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. • Find the route that gives the minimum expected time of transmission.

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 • Ynis 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 < Mland 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 < Yn, Ml < n. Thus, • Note that: • Thus:

14. Finally… • Summing over j  {0, 1, … n-1} and given that Hl,jand 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 “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.

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