Architecture Robustness Simplicity

1
Architecture Robustness Simplicity

• Mung Chiang
• www.princeton.edu/chaingm
• NSF Workshop Aug 2007

2
Beyond Optimality

• Optimization as a Language
• Distributed Algo Decomposition Architecture
• Stochastic Opt Dynamics Robustness
• Nonconvexity Suboptimality Simplicity

3
I. Architecture

• Functionality allocation How to modularize?
• Who does what? How fast?
• How to put them together?
• Communications, Control, Computation

4
Architecture of Networks?
5
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

6
II. Robustness
Lack of Union Between Stochastic Network
Theory Distributed Optimization Theory
7
Example 1 Session-level Stability
Main Results in literature 1. Stability region
Rate region 2. Maximum stability region
achieved for any ? gt0.
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
8
Example 2 Power Control
Foschini and MiljanicsDistributed 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
9
III. Simplicity
Limiting feedback messages
Simplicity
Message size
Outer
Time
Inner
Performance 2, e.g., Delay
Performance 1, e.g., Throughput
Space
10
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-a
- 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
11
Finally, Gaps
Industry
Modeling
Reality
Model
Theory
Transfer
Mathematics
12
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