (ii) IPD value, (iii) hop count
  • Request message
    • (i) src ID, seq. number, (ii) broadcast ID, (iii) dest ID and seq. number, and (iv) hop count to the src
  • Reply message
    • (i) dest ID, (ii) dest seq. number, (iii) IPD value, and (iv) hop count
  • Either an intermediate node or dest generates a reply message
    • Intermediate node – copy information from its entry
    • Dest node – initialize IPD and hop count to zero