Geographical Routing Using Partial Information for Wireless Ad Hoc Networks

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Geographical RoutingUsing Partial Information
for Wireless Ad Hoc Networks

• Rahul Jain, Anuj Puri, and Raja
  SenguptaUniversity of California, Berkeley

Published on IEEE Personal Communications, Vol.8,
Issue 1, Feb2001 Presented by Jani Saloranta at
Ad Hoc Networking Course 27.1.2004
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Outline

• Introduction
• Geograhical Routing Algorithm (GRA)
• Algorithm
• Related Issues
• Teardown protocol
• Performance
• Simulation Results
• Conclusion

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Introduction

• The algorithm for routing in wireless ad hoc
  networks using information about geographical
  location of the nodes.
• Why?
• Setting up a communication infrastructure is
  difficult.
• Mobility
• Money

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The Geographical Routing Algorithm

• Doesnt assume any hierarchical network
  architecure
• Doesnt do source routing
• Assumes nodes position via global positioning
  system (GPS) and existence of geographical
  location service (GLS).
• Optimal power
• Symmetric links
• Medium access schedule such that each node can
  transmit at a certain bit rate without
  interference.

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• Wireless network can be modellad as a graph G
  ( N, L ),
• where nodes N 1, 2, ..., n and edges (links)
  L ( i, j ) nodes i and j are neighbours .
• Each node knows about a small number of nodes in
  the network. More about the those who are nearer
  to it than those about those further away.

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D
S
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The Algorithm

• Start point Each node knows only about its
  neighbours.
• Routing table for node S is a list lt(pi, Si)gt,
  where pi is a geographical position and Si is
  neighbour of S.
• Node S checks from its routing table which pi is
  closest for packet destination D.
• Each node thus forwards the packet in the same
  way till the packet reaches the destination.

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• If node S discovers that it is closer to the
  destination than any other pi we say the packet
  is stuck. Route discovery protocol handles
  these situations.
• Route discovery protocol
• Finds a path from S to D. ( Path(S, D) ltk0,
  k1, ..., klgt ) and updates the routing table of
  the node ki ltPos(D), ki1 gt.

?
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1) from A to C
2) from A to D
3) from A to E
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Related Issues

• Positional Errors
• Node i gets its position from GPS and there is an
  error. i advertises wrong position pi instead of
  correct position pi.
• If error is big enough packet most propably get
  stuck ? Route discovery protocol.
• Multiple Route Discoveries
• Avoided by timestamps.

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Teardown protocol

• Extension which tries to maintain the centers
  property ans keep the routing tables consistent.
• Node S updates its routing table
• S receives hello msg from node Ni ? it puts (Ni,
  pos(Ni), Ni)
• If S doesnt hear anything from node Ni for
  certain time ? it removes (Di, pos(Ni), Ni) for
  every Di.
• If Table(S) contains the entry (Di, pi, Ni) and S
  receives Table(Ni) which contains the entry (Di,
  pj, ), then S updates its entry to (Di, pj, Ni).
• If Table(S) contains the entry (Di, pi, Ni) and S
  receives Table(Ni) which does not contain an
  entry (Di, , ), then S removes the entry (Dii,
  pi, Ni) from its table.
• After any change to its routing table, S
  broadcasts the new Table(S).

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Performance

• Convergence of Routing Tables
• One of the advantages of algorithm is that a node
  does not need to have a routing entry for every
  other node in the network.
• Number of route discoveries per node
• O (log n)
• Routing Table Size
• The mean routing table size is bounded above by O
  ( L1 log n )), where L1 is the mean length of the
  shortest path between any pair of nodes in an
  n-node random network.

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• Assumption network has n nodes in a unit area
  and each node has transmission radius r.
• Overhead from a single link going down
• O ( L log(n) / r 2 )
• Number of links going down due to mobility
• O (r v n 2),where v is speed of certain node.
• ? Total overhead
• O ( L v n 2 log(n ) / r ) packets get generated
  in the network per unit time.

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Simulation Results
Figure 7a
Figure 7b
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Figure 8a
Figure 8b
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Figure 9a
Figure 9b
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Conclusions

• Algorithm is asynchronous, real-time,
  distributed, and scalable. It does not require an
  architecture or hierarchy to be imposed on the
  network, but provides each node with a
  distance-dependent aggregated view of the network
  topology.
• Correctness of algorithm has been shown via
  theoretic calculus and verified through
  simulations.

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Teardown misspelling
Correct form can be found from 19. Says (di,
pi, ni) Should say (di, pj, ni)
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Blurry math

• We assume the network has n nodes in a unit area
  and each node has a transmission radius r.
• On average, each node has npr2 neighbors and
  cLlog(n) entries in its routing table. So on
  average a cLlog(n)/(npr2) entries in the
  routing table of A are using a link from node A
  to a neighbor B.
• ?

nodes radius neighbours entries
n r npr2 cLlog(n)
0.1 10 31 cL (-1)
1 10 314 0
10 10 3141 cL
2 2 25 cL (0.3)