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

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

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?

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

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

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 b testbed measurements

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

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!

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

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

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)

 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

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

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

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

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)  DiDi (r)(r) s d

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

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

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

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

802.11b Indoor Testbed

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

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

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

Distribution of Delivery Probabilities

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 ’ =

Gain of Multirate Anypath Routing

Transmission Rate Distribution

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 b 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

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