Tim Roughgarden Stanford CS

1. Quantifying Trade-Offs via Competitive Analysis(Clean Slate Seminar) Tim Roughgarden Stanford CS

2. Clean Slate Trade-Offs • Clean Slate design fraught with trade-offs between competing objectives • "There is not likely to be a unique answer for the list of requirements, and every requirement has some cost. The cost of a particular requirement may become apparent only after exploration of the architectural consequences of meeting that objective in conjunction with others...it there requires an iterative process..." • NewArch Intro paper, 2000.

3. Clean Slate Trade-Offs E.g., overprovisioning: good or bad? • Nick: inefficient, motivates Valiant load-balancing in backbone network • Bernd: good, QoS becomes easy Theme in my research: • rigorously quantify trade-offs between competing objectives • e.g., excess capacity vs. performance

4. Plan for Talk Goals: • illustrate this idea with several examples: routing, protocol design, pricing, capacity installation • models vary in direct relevance to clean slate • emphasize commonalities + flexibility of analysis approach, qualitative insights via quantitative analysis • illustrate my own interests/expertise

5. Example #1: Routing Conges-tion D [secs] Motivating example: • low capacity, prop delay vs. high capacity, prop delay • d  how close arrival rate is to “knee” of delay curve c(x) = xd s t c(x) = 1 Rate R

6. Example #1: Routing Conges-tion D [secs] Motivating example: • low capacity, prop delay vs. high capacity, prop delay • d  how close arrival rate is to “knee” of delay curve • dumb routing (source, delay-based, etc) = all on top c(x) = xd 1 s t c(x) = 1 0 Rate R

7. Example #1: Routing Conges-tion D [secs] Motivating example: • low capacity, prop delay vs. high capacity, prop delay • d  how close arrival rate is to “knee” of delay curve • dumb routing (source, delay-based, etc) = all on top • smart routing = offload some to bottom c(x) = xd 1 1-Є s t c(x) = 1 0 Є Rate R

8. Trade-offs in Routing Summary: • constraint: can’t/don’t want to implement smart routing • trade-off: excess capacity vs. performance (avg delay relative to optimal routing) Next: two related approaches for quantifying this trade-off. • [Roughgarden/Tardos 00], [Roughgarden 02]

9. Quantifying the Trade-Off Approach #1 (the ratio): • as a function of the excess capacity, what is the ratio: avg delay of delay-based routing vs. avg delay of optimal routing • at least 1, the closer to 1 the better • “competitive ratio”, “price of anarchy”

10. Quantifying the Trade-Off Approach #1 (the ratio): • as a function of the excess capacity, what is the ratio: avg delay of delay-based routing vs. avg delay of optimal routing • at least 1, the closer to 1 the better • “competitive ratio”, “price of anarchy” Answer: grows as  d/ln d • small as long as there’s some overprovisioning c(x) = xd s t c(x) = 1

11. Qualitative Insights Insight #1: • advocates overprovisioning but...

12. Qualitative Insights Insight #1: • advocates overprovisioning but... • even (say) 20% works wonders • both Nick and Bernd are right!

13. Qualitative Insights Insight #1: • advocates overprovisioning but... • even (say) 20% works wonders • both Nick and Bernd are right! Insight #2: worst-case = trivial topology • worst-case ratio does not degrade with more complex topologies, traffic matrices

14. Quantifying the Trade-Off Approach #2 (match the old optimum): • how much overprovisioning need before delay-based routing as good as optimal? with overprovisioning without overprovisioning

15. Quantifying the Trade-Off Approach #2 (match the old optimum): • how much overprovisioning need before delay-based routing as good as optimal? Answer: 100% (double the capacity) • cf., “switch speedup results” by Ashish, Nick, Balaji with overprovisioning without overprovisioning

16. Bigger Picture • had one or more constraints • not feasible to route traffic optimally • two competing objectives • minimize both overprovisioning + average delay • two ways to quantify trade-off • competitive ratio, min capacity to simulate opt • precise answers, qualitative insights • small amount of overprovisioning helps • trivial worst-case topologies

17. Ex #2: Protocols for Bandwidth Allocation Setup:[Johari/Tsitsiklis 04] + [Johari 04] • goal is to partition bandwidth (e.g. 1 link) to maximize sum of heterogeneous utilities uk Equal-slope “Pareto condition” rk

18. Trade-Offs for a Bandwidth Allocation Protocol Constraint: can’t directly implement optimum (e.g., don’t know utility functions); want decentralized protocol to do this • [Kelly]simple such protocol exists if no user “large” (has non-negligible “market power”) • [JT04] quantify trade-off between protocol performance, max market power of a player • at most 25% efficiency loss

19. Kelly mechanism still optimal Qual Insight #1: market power not a big deal. Idea: use efficiency loss as novel metric to compare different protocols. Theorem: [J04] Kelly mechanism the best one! • all protocols in a certain class have > 25% eff loss Qual Insight #2: Kelly mechanism designed for no market-power setting, but still optimal (in above sense) more generally.

20. Ex #3: Pricing a Service Motivating question: how do we price a service (e.g. a movie broadcast) so that it is (at least somewhat) economically viable? Constraint: "fairness" = every customer's cost can only go down as more customers served • economies of scale • connected to "collusion-resistance" n potential clients with valuations server edge cost = 1 s

21. Ex #3: Trade-offs Trade-off: want to charge enough to cover costs, but also want "good solution" • easy to cover costs of the empty set! • max "surplus" = benefit to served customers - cost of serving them n potential clients with valuations server edge cost = 1 s

22. Ex #3: Trade-offs Trade-off: want to charge enough to cover costs, but also want "good solution" • easy to cover costs of the empty set! • max "surplus" = benefit to served customers - cost of serving them Old result: can't have both [Moulin/Shenker]. New result (w/Sundararajan): quantify trade-off curve between them. n potential clients with valuations server edge cost = 1 s

23. Ex #3: Insights Qualitative insight #1: can have approximate versions of both goals. • approximate cost recovery + nearly maximum-possible surplus #2: trivial examples exhibit worst-case behavior (like in routing, complex topology doesn't make things worse) Open issue: trade-offs when economic viability a constraint, "fairness" an objective

24. Example #4: Valiant Load-Balancing Constraint: [Zhang-Shen/Mckeown 04,05]: allocate edge capacity w/out knowing traffic matrix Assume: know amount of traffic out of each node in backbone network (say R each) • linear # of parameters instead of quadratic • want sufficient capacity to route any traffic matrix respecting these node constraints Intuitively: lack of knowledge  need more capacity. But how much more?

25. Example #4: VLB Theorem: [ZM 04,05]: only a factor 2! • know matrix just do one-hop routing  need at most nR capacity (n = # nodes) • VLB: two-hop routing suffices, at most 2R/n capacity on each of n2 links • extensions (node-varying R, failures,...) • future: avg prop delay vs. capacity trade-offs (w.r.t. underyling physical network)

26. Summary • much of the clean slate work will be struggling with different trade-offs • quantitative analysis flexible, often tractable, often offers new qualitative insights • always looking for new problems to tackle... • future: evaluate the e2e principle? • has suggestive "smart" vs. "dumb" flavor...