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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: Approaches. S. D.

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wireless networks routing approaches
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: Approaches
delay disruption tolerant networks

S

D

Delay/disruption tolerant networks
  • Intermittent connectivity
  • Nodes mobile

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D

conventional routing protocols fail
Conventional 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
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
Example of store and forward routing

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

strategies
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
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
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
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 & schemes
  • Problem formulation
  • Single-copy strategy
    • Schemes
    • performance analysis
    • simulations
  • Multi-copy strategy
    • Schemes
    • performance analysis
    • simulations
problem formulation
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
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
Single-copy schemes
  • Direct transmission
  • Randomized routing
  • Utility-based routing
  • Seek and focus
  • Oracle-based optimal algorithm
direct transmission
Direct transmission
  • Only forward to destination

+ Single transmission

- Slow: baseline scheme

expected delay is an upper bound for any other protocol

randomized routing
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
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 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
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
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
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
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)

direct transmission k 022

A

Direct transmission: K > 0

1) EDdt = EXTA

2) EXTA = EXTY - EATY

EXTY = cNLogN

K = 3

oracle based optimal algorithm23

2

where HM-1 is the harmonic sum

1

2

Oracle-based optimal algorithm
  • M nodes
  • Tx Range = K

D

S

randomized algorithm

f(K)

D

Average step size:

d = 1 – q + q f(K)

Randomized Algorithm

Probability 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
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!

simulation vs analysis

upper bound

lower bound

Simulation vs. Analysis
  • Simulation and theoretical results are closely matched
  • Randomized algorithm is efficient for large K
simulations with contention
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 contention
scenario 1 random walk

Seek and Focus (p = 0.5)

4

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
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
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
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 analysis32
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
source spray and wait

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
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
How to choose L?
  • Determine a delay to be achieved
  • Solve for L
    • Use recursive equation
    • Use upper bound
simulation vs analysis36
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
simulation vs analysis cont d
Simulation vs. Analysis (cont’d)

(analysis)

Efficient spraying becomes more important for large L

simulations with contention waypoint model
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
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
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
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
Summary
  • Routing in DTNs
    • Store & forward: a new paradigm
    • Single-copy schemes
    • Multi-copy schemes
    • Analysis & simulation of several schemes
other routing approaches
Other routing approaches
  • Cross-layer design
  • Combined w/ network coding
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