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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 ... – PowerPoint PPT presentation

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Title: Gentian Jakllari, Stephan Eidenbenz, Nick Hengartner,


1

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

2
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)

3
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

4
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.

5
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.

6
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 !

7
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.

8
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.

9
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.

10
An Example
11
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

12
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

13
Going further
  • For the Ynth attempt, Ml n. For l lt Yn, Ml lt
    n. Thus,
  • Note that
  • Thus

14
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

15
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.

16
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).

17
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.

18
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

19
Paths with ETOP and ETX
  • ETOP improves reliability as packets reach the
    proximity of the destination

20
TCP behavior with ETOP
  • Higher reliability with ETOP allows TCP to more
    aggressively ramp up its congestion window.
  • TCP goodput improves
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