Performance Modeling of Epidemic Routing

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Performance Modeling of Epidemic Routing

• Xiaolan Zhang, Giovanni Neglia,
  Jim Kurose, Don Towsley
• Department of Computer Science
• University of Massachusetts at Amherst
• Università degli Studi di Palermo

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Disruption/Delay Tolerant Network (DTN)

• Network with intermittent connectivity
• Limited/no infrastructure gt ad hoc network
• Mobility and sparse settings gt frequent
• partition
• Examples
• Vehicular network DakNet, UMassDieselNet
• Sparse mobile sensor networks ZebraNet, under
  water sensor networks
• Disaster relief team/military ad hoc network
• Resource constrained power, bandwidth, storage

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Routing in DTN

• Adopt store-carry-forward paradigm
• Stateless routing forwarding decisions not
  dependent on node identity, mobility patterns,
  time of the day etc.
• Epidemic routing, K-hop/probabilistic/
  limited-time forwarding
• Intelligent routing
• Probabilistic routinglindgren03, MaxProp
  burgess06 etc.

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Epidemic style routing

• Epidemic routing packet propagation gt disease
  spreading vahdat00
• Whenever infected node meets susceptible
  node, a copy is forwarded
• Achieve min. delay at cost of trans. power,
  storage
• Trade-off delay for resource (power, storage)
• K-hop/probabilistic/limited-time forwarding
• Contribution rigorous, unified ODE-based
  framework to study performance of DTN routing
  schemes

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Outline

• Network model
• Related work
• Ordinary Differential Equation Model
• Summary and future work

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Network setting

• N1 nodes
• Random waypoint/direction model
• fixed, small transmission range, r
• Infinite bandwidth, unlimited buffer

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Forwarding recovery schemes

• Forwarding schemes
• Epidemic routing
• K-hop/probabilistic/limited-time forwarding
• Recovery deletion of obsolete copies after
  delivery to dest., e.g.,
• IMMUNE dest. cures infected nodes
• VACCINE on pkt delivery, dest propagates
  anti-pkt through network

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Performance metrics

• Under infinite bandwidth, unlimited buffer,
  different pkts propagate independently
• For a pkt in the network
• Delivery delay, the time from pkt generated at
  source until delivery to dest, Td
• Avg. num. of copies in system by delivery time, C
• Avg. total num. of copies made, G
• Avg. buffer occupancy

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Related work hybrid analytic/simulation model

• ODE model small03
• Delivery delay under basic epidemic routing
• Involve avg. pair-wise meeting rate obtained from
  simulation
• Markov chain model haas06
• N-1 parameters to capture nodes mobility
  (obtained from simulations)
• Numerical solution complexity increases with N

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Related work model random contacts Groenevelt05

• Pair-wise inter-meeting time is close to
  exponential random variables, if
• Nodes move according to random waypoint or random
  direction mobility
• Trans. range r small compared to network area A,
• Velocity sufficiently high

? pair-wise meeting rate w mobility
specific constant r transmission range
V average relative speed A terrain
area
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Related work a Markov model groenevelt05

• N1 nodes, pair-wise meeting rate
• States NI 1,, N num. of infected node, not
  delivered A delivered
• Transient analysis to derive delay, copies made
  by delivery hard to obtain closed form, even so
  for more complex schemes

Infection rate Delivery rate
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ODE as fluid limit of Markov model

• Rewrite transition rate
• rN(NI)?NI(N-NI)N(?N)(NI/N)(1-NI/N)
• density-dependent form (if remains
  constant)
• Kurtz70 as N?8, NI/N ? i(t),
• , initial condition
• (i.e., initially a given fraction of nodes are
  infected)
• For sufficiently large N and initially infected
  node, NI(t) is close to I(t)

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Derive delivery delay

• Delivery delay Td time from pkt generation at
  the src until the dest. receives the pkt
• CDF of Td, P(t) Pr(Tdltt) given by
• Average delay
• Avg. num. of copies sent by delivery

prob. that pkt is not delivered yet
delivery rate at time t
rate that infected nodes meet dest node.
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Derive copies sent storage

• Consider recovery process, eg IMMUNE (dest. node
  cures infected nodes)
• Total num. of copies made
• Total buffer usage

R(t) num. of recovered nodes
Num. of susceptible nodes
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Extensions

• Extensible to other schemes

Epidemic routing
2-hop forwarding
Prob. forwarding
Matching results from Markov chain model,
obtained much easier
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Model validation through simulation

• Our own simulator
• Ignore physical/MAC layer details
• Setting
• Square area 20 x 20 with wrap-around boundary
• Transmission range r0.1
• Random direction model
• Speed chosen uniformly in 4,10
• Trip duration exp. with mean 0.25
• Resulting pair-wise meeting rate

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Average delay under varying N

• Average delay under epidemic routing

ODE provides good prediction on average delay
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Delay distribution

• CDF of delay under epidemic routing, N160

Modeling error mainly due to approx. of ODE
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Summary

• ODE model for epidemic style routing
• As limiting process of Markov Chain
• Study metrics delay, copies made, storage
• Easier to derive closed form results numerical
  solution complexity does not increase with N
• Extensions to various schemes
• Model validation through simulation
• Not covered here ODE with second moment, buffer
  constrained case

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Future works

• Model storage/transmission overhead of anti-pkts
• Evaluate schemes such as spray and wait

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Questions ? Comments ?

• Thanks!

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Poisson Meeting Process

• Example settings considered in groenevelt05
• Terrain 4 km X 4 km
• Transmission range r50/100/250 m
• Speed in 4,10 km/h
• Trip duration (for random direction) exp. with
  mean ¼ hr