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reactive & proactive approaches

being standardized

optimization approach

provably optimal properties

routing in delay/disruption tolerant networks

a different paradigm

other approaches

cross-layer design, network coding, …

Wireless networks routing: ApproachesConventional routing protocols fail

- Reactive protocols (e.g. DSR, AODV)
- route request cannot reach destination!
- path breaks right after or even while being discovered
- Proactive protocols (e.g. DSDV)
- will fail to converge!
- deluge of topology-update packets

A different routing paradigm

- Exploit node mobility to deliver messages

Idea: If we overlap many snapshots over time, an end-to-end path will be formed eventually!

- Store-and-forward model of routing:
- a node stores a message until an appropriate communication opportunity arises
- a series of independent forwarding decisions {time + next hop} that will eventually bring the packet to its destination

Example of store and forward routing

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Main Issue: What is an “appropriate” next hop?

Strategies

- “Single-Copy”: only a single copy of each message exists in the network at any time
- “Multiple-Copy”: multiple copies of a message may exist concurrently in the network

Single Copy

Multiple Copy

+ lower number of transmission

+ lower contention for shared resources

+ lower delivery delay

+ higher robustness

Single copy strategy

- Direct transmission
- Source only forwards message to destination
- Randomized routing
- Node A forwards message to node B with probability p
- Other schemes?
- Design tradeoff?
- Delay versus resource (power, storage)

Multicopy strategy

- Epidemic routing
- Spread of “disease”
- Whenever “infected” node meets “susceptible” node, a copy is forwarded
- Probabilistic forwarding
- When “infected” node meets “susceptible” node, a copy is forwarded w/ prob. of p
- Other schemes?
- Design tradeoff?
- Delay versus resource (power, storage)

DTN routing schemes

- Design space large
- Single-copy or multi-copy?
- Single-copy
- Which node to forward to? When?
- Multi-copy
- Which nodes to forward to? When?
- Who is allowed to forward?
- How to limit the # of copies in network?
- Once delivered to destination, how to “recover”?
- How to evaluate schemes?
- Simulation? Analysis (what techniques)?

Problem formulation & schemes

- Problem formulation
- Single-copy strategy
- Schemes
- performance analysis
- simulations
- Multi-copy strategy
- Schemes
- performance analysis
- simulations

Problem formulation

- M nodes move independently on an grid of size N
- mobility models: random walk, random waypoint
- Transmission range K
- small enough to have partial connectivity
- transmission is faster than movement
- Use beaconing to know its neighbors
- Proximity measure between positions A and B
- Manhattan distance: dAB = |xA – xB| + |yA – yB|
- Performance evaluation metrics
- average delivery delay
- number of transmissions (per message delivered)

Problem Formulation (cont’d)

- Each node maintains a timer for each other node
- TX(Y): time elapsed since X last “encountered” Y
- “encounter” = come within transmission range
- only information available to a node X regarding the network (no location, speed, direction, etc.)
- Timer maintenance
- Initially: TX(Y) =
- When X encounters Y: TX(Y) = 0
- At every time step (unless case b applies): TX(Y) = TX(Y) + 1

Single-copy schemes

- Direct transmission
- Randomized routing
- Utility-based routing
- Seek and focus
- Oracle-based optimal algorithm

Direct transmission

- Only forward to destination

+ Single transmission

- Slow: baseline scheme

expected delay is an upper bound for any other protocol

Randomized routing

- A forwards message to B with probability p
- B is not allowed to forward it back to A for a given amount of time
- Property
- Blind forwarding
- yet, because transmission is faster than movement, forwarding a message results in a reduction of the expected delivery time to destination

Utility-based Routing

- In most mobility models, if TB(D) < TA(D),

P(B closer to D than A) > P(A closer to D than B)

- Define an appropriate utility function UX(Y) based on timer value TX(Y)
- UX(Y) is a monotonically decreasing function of TX(Y)
- Utility-based routing:

Node A forwards a message for node D to node B iff UA(D) < UB(D)

Randomized vs. utility-based routing

- Randomized strategy

+ transmissions are faster than movement

- many transmissions for marginal gain (forwards message blindly)

- Utility-based strategy

+ takes advantages of indirect location info to make better forwarding decisions

- slow start: in a large network, source and destination are far => all nodes around source have very low utility => takes a long time until a good next hop is found initially

Seek and focus

IDEA: Avoid the slow start phase of utility-based schemes, while still taking advantage of the higher efficiency of utility-based forwarding

- Seek phase: if utility around node is low, perform randomized forwarding to quickly search nearby nodes
- Focus phase: when a high utility node (i.e. above a threshold)is discovered, switch to utility-based forwarding
- look for a good leadto the destination and follow it

Oracle-based optimal algorithm

- Assume all nodes trajectories (future movements) are known
- Then, picks the sequence of forwarding decisions that minimizes delay
- Note that epidemic routing has the same delay as this algorithm when there is no contention

Performance analysis

- Metric: expected delivery delay (ED)
- Assumptions
- mobility model: random walk on grid (torus)
- no contention in the wireless channel
- no limit in buffer space
- Hitting time
- time takes to “encounter” destination (within transmission range)
- EXTY: expected hitting time from X to Y
- ET: expected hitting time from stationary distribution

Direct transmission: K = 0

- ED = ET
- Hitting time distribution approximately exponential:
- Results from D. Aldous and J. Fill “Reversible Markov chains and random walks on graphs”

ET = (NlogN)

D

Average step size:

d = 1 – q + q f(K)

Randomized AlgorithmProbability q: Tx jump

q =

p •

P(at least one node within range)

f(K): average transmission distance

Probability 1-q: Random walk

Randomized Algorithm (cont’d)

- Approximate actual message movement with a random walk performing d independent 1-step moves at each time slot
- Note: This walk is slower than the actual walk
- would reach destination later, on the average
- Define an appropriate martingale to show that:

Destination movement

Message movement

Note: d + 1 ≥ 2 randomized is faster than direct transmission!

lower bound

Simulation vs. Analysis- Simulation and theoretical results are closely matched
- Randomized algorithm is efficient for large K

Simulated schemes

Randomized with probability p = 0.5

Randomized with probability p = 1.0

Utility-based routing

Seek and Focus (with probability p = 0.5 in seek phase)

Seek and Focus (with probability p = 1.0 in seek phase)

Direct transmission

MAC: slotted CSMA to handle contention

Simulations with contention4

Utility-based

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Seek and Focus (p = 1.0)

Scenario 1 (random walk)- 500x500 grid, 50 nodes, transmission range = 60
- 50 messages are routed between randomly chosen nodes

Randomized (p = 0.5)

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Randomized (p = 1.0)

- Randomized routing: low delay, many trans.
- utility based: slow, # of transmission small.
- Seek and focus: low delay, # of transmission small

Multi-copy schemes

- Epidemic Routing (flooding): handover a copy to everyone
- minimum delay under no contention
- Randomized Flooding: handover a copy w/ probability p
- Utility-based Flooding: handover a copy to a node w/ utility at least Uth higher than current
- Constrained Utility-based Flooding: like previous, but may only forward a bounded number of copies of the same message

Spray and wait

- Performance goals
- significantly reduce transmissions by bounding the total # of copies/transmissions per message
- under low traffic: minimal penalty on delay (close to optimal)
- under high traffic: reduce the delay of existing flooding- and utility-based schemes thanks to less contention
- 2 phases:
- “Spray phase”: spread L message copies to L distinct relays
- “Wait phase”: wait until one of the L relays finds the destination (i.e. use direct transmission)

Spray and Wait Variations

- Source Spray and Wait
- Source starts with L copies
- whenever it encounters a new node, it hands one of the L copies
- this is the slowest among all (opportunistic) spraying schemes
- Optimal Spray and Wait
- source starts with L copies
- whenever a node with n > 1 copies finds a new node, it hands half of the copies that it carries
- spreads the L copies faster than any other spraying scheme

Performance analysis

- Metric: expected delivery delay (ED)
- Assumptions
- mobility model: random walk on grid (torus)
- no contention in the wireless channel
- no limit in buffer space
- Recall EDdt denotes the expected delivery delay of direct transmission

If new node found by source, forward another copy

If not destination, add extra term

Expected remaining delay after i copies are spread

Time until a new node is found

P(not destination)

If found by relay, do nothing

Source spray and wait- ED(i): expected remaining delay after i copies are spread
- Clearly EDsrc = ED(1)
- ED(1) can be calculated through a system of recursive equations

If destination, stop

- A similar recursion procedure gives the delay of Optimal Spray and Wait

Upper bound

- Exact delay not in closed form
- Derive a bound in closed form
- This is an upper bound for any Spray and Wait algorithm

Probability a wait phase is needed

Wait Phase

Spray Phase

Bound is tight for L<<M

How to choose L?

- Determine a delay to be achieved
- Solve for L
- Use recursive equation
- Use upper bound

Simulation vs. Analysis

(analysis)

- Good match between theory and simulations
- Spray and Wait achieves a delay only 1.5-2 times that of the optimal

Simulated schemes

Epidemic routing

Randomized flooding (p = 0.03)

Utility-based flooding (Uth = 0.02)

Constrained utility-based flooding

Source Spray and Wait (L = 10)

Optimal Spray and Wait (L = 10)

Seek and Focus

Oracle-based optimal algorithm

Same collision avoidance MAC protocol and utility function as before

Simulations (with contention, waypoint model)Scenario A (low traffic)

500x500, M = 50 nodes, K = 20

- Spray and Wait
- Low delay (twice that of the optimal), small # of transmissions (even less than seek and focus)
- achieves a lower delay than utility-based schemes

Scenario B (high traffic)

500x500, M = 50, K = 20 (6% coverage), 40 (25% coverage)

- Spray and Wait achieves up to an order of magnitude reduction in number of transmission compared to flooding and utility-based schemes
- and a delivery delay lower than all other schemes

Performance of multi-copy routing: other approaches

- Use Markov chains
- Use ordinary difference equations (limits of Markovian models for large # of nodes)
- Flexible
- Much easier than using Markov chains
- Also models
- recovery from “epidemic”
- resource usage (buffer usage, # of copies sent)
- See reading list

Summary

- Routing in DTNs
- Store & forward: a new paradigm
- Single-copy schemes
- Multi-copy schemes
- Analysis & simulation of several schemes

Other routing approaches

- Cross-layer design
- Combined w/ network coding
- …

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