Quantifying TradeOffs via Competitive Analysis Clean Slate Seminar

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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.

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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

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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

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Example 1 Routing

• Motivating example
• low capacity, prop delay vs. high capacity, prop
  delay
• d ? how close arrival rate is to knee of delay
  curve

Conges-tion D secs
c(x) xd
s
t
c(x) 1
Rate R
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Example 1 Routing

• 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

Conges-tion D secs
c(x) xd
1
s
t
c(x) 1
0
Rate R
7
Example 1 Routing

• 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

Conges-tion D secs
c(x) xd
1
1-?
s
t
c(x) 1
0
?
Rate R
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Trade-offs in Routing

• Summary
• constraint cant/dont 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

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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

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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 theres
  some overprovisioning

c(x) xd
s
t
c(x) 1
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Qualitative Insights

• Insight 1
• advocates overprovisioning but...

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Qualitative Insights

• Insight 1
• advocates overprovisioning but...
• even (say) 20 works wonders
• both Nick and Bernd are right!

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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

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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
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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
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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

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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
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Trade-Offs for a Bandwidth Allocation Protocol

• Constraint cant directly implement optimum
  (e.g., dont 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

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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 gt 25 eff
  loss
• Qual Insight 2 Kelly mechanism designed for no
  market-power setting, but still optimal (in above
  sense) more generally.

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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
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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
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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
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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

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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?

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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)

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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...