Gentian Jakllari, Stephan Eidenbenz, Nick Hengartner,

Srikanth V. Krishnamurthy & Michalis Faloutsos

Paper in Infocom 2008

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

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)

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

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 p i = 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. Find the route that gives the minimum expected time of transmission.

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.

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 !

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.

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.

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.

An Example

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:

Simplifying things

• Consider the inner term. We condition on Ml to get:

• Consider the case where link “j” is successfully traversed; then

j < 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:

Going further …

• For the Ynth attempt, Ml = n. For l < Yn, Ml < n. Thus,

• Note that:

• Thus:

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:

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 “n+1” hop path can be computed using the cost of the “n” hop sub-path and the “(n+1)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 Dijkstra’s algorithm where the above cost function is recursively used.

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).

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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TCP Goodput (Kbps)

Cumulative Fraction

of Node PairsETX-RETOP-R

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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Node Pairs

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Paths with ETOP and ETX

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

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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Time (sec)

TCP Goodput (Kbps)

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Sample

Sender's Congestion

Window

ETX-R ETOP-R