Information Theory for Mobile Ad-Hoc Networks (ITMANET): The FLoWS Project Thrust 3 Application Metrics and Network Performance Asu Ozdaglar and Devavrat Shah

Capacity Delay Power Upper Bound Lower Bound Capacity and Fundamental Limits Capacity Delay Power Utility=U(C,D,E) Application and Network Optimization (C*,D*,E*) Constraints Degrees of Freedom Models and Dynamics Application Metrics and Network Performance Layerless Dynamic Networks New Paradigms for Upper Bounds MANET Metrics Fundamental Limits of Wireless Systems Application Metrics Models New MANET Theory Metrics

Thrust Motivation Fundamental problems in related disciplines: Information Theory Capacity and fundamental limits Shannon: Economics Multi-agent systems Nash: Equilibrium Networks Resource Allocation Optimization - Algorithms Thrust 3 Application Metrics and Network Performance Robust against non- cooperative behavior Physical layer considerations General application metrics Thrust Objective: Develop a framework for resource allocation with heterogeneous and dynamically varying application metrics while ensuring efficient (stable) operation of decentralized networks with uncertain capabilities

Thrust Areas Resource Allocation Optimization StochasticsGame Theory FLoWS Thrust Achievements Different metrics require different methodology Distributed optimization/ algorithms Wireless Dynamic NUM Ozdaglar, Shah Boyd, Goldsmith Cross-Layer Optimization Boyd, Goldsmith, Medard, Ozdaglar Integration of macro level control and micro level system design Johari, Meyn, Shah Cognitive radio design Goldsmith, Johari Topology formation Noncooperative scheduling Johari Ozdaglar Noncooperative coding Effros

Recent Thrust Achievements: Optimization Methods for General Application Metrics Stochastic Resource Allocation (Boyd, Goldsmith 09) Existing wireline NUM theory assumes fixed capacity links, steady state operation A new wireless NUM theory –Dynamic NUM: Multi-period model and distributed algorithm for dynamic network utility maximization with time-varying utilities and hard-delay requirements –Formulated as a stochastic control problem over finite time horizon –Backward induction yields simple affine control laws which are adaptive to unknown random link capacities Focus Talk

Recent Thrust Achievements: Optimization Methods for General Application Metrics A Distributed Newton Method for Optimization (Jadbabaie, Ozdaglar 09) –Almost all distributed optimization relies on first order (gradient type) methods Easy to distribute, but slow! –We developed a Newton (second-order) method that solves minimum cost network flow problems in a distributed manner Relies on computing the dual Newton step by solving a discrete Poisson equation involving the graph Laplacian Consensus-based averaging scheme leads to distributed implementation

Recent Thrust Achievements: Optimization Methods for General Application Metrics Distributed and low-complexity scheduling for maximal throughput in network coded multicast (Koetter, Medard 09) For the joint scheduling and subgraph selection problem, we model valid network configurations as stable sets in an appropriately defined conflict graph We develop algorithms to solve the arising optimization problem in a distributed manner and with low complexity Using conflicting hyperarcs as a model for scheduling constraints, we can formulate a linear program that jointly optimizes the network coding subgraph and the underlying schedule

Recent Thrust Achievements: Stochastic Network Algorithms Relaxation Techniques for Network Optimization (Meyn 09) –Policy synthesis using adaptive learning methods and based on dynamic hotspots in the network –Relies on workload relaxation techniques and fluid models Fluid Limits for Gossip Processes (Johari 09) –Studied macro models (or mean-field models) for gossip processes over random graphs (i.e., instead of tracking nodes individually, consider the dynamics of a fraction of the nodes) –Characterized the relation between micro and macro models

Recent Thrust Achievements: Game-Theoretic Models and Algorithms Distributed Scheduling and Equilibrium Dynamics with Correlated Fading Channels (Ozdaglar, Parrilo 08) –Game-theoretic scheduling models allow the flexibility to incorporate different user objectives and reach an efficient operating point in a distributed manner –Distributed convergent dynamics and equilibrium characterization with correlated channels, which model joint fading effects Uses and develops tools from potential games Oblivious Equilibrium for Stochastic Games with Concave Utility (Johari, Goldsmith 09) –Goal: understand competition among wireless nodes in dynamic settings –Necessitates a stochastic game formulation, which is computationally prohibitive –Identified a set of conditions on model primitives under which oblivious equilibrium can approximate the (more computationally difficult) Markov perfect equilibrium.

Recent Inter-Thrust Achievements: Queuing Analysis for Coded Networks with Feedback (Shah, Medard 09) –A novel ACK mechanism based on remaining degrees of freedom (instead of confirmation of decoding), which allows nodes to manage queue occupancy effectively –The proposed queue management approach will play a key role in interfacing TCP with network coding A Game Theoretic Approach to Network Coding (Effros 09) –Greedy flows (users) choose minimum cost path for themselves –Provide incentives to the flows to create coding opportunities to improve efficiency Interference Mitigating Mobility Strategies in MANETs (Moulin 09) –Mobility viewed as a resource to avoid interference form other nodes and dynamically enlarge capacity regions –Formulated as a pursuit-evasion game and derived optimal greedy strategies Focus Talk

Achievements Overview (Previous) Shah: Low complexity throughput and delay efficient scheduling Ozdaglar: Distributed optimization algorithms for general metrics and with quantized information Johari: Local dynamics for topology formation Meyn: Generalized Max-Weight policies with performance optim- distributed implementations Goldsmith, Johari: Game-theoretic model for cognitive radio design with incomplete channel information Boyd, Goldsmith: Wireless network utility maximization (dynamic user metrics, random environments and adaptive modulation ) Optimization Distributed and dynamic algorithms for resource allocation Stochastic Network Analysis Flow-based models and queuing dynamics Game Theory New resource allocation paradigm that focuses on hetereogeneity and competition Medard, Ozdaglar: Efficient resource allocation in non-fading and fading MAC channels using optimization methods and rate-splitting Shah: Capacity region characterization through scaling for arbitrary node placement and arbitrary demand Ozdaglar: Competitive scheduling in collision channels with correlated channel states Medard, Ozdaglar: Cross-Layer optimization for different application delay metrics and block- by-block coding schemes Boyd: Efficient methods for large scale network utility maximization Goldsmith: Layered broadcast source-channel coding Medard, Shah: Distributed functional compression

Achievements Overview (Most Recent) Shah, Medard: Queueing analysis for coded networks with feedback Johari: Fluid limits for gossip Meyn: Relaxation techniques for network optimization Goldsmith, Johari: Oblivious equilibrium for stochastic games with concave utility Boyd, Goldsmith: Wireless network utility maximization as a stochastic optimal control problem Optimization Distributed and dynamic algorithms for resource allocation Stochastic Network Analysis Flow-based models and queuing dynamics Game Theory New resource allocation paradigm that focuses on hetereogeneity and competition Ozdaglar: Distributed second order methods for network optimization Ozdaglar: Noncooperative scheduling with correlated channel states Effros: Noncooperative network coding Moulin: Interference mitigating mobility Koetter, Medard: Distributed and low- complexity scheduling for maximal throughput in network coded multicast

Thrust Synergies: An Example T3 solves this problem: Using distributed algorithms Considering stochastic changes, physical layer constraints and micro- level considerations Modeling information structures (may lead to changes in the performance region) Algorithmic constraints and sensitivity analysis may change the dimension of performance region Thrust 1 Upper Bounds Thrust 2 Layerless Dynamic Networks Capacity Delay Energy Upper Bound Lower Bound Thrust 3 Application Metrics and Network Performance Capacity Delay Energy (C*,D*,E*) (C*,D*,E*) optimal solution of Combinatorial algorithms for upper bounds Effros: Noncooperative network coding Moulin: Interference mitigating mobility Boyd, Goldsmith: Wireless network utility maximization as a stochastic optimal control problem Koetter, Medard: Distributed and low- complexity scheduling for maximal throughput in network coded multicast

Thrust Alignment with Phase 2 Goals Evolve results in all thrust areas to examine more complex models, robustness/security, more challenging dynamics, and larger networks. –Wireless NUM for time-varying user metrics and dynamic network conditions Demonstrate synergies between thrust areas: compare and tighten upper bounds and achievability results for specific models and metrics; apply generalized theory of distortion and utility based on performance regions developed in Thrusts 1-2. –Joint optimization of coding, delay metrics, and power allocation –Joint optimization of rate and power over information-theoretic capacity region of fading multiple access channels –Distributed and low-complexity scheduling for maximal throughput in network coded multicast –A game-theoretic approach to network coding –Interference-mitigating mobility strategies through game theory –Queueing analysis of coded networks Demonstrate that key synergies between information theory, network theory, and optimization/control lead to at least an order of magnitude performance gain for key metrics. –Throughput gains of hyperarc scheduling –Rate-reliability tradeoffs and performance gains for wireless NUM –Performance improvement for generalized Maxweight policies