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Architecture Robustness Simplicity. Mung Chiang www.princeton.edu/~chaingm NSF Workshop Aug 2007. Beyond Optimality. Optimization as a “Language” Distributed Algo : Decomposition : Architecture Stochastic Opt : Dynamics : Robustness

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Architecture Robustness Simplicity


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architecture robustness simplicity

Architecture Robustness Simplicity

Mung Chiang

www.princeton.edu/~chaingm

NSF Workshop Aug 2007

beyond optimality
Beyond Optimality

Optimization as a “Language”

  • Distributed Algo: Decomposition: Architecture
  • Stochastic Opt: Dynamics: Robustness
  • Nonconvexity: Suboptimality: Simplicity
i architecture
I. Architecture
  • Functionality allocation: How to modularize?
    • Who does what? How fast?
    • How to put them together?
  • Communications, Control, Computation:
layering as optimization decomposition
Layering As Optimization Decomposition

Network:Generalized Network Utility Maximization

Layering:Decomposition Scheme

Layers: Decomposed subproblems

Interface:Functions of primal or dual variables

  • Horizontal decomposition and Vertical decomposition
  • Implicit message passing or explicit message passing

1. Formulating NUM

2. A solution architecture

3. Alternative architectures

A simple conceptual framework despite complexities of networks

ii robustness
II. Robustness

Lack of Union Between:

Stochastic Network Theory

Distributed OptimizationTheory

example 1 session level stability
Example 1: Session-level Stability

Main Results in literature

1. Stability region = Rate region

2. Maximum stability region

achieved for any  >0.

Q1.R is non-convex? e.g., discrete control, random access, power control

Q2.R(t) is time-varying? e.g., link failures, routing table changes, and user mobility

more fairness

Main Results:

1. Stability regions: depends on 

2. Tradeoff between stability and fairness

3. Characterization of stability region by NUM and max. stability region, no longer equivalent

example 2 power control
Example 2: Power Control

Foschini and Miljanic’sDistributed algorithm

SIR

User mobility SIR disturbances to existing users

User comes in

Active Link Protection by protection margin (Bambos et al. 00)

Time

Robustness

Robust Distributed Power Control

DPC-ALP

R-DPC.

DPC

Energy

iii simplicity
III. Simplicity

Limiting feedback messages

Simplicity

Message size

Outer

Time

Inner

Performance 2, e.g., Delay

Performance 1, e.g., Throughput

Space

simple and stable if right architecture
Simple and Stable, if Right Architecture

•Utility-optimizer is difficult to achieve in practice − Due to convergence time, non-convexity, etc• Utility-suboptimal allocations can − Retain maximum flow-level stability, if Gap/Utility→0 as queue length tends large − Otherwise, reduce stability region by at most a factor of (1-r)1/|1-α| − May even enhance other network performance metrics, e.g., increase throughput and reduce link saturation

Key Message: Turn attention from optimal but complex solutions to those that are simple even though suboptimal

finally gaps
Finally, Gaps

Industry

Modeling

Reality

Model

Theory

Transfer

Mathematics

example qft princeton collaboration
Example: QFT-Princeton Collaboration

Well-known by 2005:

  • Fixed, feasible target SIR
  • Variable SIR, centralized and optimal solution
  • Variable SIR, decentralized and suboptimal solution
  • Convexity of feasible region

Not-known till 2006:

Variable SIR, distributed, and optimal solution (for convex feasible region)

Load-spillage Power Control Algo:

Key difficulty: coupled feasibility constraint set

Key idea: left eigenvector parameterization