1. Load Balancing for Routing Sundar Iyer Stanford University

2. What is Load Balancing? … 1 Shortest Path Routing Shortest Path Routing Flow (E, A) <= 10 Lowest Capacity on Shortest Path = 10

3. What is Load Balancing? …….2 Routing using multiple paths Load Balancing Flow (E, A) <=40 Min Cut Size = 40

4. Will this always work better? No knowledge of the OD Matrix Link from (B, A) is more highly loaded than with Shortest Path Routing

5. Optimal Routing MDRP (Gallager) –Given a network, and a OD traffic matrix D(i,j), and delays associated with each link, find the split for each D(i,j,k), from source i to destination j, along neighbor k, which will minimize total expected delay. –Optimal Routing cannot be achieved using only single path routing

6. Approaches to Optimal Routing Do not change routing, minimal change to forwarding –Randomized Routing Change forwarding structure only –Overlay Approach Change both routing and forwarding, and calculate unequal cost multiple paths

7. Randomized Routing Valiant’s Scheme + Packet goes from (s,d) + Two phase routing + Choose intermediate node “r” at random -Route from (s,r) and then (r,d) deterministically -Analysis for Hypercube, Butterfly and Mesh Networks

8. LBR Routing (Bak) + Choose “r” from “s” at random - Can use bad paths, too much delay + Choose “r” from “s”, such that the distance is not greater than f(s) -F(s) = average radius of the network at “s” -Can be too weak a restriction (Star Network) -Can limit capacity to less than the Min cut. -F(s) does not depend on “d” + Incorporate destination -F(s) = dist(s,d) [ 1 – 1/max radius]

9. Overlay Approach - Present Status OSPF and IS-IS –Multipath routing supported –But only for shortest equal paths –This enforces a very severe restriction on the number of paths available for Load Balancing IGRP –Supports all paths which are less than c *(shortest path)

10. Overlay Approach - Present Status Given multiple paths –There is nothing which enforces the ratio of the forwarding split Cisco used to provide –Flow Caching, which does not enforce any split Cisco Express Forwarding –Per- Destination Load Balancing –Per- Packet Load Balancing –Round Robin i.e. equal splits –Weighted Round Robin is needed to control the split ratio

11. Overlay Approach Link Weight Optimization under equal load sharing is NP Hard Equal load sharing can reach near optimal only for certain topologies It is possible to convert MDRP into link weights such that shortest paths to a destination “d” at a node are the paths used by MDRP. [Wang, Infocom ’01] Caveat: The flow split ratio is not known!

12. Questions Is it possible to convert MDRP into link weights such that shortest paths to a destination “d” at a node are the paths used by MDRP, such that –the flow split is equal? –the paths are such that the flow split is in the inverse ratio of weights. Answer is probably no to both

13. Basic Multipath Routing Approach Try and Approximate MDRP Partition MDRP into two parts –Find multiple loop free paths between (s,d) –Split each flow along these paths using heuristics Heuristics –Solve difference equations –For paths with more delay give less weightage

14. Problems in Multipath Routing Main Problem –Avoiding Loops 3- node Triangle –Nodes (A,B,C) –Each node “s” has two paths to every destination “d” –Example: (s,d) and (s,x,d), where x is the other node. –Packet from A to B, can loop: “A” chooses second best path to “B” (A, C) “C” chooses second best path to “B” (C, A).. and loop

15. Multipath Routing Protocols Distance Vector Extensions –DASM (Garcia, Zaumen) Maintain DAG instead of a tree on each router for each destination Maintains an ordering constraint for every destination, valid for all nodes in the network to prevent multipath loops –MDVA (Vutukury) Loop Free Link State Extensions –MPDA (Vutukury) Loop Free