1. Multirate Anypath Routing in Wireless Mesh Networks Rafael Laufer †, Henri Dubois-Ferrière ‡, Leonard Kleinrock † Acknowledgments to Martin Vetterli and Deborah Estrin † Computer Science Department University of California at Los Angeles ‡ Riverbed Technology, Inc. Lausanne, Switzerland

2. Loss and Instability M. Lukac, Measuring Wireless Link Quality, 2007

3. Wireless Networks  Different properties for the wireless medium  Lossy and unstable links  Limited transmission range  Collisions and hidden terminals  Intra- and inter-flow interference  Broadcast nature  Same routing paradigm for wireless networks?  Can the broadcast medium work in our favor?

4. Anycast Forwarding  Packet sent to multiple nodes simultaneously  High chance of at least one node receiving it  Node with the shortest distance forwards it on  Coordination with overhearing and suppression

5. Anypath Routing  Every node forwards the packet to a set of nodes  A set of paths from the source to the destination  This set of paths is called an anypath

6. Our Contributions  Potential issues with single-rate anypath routing  New routing paradigm for wireless networks  Anypath routing with multiple bit rates  Rate diversity imposes new challenges  Introduction of a routing metric for multirate  Routing algorithm for a single and multiple rates  Not exponential  Same complexity as Dijkstra’s and optimal  Indoor 18-node 802.11b testbed measurements

7. Single-Rate Anypath Routing  Under-utilization of available bandwidth resources  Some hyperlinks perform well at higher rates  Others may only work at low rates Transmission Rate Delivery probability Optimal operation point

8. Single-Rate Anypath Routing  Network disconnection at high rates  Higher rates have a shorter transmission range  Significant decrease in network density  Lossier links and eventually disconnection  Connectivity guaranteed only at low rates!

9. Multirate Anypath Routing  Every node forwards the packet to a set of nodes  A transmission rate for each forwarding set  A set of paths with potentially different rates  We call this a multirate anypath

10. Challenges  Loss ratios usually increase with rate  Higher rate is not always beneficial  Shorter radio range for higher rates  Different connectivity and density for each rate  Higher rates  Less spatial diversity and more hops between nodes  Lower rates  More spatial diversity and less hops between nodes  How to choose both the forwarding set and rate?  Shortest multirate anypath problem

11. Multirate Anypath Cost  What is the cost of a multirate anypath?  Composed of two different components  Hyperlink cost  Remaining cost d iJ DJDJ DJDJ i J (r)(r) (r)(r) (r)(r) (r)(r)

12.  Expected transmission time (ETT)  Average time used to transmit a packet  Assuming a link with delivery probability  Transmission rate and packet size  Expected anypath transmission time (EATT)  Tradeoff between bit rate and delivery probability Routing Metric

13. Remaining Cost  Weighted average of the distances of nodes in J  If D 1 ...  D n, node j is the relay with probability  Weight w j (r) defined as with

14. The Single-Rate Case  Link-state routing protocol  Shortest Anypath First algorithm  Running time of O ( V log V + E )     0       .4.6.4.6.3.5.8.2.7.8.9.7.6.9.5.7.5.3.2.9.4.7 0 40 60 40 60 84 60 78 60 90 75 90 87 82 7882 73 8685 89 8589 s d

15. 0 The Single-Rate Case  Link-state routing protocol  Shortest Anypath First algorithm  Running time of O ( V log V + E )           .2.1.5.2.1.2.4.1.2.4.2.3.6.1.3.4.3.1.2 02090878069606265383024 s d

16. 0 The Multirate Case  Shortest Multirate Anypath First algorithm  A distance estimate for each rate  Running time of O ( V log V + ER )           (.4,.2) (.6,.1) (.4,.1) (.6,.5) (.3,.2) (.3,.1) (.5,.2) (.8,.4) (.2,.1) (.7,.2) (.8,.2) (.9,.4) (.7,.2) (.6,.3) (.9,.6) (.5,.1) (.5,.4) (.3,.3) (.2,.1) (.2,.2) (.9,.2) (.4,.2) (.7,.2) 0 (.7,.3) 40 60 20 30 20 2924  448444 30 38 70 43 50 90 60 38 70 43 38 43 5365 62 53 43 58 73 58 43 5753 56 5764 53 57 53 113 57 65 70 66 69 65 7068 DiDi (r)(r) s d

17. Shortest Multirate Anypath First  Why does it work?  Three properties assuming D 1  D 2 ...  D n  Property 1  Shortest forwarding set is of the form J = { 1, 2,..., j } D1D1 D2D2 D3D3

18. Shortest Anypath First  Why does it work?  Still assuming D 1  D 2 ...  D n  Property 2  Nodes are settled in order { 1, 2,..., n }  Forwarding sets tested in order { 1 }, { 1, 2 },..., { 1, 2,..., j } {1}{1,2}{1,2,3} D1D1 D2D2 D3D3

19. DiDi Di’Di’ D i ’’ Shortest Multirate Anypath First  Why does it work?  Still assuming D 1  D 2 ...  D n  Property 3  Distance using { 1 } higher than distance using { 1,2 }, which is higher than using { 1,2,3 }, until { 1, 2,..., j } D i  D i ’  D i ’’ {1}{1,2}{1,2,3} D1D1 D2D2 D3D3

20. Shortest Multirate Anypath First  Putting it all together  Three properties assuming D 1  D 2 ...  D n  Shortest forwarding set is of the form J = { 1, 2,..., j }  Forwarding sets tested in order { 1 }, { 1, 2 },..., { 1, 2,..., j }  Distance using { 1 } higher than distance using { 1,2 }, which is higher than using { 1,2,3 }, until { 1, 2,..., j }  All properties and optimality proven in the paper

21. 802.11b Indoor Testbed

22.  Stargate microserver  Intel 400-MHz Xscale PXA255 processor  64 MB of SDRAM  Linux OS  SMC EliteConnect SMC2532W-B PCMCIA  IEEE 802.11b  Prism2 chipset and HostAP driver  Maximum transmission power of 200 mW  Proprietary power control algorithm

23. 802.11b Indoor Testbed  Wireless mesh network  3-dB omni-directional rubber duck antenna  30-dB SA3-XX attenuator  Weaker signal during both transmission and reception  Larger distance emulated  Network diameter  At 11 Mbps, up to 8 hops with 3.1 hops on average  At 1 Mbps, up to 3 hops with 1.5 hops on average

24. 802.11b Indoor Testbed  Software  Click modular router  MORE software package  Modified HostAP driver  Raw 802.11 frames  Measure the delivery probability of each link  1500-byte frames  Transmitted at 1, 2, 5.5 and 11 Mbps

25. Distribution of Delivery Probabilities

26. Evaluation Metric  Multirate anypath routing  Always lower cost than single-rate anypath  Gain of multirate over single-rate anypath  Ratio between single-rate and multirate distances  How many times is multirate anypath better? G DiDi DiDi ’ =

27. Gain of Multirate Anypath Routing

28. Transmission Rate Distribution

29. Conclusions  Opportunistic routing paradigm for multiple rates  Range and delivery probability change with rate  Shortest multirate anypath problem  Introduction of the EATT routing metric  Shortest Multirate Anypath First algorithm  Measurements from an indoor 802.11b testbed  Single rate may lead to network disconnection  Multirate outperforms 11-Mbps anypath routing by 80% on average and up to 6.4x with full connectivity  Distribution of bit rates not concentrated at any rate

30. Multirate Anypath Routing in Wireless Mesh Networks Rafael Laufer †, Henri Dubois-Ferrière ‡, Leonard Kleinrock † Acknowledgments to Martin Vetterli and Deborah Estrin † Computer Science Department University of California at Los Angeles ‡ Riverbed Technology, Inc. Lausanne, Switzerland