Totally Disjoint Multipath Routing in Multihop Wireless Networks Sonia Waharte and Raoef Boutaba Presented by: Anthony Calce

Overview Introduction Problem Definition Design Assumptions Throughput Estimation Multipath vs. Single Path Routing Comparison Single Source-Destination Scenario Analysis Validation Multiple Source-Destination Scenario Conclusion

Introduction Multipath Routing Multiple paths are kept track of Saves time by not doing route discovery when broken path Previous Works Optimizing path reliability [Lee, Nasipuri, Raju] Lower power consumption [Ganesan, Liu] Optimized load Distribution [Lee, Pearman] Performance Metrics Analyzed Node mobility, energy limitations, high density Multipath routing 1) benefits are: ease congestion, overcome node failure, increase bandwidth 2) Previous works try to implement AODV/DSR with a multipath approach. 3

Problem Definition Focuses on the 2-path routing problem Given two nodes (s,t) find two paths P1 , P2 All nodes in P1 and P2 form a connected graph No edges exist between any node in P1 and P2 Evaluation of throughput while considering node interference 4

Design Assumptions Fixed nodes Non-energy constrained wireless backbone Uniform node density in area radius R Interference range = transmission range High density -> straight line shortest path Paths are assumed to be of distance at least r (interference range) Prevents the route coupling effect 5

Throughput Estimation (Multipath vs. Single Path) Simulation was done using NS-2 to estimate benefits of multipath vs. single path 6

Throughput Estimation (Single Source-Destination) Let A, B be a source-destination pair and F a node part of a path between A and B Two step process Determine maximum number of paths through F Determine probability of participation of F in the forwarding process Compute tangents to circle centered at F Tangents and their parallels located at ε define area which source/destination reside Equation of circle centered at F Equation of tangents to CF at point P1 7

Analysis (Max Paths) Max number of paths through F at P1 Need to remove paths less than r Can be derived using Crofton’s formula Number of paths through F at P1 (Nmax – Nrem) Transform P1’s coordinates to polar Max number of paths through F r – source and destination are in direct transmission range of each other Final formula obtained by converting to polar coordinates 8

Analysis (Forwarding Nodes) Define term: expected progress distance covered in one hop Let z be the maximum expected process With uniform node distribution, number of nodes is Poissonian To have z, there should be at least one node located between 0 and z Very small probability p0 that there is no node between 0 and z We derive the epsilon term Expected relay traffic per node The greater the expected progress, the lower number of hops. - depends on network density and node distribution 9

Validation Two methods to validate analysis Implement a routing algorithm based on node positioning Compute total relay traffic in single path routing and compare against total relay traffic in 2-path routing 10

Validation (Multipath Routing Algorithm) Localization-based routing algorithm created Iteratively finding next hop on each path within r of current relay node and satisfying the interference constraints The greater the expected progress, the lower number of hops. - depends on network density and node distribution 11

Validation (Single Path Routing) Need to calculate Total number of paths Probability path length < transmission distance (exclude these) Average path length Probability density distance between two points in circle radius R Probability path length > transmission range 12

Validation (Single Path Routing) Let D be mean distance between a node on the circle and a node in the circle Average path length Total relay traffic for single path routing 13 13

Validation Results Both methods (multipath algorithm and single path routing) return the same results, referred to as “theory.” Simulated in Matlab 14

Throughput Estimation (Multiple Source-Destination Scenario) Previous analysis did not consider interference between paths Single Path Routing – maximum throughput is B / 8 Multipath Routing – Maximum throughput is B / 7 (8 * λ/2 + 3λ) Simulations done is NS-2 15

Conclusion Two problems were looked at Estimation of throughput of the interference of single source- destination pair Impact of interference of multiple source-destination pairs Multipath routing only slightly better performance than single path routing when interference is considered This benefit becomes almost insignificant when actual cost of path establishment is considered. In the context of path interference, multipath routing is not a sound strategy Multipati is only good if - traffic distribution is known - effect of interference can be properly evaluated both of these is unrealistic in WNs (instability of network conditions, staleness of information) 16