Architecture Robustness Simplicity Mung Chiang www princeton educhaingm

Architecture Robustness Simplicity Mung Chiang www. princeton. edu/~chaingm NSF Workshop Aug 2007 1

Beyond Optimality Optimization as a “Language” ® Distributed Algo: Decomposition: Architecture ® Stochastic Opt: Dynamics: Robustness ® Nonconvexity: Suboptimality: Simplicity 2

I. Architecture ® Functionality allocation: How to modularize? Who does what? How fast? How to put them together? ® Communications, Control, Computation: 3

Architecture of Networks? 4

Layering As Optimization Decomposition Network: Layering: Layers: Interface: Generalized Network Utility Maximization Decomposition Scheme Decomposed subproblems 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 5

II. Robustness Lack of Union Between: Stochastic Network Theory Distributed Optimization Theory 6

Example 1: Session-level Stability Main Results in literature 1. Stability region = Rate region 2. Maximum stability region achieved for any >0. Q 1. R is non-convex? e. g. , discrete control, random access, power control Q 2. 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 7

Example 2: Power Control Foschini and Miljanic’s Distributed 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 R-DPC. DPC-ALP DPC Energy 8

III. Simplicity Limiting feedback messages Message size Simplicity Time Outer Inner Performance 2, e. g. , Delay Space Performance 1, e. g. , Throughput 9

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 1 0

Finally, Gaps Industry Modeling Reality Model Transfer Theory Mathematics 1 1

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 1 2