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Optimal Multi-Path Routing and Bandwidth Allocation under Utility Max-Min Fairness

Optimal Multi-Path Routing and Bandwidth Allocation under Utility Max-Min Fairness. Jerry Chou and Bill Lin University of California, San Diego IEEE IWQoS 2009 Charleston, South Carolina July 13-15, 2009. Outline. Problem Approach Application to optical circuit provisioning Summary.

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Optimal Multi-Path Routing and Bandwidth Allocation under Utility Max-Min Fairness

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  1. Optimal Multi-Path Routing and Bandwidth Allocation under Utility Max-Min Fairness Jerry Chou and Bill Lin University of California, San Diego IEEE IWQoS 2009 Charleston, South Carolina July 13-15, 2009

  2. Outline • Problem • Approach • Application to optical circuit provisioning • Summary

  3. Basic Max-Min Fair Allocation Problem Saturated flows Fully allocated link C1 C2 C3 5 Max increase • Motivation: Bandwidth allocation is a common problem in several network applications • Example: C1: AD C2: BD C3: CD B 10 10 A D 10 10 C

  4. Utility Max-Min Fairness C1: AD C2: BD C3: CD 1 1 1 utility utility utility 0 0 0 0 BW 10 0 BW 10 0 BW 10 B 10 10 A D 10 10 C Utility functions capture differences in benefits for different commodities

  5. Utility Max-Min Fairness C1: AD C2: BD C3: CD 1 1 1 utility utility utility 0 0 0 0 BW 10 0 BW 10 0 BW 10 B 10 10 A D 10 10 C Utility functions capture differences in benefits for different commodities

  6. Utility Max-Min Fairness C1: AD C2: BD C3: CD 1 1 1 utility utility utility 0 0 0 0 BW 10 0 BW 10 0 BW 10 B 10 10 A 6 D 10 10 2 C Freedom of choosing multi-path routing achieves higher min utility and more fair allocation

  7. Prior Work • Utility max-min fair allocation only considered fixed (single-path) routing • Optimal multi-path routing only considered weighted max-min and max-min fairness

  8. Why is the Problem Difficult? • Why is optimal multi-path routing and allocation under utility max-min fairness difficult? • Unlike conventional fixed (single) path max-min fair allocation problems • Cannot assume a commodity is saturated just because a link that it occupies in the current routing is full • Once a commodity is saturated, cannot assume its routing is fixed in subsequent iterations

  9. Example • At iteration i, suppose we route both flows AD and AE with 5 units of demand If routing is fixed after iteration, AD would be at most 5 B 0/10 0/10 A D AD:5 5/10 10/10 E AE:5 C 5/5

  10. Example • At iteration i+1, suppose we want to route AD with 10 units of demand Route of AD must change to increase B 10/10 10/10 A D AD:10 0/10 5/10 E AE:5 C 5/5

  11. Outline • Problem • Approach • OPT_MP_UMMF • ε-OPT_MP_UMMF • Application to optical circuit provisioning • Summary

  12. OPT_MP_UMMF • Step 1: Find maximum common utility that can be achieved by all unsaturated commodities • Step 2: Identify newly saturated commodities • Step 3: Assign the utility and allocation for each newly saturated commodity

  13. Key Differences Fix utility, not routing • A commodity is truly saturated only if its utility cannot be increased by any feasible routing • Requires testing each commodity for saturation separately • To guarantee optimality, fix the utility, not the routing after each iteration

  14. Comments • Although OPT_MP_UMMF achieves optimal solution, both Steps 1 & 2 require solving non-linear optimization problems Step 1 Step 2

  15. ε-OPT_MP_UMMF • Instead of solving a non-linear optimization problem, find maximum common utility by means of binary search • Test if a common utility has feasible multi-path routing by solving a Maximum Concurrent Flow (MCF) problem

  16. Maximum Concurrent Flow (MCF) • Given network graph with link capacities and a traffic demand matrix T, find multi-path routing that can satisfy largest common multiple l of T • If l < 1, means demand matrix cannot be satisfied • If l > 1, means bandwidth allocation can handle more traffic than specified demand matrix • MCF well-studied with fast solvers

  17. Find Maximum Utility • Determine demand matrix by utility functions • Find feasible routing by querying MCF solver • If l<1, decrease utility, otherwise increase utility 100 100 100 100 Utility(%) Utility(%) Utility(%) Utility(%) 80 80 80 80 60 60 60 60 40 40 40 40 20 20 20 20 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50 BW BW BW BW C = 100

  18. Outline • Problem • Approach • Application to optical circuit provisioning • Summary

  19. Optical Circuit Provisioning Application Boundary routers WDM links Optical circuit switches Optical circuit-switched long-haul backbone cloud • Provision optical circuits for Ingress-Egress (IE) pairs to carry aggregate traffic between them • Goal is to maximize likelihood of having sufficient circuit capacity to carry traffic

  20. Optical Circuit Provisioning (cont’d) • Utility curves are Cumulative Distribution Functions (CDFs) of “Historical Traffic Measurements” • Maximizing likelihood of sufficient capacity by maximizing utility functions • Route traffic over provisioned circuits by default • Adaptively re-route excess traffic over circuits with spare capacity • Details can be found in • Jerry Chou, Bill Lin, “Coarse Circuit Switching by Default, Re-Routing over Circuits for Adaptation”, Journal of Optical Networking, vol. 8, no. 1, Jan 2009

  21. Experimental Setup • Abilene network • Public academic network • 11 nodes, 14 links (10 Gb/s) • Historical traffic measurements • 03/01/4 – 04/21/04

  22. Example Seattle New York Chicago Sunnyvale Denver Indianapolis Los Angeles Washington Kansas City Atlanta Houston SeattleNY: 90% time ≤ 6Gb/s 50% time ≤ 4Gb/s Allocate: 6Gb/s SunnyvaleHouston: 90% time ≤ 6Gb/s 80% time ≤ 4Gb/s Allocate: 4Gb/s Seattle NY has 90% acceptance probability Sunnyvale Houston has 80% acceptance probability

  23. Comparison of Allocation Algorithms • WMMF: Single-path weighted max-min fair allocation • Use historical averages as weights • Only consider OSPF path • UMMF: Single-path utility max-min fair allocation • Only consider OSPF path • MP_UMMF: Multi-path utility max-min fair allocation • Computed by our algorithm

  24. Individual Utility Comparison • Reduce link capacity to 1 Gb/s • MP_UMMF has higher utility for most flows

  25. Minimum Utility Comparison • MP_UMMF has greater minimum utility improvement under more congested network

  26. Excess Demand Comparison • Simulate traffic from 4/22/04-4/26/04 • MP_UMMF has much less excess demand

  27. Summary of Contributions • Defined multi-path utility max-min fair bandwidth allocation problem • Provided algorithms to achieve provably optimal bandwidth allocation • Demonstrated application to optical circuit provisioning

  28. Thank You

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