Download Maximizing Path Durations in Mobile Ad-Hoc Networks

Maximizing Path
Durations in Mobile AdHoc Networks
Yijie Han and Richard J. La
Department of ECE & ISR
University of Maryland, College Park
CISS, Princeton University
March 22nd, 2006
Outline
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Background
Basic Model
Setup
Distributional convergence
Proposed algorithm
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NS-2 simulation results
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Maximizing expected path durations
Parameter update
Conclusion & Future Directions
Background
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Ad hoc network routing protocols
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Table-driven routing protocols (proactive)
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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
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On-demand routing protocols in ad-hoc networks
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Path recovery procedure initiated when an existing path
is broken
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Disruption in network service to applications
Performance and overhead shaped by the distribution of
link and path durations
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Suggests that (expected) path duration should be taken
into account when selecting a path
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Reduce overhead
Provide more reliable network service to applications
Requires understanding of statistical properties of path
duration
Existing protocols
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Ad-hoc On-demand Distance Vector (AODV)
 Selects the first discovered route
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Dynamic Source Routing (DSR)
 Selects the min-hop route
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Associativity Based Routing (ABR)
 Each node maintains “associativity” for each neighbor from
beacons
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Higher beacon counts = more stable links
Destination selects the path with the highest average
associativity
Outline
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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)
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V = {1, …, I} - set of mobile nodes moving across a
domain D of R2 or R3
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- location/trajectory of node i
Connectivity between nodes
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{0, 1}-valued reachability process
between two nodes
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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
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Link durations
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{Uij(k), k = 1, 2, ,…} and {Dij(k), k = 1, 2, …}
 Uij(k) (resp. Dij(k)) – duration of k-th up (resp. down) time
t
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Time-varying graph (V, E(t))
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Basic Model
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Path discovery phase
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Path available between s and d if a set of links provides
connectivity
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May not be unique
Routing algorithm selects one
Denote the set of links along the selected path by Lsd(t)
n4
n1
n2
s
n3
d
Excess Life and Path Duration
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For each link
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- time to live or excess
life after time t
Time to live or duration of a
path
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Path available till one of the
links goes down
Path duration = amount of
time that elapses till one of
the links in
breaks
down
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Question: What does the distribution of
look
like?
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In particular, when the hop counter
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is large
In a large scale MANET, the number of hops is expected to
be large
Outline
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Background
Basic Model
Setup – Parametric Scenario and Difficulties
Distributional convergence
Proposed algorithm
NS-2 simulation results
 Parameter update
Conclusion & Future Directions
Parametric Scenario
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Scaling: For each fixed n = 1, 2, …,
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Stationarity: Reachability processes jointly stationary
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-- set of mobile nodes
-- domain across which nodes move
constitutes a
stationary sequence with generic marginals
- CDF of
A pair of source and destination nodes selected at time
t = 0 for each n
Parametric Scenario (cont’d)
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Define
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Excess or residual life of a link
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Distribution of forward recurrence time
Follows from elementary renewal theory
Parametric Scenario (cont’d)
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Path duration -
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Explore the distributional properties of the rvs
as
Sources of Difficulty
- random set that depends on
1.
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Assume
with
is a deterministic sequence
for convenience
Example:
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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
Sources of Difficulty (cont’d)
2.
Dependence of reachability processes
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Introduces dependence in link excess lives
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Asymptotic independence – dependence in link excess
lives goes away asymptotically as hop distance
increases
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Mixing conditions
Outline
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Background
Basic Model
Setup
Distributional convergence
Proposed algorithm
NS-2 simulation results
 Parameter update
Conclusion & Future Directions
Assumptions
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Assumption 1: (scaling) There exists
such that
where
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Scaling introduced for defining limit distribution parameter
Assumption 2: For every
there exists an integer
and any given
such that
-Interpretation: probability that a link duration is strictly
positive is one
Definitions
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Array of
-valued rvs
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for notational convenience
Definitions
 Let
numbers
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Usually increases with n
be a sequence of real
Definitions
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Sufficient condition:
Assumptions
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Define
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A sufficient condition is that there exists an arbitrarily small
constant e > 0 such that
for all
and
Assumptions
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Interpretation of Assumption 4
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Distributional convergence
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Implications: For sufficiently large hop count, the expected
path duration can be approximated by
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Outline
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Background
Basic Model
Setup
Distributional convergence
Proposed algorithm
NS-2 simulation results
 Parameter update
Conclusion & Future Directions
Proposed algorithm
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Link durations seen by a node likely to depend on its own
type and the types of neighbors
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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)
Outline
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Background
Basic Model
Setup
Distributional convergence
Proposed algorithm
NS-2 simulation results - AODV
 Parameter update
Conclusion & Future Directions
NS-2 simulation - Setup
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Modified AODV routing protocol
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200 nodes in 2 km x 2 km rectangular region
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Transmission range = 250 m
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Two classes of nodes
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Nodes with different speed (e.g., soldiers vs. jeeps or tanks)
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Class 1 node speed ~ [1, 5] m/s
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Class 2 node speed ~ [10, 30] m/s
Varying mixture
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Class1:Class2 = 140:60, 160:40, and 180:20
NS-2 simulation
NS-2 simulation
NS-2 simulation
Outline
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Background
Basic Model
Setup
Distributional convergence
Proposed algorithm
NS-2 simulation results
 Parameter update
Conclusion & Future Directions
Estimation of expected path duration
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Recall: For sufficiently
large hop count, the
expected path duration
can be approximated by
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Question: For finite hop
counts, how good is this
approximation?
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For back-up paths
Local recovery after a link
failure
Threshold update – local recovery
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Select a back-up path only if the estimated probability of
being available exceeds a certain threshold
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Probability of being available estimated to be
Amount of time since last update
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Not accurate due to discrepancy in exp. parameter and
collected IPD value (sum of inverses of expected link
durations)
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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
Threshold update
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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
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Assume (i)
is strictly increasing in
such that
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, and (ii) there exists
Outline
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Background
Basic Model
Setup
Distributional convergence
Proposed algorithm
NS-2 simulation results
 Parameter update
Conclusion & Future Directions
Conclusions & Future Directions
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Studied the statistical properties of path durations in MANETS
 Showed distributional convergence with increasing hop count
 Relationship between link durations and path duration
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Proposed an algorithm for maximizing expected durations of
selected paths
 Stochastic approximation based algorithm for handling the
discrepancy between IPD values and exponential parameters
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Plan to implement with other on-demand routing protocols
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Validation of assumptions
Convergence speed
Proposed algorithm in AODV
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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
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