Routing Table Dynamics in Mobile Ad-Hoc Networks: A Continuum Model

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Routing Table Dynamics in Mobile Ad-Hoc
NetworksA Continuum Model

• Ernst W Grundke
• Faculty of Computer ScienceDalhousie
  UniversityHalifax NS

www.cs.dal.ca/grundke/ants/routingTable.html
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Routing in a Mobile Ad-Hoc Network
Mobility
Routing Protocol

• How does this competition play out?
• Fraction of valid Routing Table entries?
• How fast does the routing table fill up?

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Model of the Routing Protocol

• Proactive routing
• Routing protocol behaviour
• A node receives data about r destinations per
  second on average
• r ?(N) N number of nodes
• Randomness

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Model of Mobility

• Link event making or breaking a wireless link
• pm link events per second
• Randomness
• How many paths are broken when a link breaks?

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• c (?/2)(N-1)/(g-1) paths per link where
  (Grundke Zincir-Heywood, Ad-Hoc Now03)
• g avg count of nodes competing for a single
  channel (Rr1)2/r12
• R radio range
• ? forwarding overhead (r1/R)(?N-1)
• 2r1 avg distance between neighbours
• For small R (R ? 2r1), c ? N1.5/32

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The Routing Table 3 kinds of entries

• Dest Next Hop A N ? B M ? n1 valid
  entries C N ? D N ? E O ? n0 invalid
  entries F P ? G ? N-n1-n0
  missing H ? entries

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Effect of Events

• Entry Routing Link Type Event Event
• Missing n1 None
• Valid None n0 c/N, n1- c/N
• Invalid n0--, None n1

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Rate Equations for n0(t), n1(t)

• dn0/dt kan0 kmn1
• dn1/dt (kakm)n1 kaN
• where
• km cpm/N mobility rate
• ka r/N routing data rate

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Equilibrium Solution

• n0/N km/(kakm)
• n1/n0 ka/km
• n1/N ka/(kakm)
• n N
• Linear (non-catastrophic) degradation with
  mobility

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General Solution
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General Solution

• General solution includes
• constant terms
• exponential terms exp(?kat) and
  exp?(kakm)t
• Slowest term depends on the routing protocol
  only.

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Dynamic Solution
kat
Fraction of Routing Table Entries vs kat, for
ka/km3.
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Tuning a routing protocol

• Estimate km cpm/N from the expected mobility
• Pick a tolerable fraction of invalid entries
  n0/N
• Solve for ka km(N/n0 ? 1)
• Adjust protocol parameters to achieve the rate ka

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Conclusions

• Simple, widely applicable model
• Rate constants characterize
• the proactive routing protocol (ka)
• the mobility (km)
• Analytic expressions
• for the of valid routing table entries
• for the time-dependent behaviour
• Linear degradation with mobility
• Protocol tuning procedure

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Acknowledgements

• Discussions with
• Nur Zincir-Heywood
• Donald Morrison
• Nick Pilon
• The Ant Colony at Dalhousie
• Nur Zincir-Heywood Allan Jost
• Franklin Fezeu Wei Guo
• Cong Feng Lin Donald Morrison
• Nick Pilon Satwant Sandhu
• Keith Slade Sesha Thota
• Owen Yue

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Comments?Questions?
?
www.cs.dal.ca/grundke/ants/routingTable.html