Gentian Jakllari, Stephan Eidenbenz, Nick Hengartner,

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Link Positions Matter A Non-Commutative Routing
Metric for Wireless Mesh Networks

• Gentian Jakllari, Stephan Eidenbenz, Nick
  Hengartner,
• Srikanth V. Krishnamurthy Michalis Faloutsos
• Paper in Infocom 2008

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Research on Routing

• In spite of a large body of work on routing in
  multi-hop wireless networks, issues remain.
• Many previous proposals on wireless routing used
  approaches that were similar to that used in
  wire-line networks (using shortest path routing)

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Focus of this talk

• Goal To show some of the intricacies that
  arise when designing routing policies/metrics in
  multi-hop wireless networks
• Describe some of the recent work that we have
  done on routing in multi-hop wireless networks
  towards improving
• Performance
• Security
• Describe some of the challenges going forward

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Routing Metrics

• Shortest path
• Good for wireline networks.
• In wireless networks, leads to long links of poor
  quality -- leads to packet losses and therefore
  poor performance.
• Estimating link quality
• No ideal way
• Choices could be RSSI, SINR, PDR, BER -- none are
  very good.
• Current trend -- use of PDR (although it incurs
  overhead)
• ETX and beyond
• ETX stands for Expected Transmission Count
• In a nutshell, to compute ETX
• Each node sends probes packets to neighbors.
• It estimates the probability of probe packet
  success on a link i to be pi Total Probes
  Received/Total Sent
• Compute the ETX value of the link to be ETXi
  1/ pi.
• Choose the route with the minimum ETX
• The ETX of the route is the sum of the ETX values
  of the component links.
• The ETX metric does not account for multiple
  transmission rate possibilities.
• An extension was proposed with ETT (For expected
  transmission time)
• Send probes at multiple rates
• Use the probability of success with each rate to
  compute the expected transmission time on the
  link with that rate.

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Factors to be considered

• Order matters!
• The ETX and ETT metrics are commutative.
• The relative positions of the links (of varying
  qualities) on the path does not matter when
  computing the metric.
• It does matter! We will see why.

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Link Positions Matter

• Consider the example network below
• Link costs between nodes are shown (e.g.
  probability of success)

• Link layer retransmissions -- finite in number.
• End to end retransmissions (using as an example,
  TCP)
• The expected cost of the path S,X,Y,R
  considering 2 transmissions at the link layer is
  20, the cost of the path S,A,B,C,R, is 13.
• A routing protocol that ignores the links
  positions would choose S,X,Y,R !

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ETOP -- Our proposed metric in a nutshell

• ETOP is designed to accurately capture the three
  factors that effect the cost of a path
• The number of links on the path
• The quality of the links
• The relative position of the links -- ETOP is
  non-commutative on the links comprising a path.
• Surprisingly, ETOP is amenable to a greedy
  implementation!
• It can be integrated into any source based
  routing protocol
• The protocol yields the path with the minimum
  ETOP cost.
• Note For now, we only consider a single rate.

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The System Model

• We use the following model and make the following
  assumptions
• The link layer performs a finite number of
  retransmissions for a given packet.
• The packet is dropped if a preset retransmission
  limit is exceeded.
• Previous metrics such as ETX assume that the link
  layer has no limit on the number of
  retransmission attempts.
• This assumption renders the position of a lossy
  link on the path irrelevant to the performance of
  the path.
• If a packet is dropped by the link layer, the
  transport layer will initiate an end-to-end
  retransmission of the packet starting at the
  source.
• Depending on where the packet is dropped, the
  cost of the end-to-end retransmissions will vary.
• The probability of transmission failures on
  successive attempts on a link are independent and
  identically distributed.

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The ETOP Path metric

• The ETOP cost of an n hop path is the expected
  number of transmissions retransmissions
  required to deliver a packet over the path.
• K is the limit on the number of link layer
  transmissions retransmissions
• Yn is the random variable that represents the
  number of end-to-end attempts
• H is the random variable that represents the cost
  incurred in every link layer attempt
• M is a random variable that represents the number
  of hops traversed before the packet is either
  delivered or dropped.

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An Example
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Computing ETOP

• The number of link layer transmissions is given
  by
• We first condition on the number of end-to-end
  attempts Yn to get

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Simplifying things

• Consider the inner term. We condition on Ml to
  get
• Consider the case where link j is successfully
  traversed then
• j lt Ml and l Yn.
• Then there are at most K transmissions on link j
  -- Hl,j K
• If there is a failure on link j, then Hl,j K
  and Ml j
• Thus

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Going further

• For the Ynth attempt, Ml n. For l lt Yn, Ml lt
  n. Thus,
• Note that
• Thus

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Finally

• Summing over j ? 0, 1, n-1 and given that
  Hl,j and Ml can be represented by Hj and M
  (since they are iid) we get the ETOP Cost
• If the link success probabilities ?i are known,
  this can be reduced to

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Computing Minimum ETOP paths

• The ETOP cost can be further simplified to give
• It is easy to see that this cost satisfies
• The optimal sub-structure property
• A sub-path of the optimal path is optimal
• Proof by contradiction.
• The greedy choice property
• The cost of a n1 hop path can be computed
  using the cost of the n hop sub-path and the
  (n1)st link.
• Simplification of the above expression yields the
  proof.
• Given that these properties are satisfied, the
  minimum ETOP path can be found using a greedy
  algorithm.
• One can use the Dijkstras algorithm where the
  above cost function is recursively used.

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ETOP implementation

• Implementation on UCR Wireless testbed
• 25 Soekris net4826 nodes
• Each node runs a Debian 3.1 Linux distribution
• Wireless cards embed the Atheros AR5006 chipset
  with the MadWifi Driver.
• ETOP is implemented in Linux as part of DSR
  (Dynamic Source Routing) protocol
• Built on the Click Implementation from MIT
• Link Quality Estimation is by sending probes
  (used the implementation by DeCouto et al., from
  MIT).

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Performance Results TCP Goodputs

• These are results from TCP sessions run for 3
  minutes over 110 source destination pairs
  selected uniformly at random.
• The CDFs of the goodput distribution is to the
  left
• The median goodput for different path lengths is
  to the right
• ETOP routing provides as much as a 65
  improvement over ETX routing for paths that are
  separated by 3 hops or higher.

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Experiments on Specific Node Pairs

• We consider five specific node pairs
• We look at the retransmission costs (total number
  of MAC layer transmissions)
• ETOP reduces retransmission cost and thus,
  improves TCP goodput

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Paths with ETOP and ETX

• ETOP improves reliability as packets reach the
  proximity of the destination

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TCP behavior with ETOP

• Higher reliability with ETOP allows TCP to more
  aggressively ramp up its congestion window.
• TCP goodput improves