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## Maximizing Path Durations in Mobile Ad-Hoc Networks

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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
- Maximizing expected path durations
- NS-2 simulation results
- Parameter update
- Conclusion & Future Directions

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

- 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

- 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

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

- {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

- V = {1, …, I} - set of mobile nodes moving across a domain D of R2 or R3
- - location/trajectory of node i

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

- 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

- 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

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

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

- 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

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

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

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

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

- 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

- Array of -valued rvs
- for notational convenience

Definitions

- Let be a sequence of real numbers
- Usually increases with n

- Sufficient condition:

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

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

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

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)

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

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

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

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

- 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

- 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

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

- 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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