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

2. 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

3. 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

4. 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

5. 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

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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

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

15. 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

16. 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