/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

This text presents a modern theory of analysis, control, and optimization for dynamic networks. Mathematical techniques of Lyapunov drift and Lyapunov optimization are developed and shown to enable constrained optimization of time averages in general stochastic systems. The focus is on communication and queueing systems, including wireless networks with time-varying channels, mobility, and randomly arriving traffic. A simple drift-plus-penalty framework is used to optimize time averages such as throughput, throughput-utility, power, and distortion. Explicit performance-delay tradeoffs are provided to illustrate the cost of approaching optimality. This theory is also applicable to problems in operations research and economics, where energy-efficient and profit-maximizing decisions must be made without knowing the future. Topics in the text include the following: - Queue stability theory - Backpressure, max-weight, and virtual queue methods - Primal-dual methods for non-convex stochastic utility maximization - Universal scheduling theory for arbitrary sample paths - Approximate and randomized scheduling theory - Optimization of renewal systems and Markov decision systems Detailed examples and numerous problem set questions are provided to reinforce the main concepts. Table of Contents: Introduction / Introduction to Queues / Dynamic Scheduling Example / Optimizing Time Averages / Optimizing Functions of Time Averages / Approximate Scheduling / Optimization of Renewal Systems / Conclusions

Stochastic Network Optimization with Application to Communication and Queueing Systems

Information flow in a telecommunication network is accomplished through the interaction of mechanisms at various design layers with the end goal of supporting the information exchange needs of the applications. In wireless networks in particular, the different layers interact in a nontrivial manner in order to support information transfer. In this text we will present abstract models that capture the cross-layer interaction from the physical to transport layer in wireless network architectures including cellular, ad-hoc and sensor networks as well as hybrid wireless-wireline. The model allows for arbitrary network topologies as well as traffic forwarding modes, including datagrams and virtual circuits. Furthermore the time varying nature of a wireless network, due either to fading channels or to changing connectivity due to mobility, is adequately captured in our model to allow for state dependent network control policies. Quantitative performance measures that capture the quality of service requirements in these systems depending on the supported applications are discussed, including throughput maximization, energy consumption minimization, rate utility function maximization as well as general performance functionals. Cross-layer control algorithms with optimal or suboptimal performance with respect to the above measures are presented and analyzed. A detailed exposition of the related analysis and design techniques is provided.

/pdf/resource-allocation-and-cross-layer-control-in-wireless-1bikwdtjww.pdf

Resource Allocation and Cross Layer Control in Wireless Networks

Wireless systems comprised of rechargeable nodes have a significantly prolonged lifetime and are sustainable. A distinct characteristic of these systems is the fact that the nodes can harvest energy throughout the duration in which communication takes place. As such, transmission policies of the nodes need to adapt to these harvested energy arrivals. In this paper, we consider optimization of point-to-point data transmission with an energy harvesting transmitter which has a limited battery capacity, communicating in a wireless fading channel. We consider two objectives: maximizing the throughput by a deadline, and minimizing the transmission completion time of the communication session. We optimize these objectives by controlling the time sequence of transmit powers subject to energy storage capacity and causality constraints. We, first, study optimal offline policies. We introduce a directional water-filling algorithm which provides a simple and concise interpretation of the necessary optimality conditions. We show the optimality of an adaptive directional water-filling algorithm for the throughput maximization problem. We solve the transmission completion time minimization problem by utilizing its equivalence to its throughput maximization counterpart. Next, we consider online policies. We use stochastic dynamic programming to solve for the optimal online policy that maximizes the average number of bits delivered by a deadline under stochastic fading and energy arrival processes with causal channel state feedback. We also propose near-optimal policies with reduced complexity, and numerically study their performances along with the performances of the offline and online optimal policies under various different configurations.

Transmission with Energy Harvesting Nodes in Fading Wireless Channels: Optimal Policies

We seek to maximize the average data throughput of a single transmitter sending data over a fading channel to a single user class. The transmitter has a fixed amount of energy and a limited amount of time to send data. Given that the channel state determines the throughput obtained per unit of energy expended, the goal is to obtain a policy for scheduling transmissions that maximizes the expected data throughput. We develop a dynamic programming formulation that leads to an optimal transmission schedule, first where the present channel state is known just before transmission, and then to the case where the current channel state is unknown before transmission, but observed after transmission and evolves according to a Markov process. We then extend our approach to the problem of minimizing the expected energy required to send a fixed amount of data over a fading channel given deadline constraints.

/pdf/optimal-transmission-scheduling-over-a-fading-channel-with-11grwz4qm5.pdf

Optimal transmission scheduling over a fading channel with energy and deadline constraints

We seek to maximize the data throughput of an energy and time constrained transmitter sending data over a fading channel. The transmitter has a fixed amount of energy and a limited amount of time to send data. Given that the channel fade state determines the throughput obtained per unit of energy expended, the goal is to obtain a policy for scheduling transmissions that maximizes the expected data throughput. We develop a dynamic programming formulation that leads to an optimal closed-form transmission schedule. We then extend our approach to the problem of minimizing the energy required to send a fixed amount of data over a fading channel given deadline constraints.

/pdf/optimal-energy-allocation-for-delay-constrained-data-2yi2n9zwei.pdf

Optimal energy allocation for delay-constrained data transmission over a time-varying channel

We address the issue of optimal energy allocation and admission control for communications satellites in earth orbit. Such satellites receive requests for transmission as they orbit the earth, but may not be able to serve them all, due to energy limitations. The objective is to choose which requests to serve so that the expected total reward is maximized. The special case of a single energy-constrained satellite is considered. Rewards and demands from users for transmission (energy) are random and known only at request time. Using a dynamic programming approach, an optimal policy is derived and is characterized in terms of thresholds. Furthermore, in the special case where demand for energy is unlimited, an optimal policy is obtained in closed form. Although motivated by satellite communications, our approach is general and can be used to solve a variety of resource allocation problems in wireless communications.

Optimal energy allocation and admission control for communications satellites

We address the issue of optimal energy allocation and admission control for communications satellites in Earth orbit. These satellites receive requests for transmission as they orbit the Earth, but may not be able to serve them all, due to energy limitations. The objective is to choose which requests to serve so that the expected total reward is maximized. The special case of a single energy-constrained satellite is considered. Rewards and demands from users for transmission (energy) are random and known only at request time. Using a dynamic programming approach, an optimal policy is derived and is characterized in terms of thresholds. Furthermore, in the special case where demand for energy is unlimited, an optimal policy is obtained in dosed form. Although motivated by satellite communications, our approach is general and can be used to solve a variety of resource allocation problems in wireless communications.

/pdf/optimal-energy-allocation-and-admission-control-for-12mzm1nr0f.pdf

A. Fu

Papers

Optimal transmission scheduling over a fading channel with energy and deadline constraints

Optimal energy allocation for delay-constrained data transmission over a time-varying channel

Optimal energy allocation and admission control for communications satellites

Optimal energy allocation and admission control for communications satellites