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Author: Publisher: ISBN: Category : Languages : en Pages :
Book Description
This dissertation is concerned with heavy traffic and Markov modulated diffusion models that are applied to resource allocation problems in wireless communication system and the numerical analysis for their associated continuous time stochastic control problems. To be specific, the heavy traffic model is a two-dimensional stochastic differential equation with reflection (SDER), and the other model is a second-order Markov modulated diffusion process. With the proliferation of wireless applications having large capacity requirements, such as multimedia, internet, gaming, etc., and the limitations of realizing spectral efficiency gains, wireless queueing systems will be operating a near-capacity levels, so called "Heavy traffic". Under this assumption, SDER has been developed as an approximation model for a multi-buffer and various channel state wireless communication system. Building on the seminal work of Buche and Kushner [13], we study how the reflection process can affect the solution of the SDER and the resource (reserve power) allocation theoretically and numerically. We have shown that Multi-Completely S is a necessary condition for the existence and uniqueness for the SDER instead of the well known Completely S in the wireline system [69]. The whole resource (reserve transmission power) allocation is modeled as a stochastic control problem subject to the SDER. Using Markov Chain Approximation (MCA) method [51], various effects of factors, especially the reflection processes (nominal power reallocation) are studied via numerical experiments. After optimal control policies are obtained via MCA method under an appropriate grid size setting, Monte Carlo and real time simulation experiments are done using heavy traffic policies v.s. heuristic wedge control policies. The performance of heavy traffic policies is better than that of wedge policies under various traffic patterns including aggregated OND FF process (Long Range Dependence & Heavy Tailed) which.
Author: Publisher: ISBN: Category : Languages : en Pages :
Book Description
This dissertation is concerned with heavy traffic and Markov modulated diffusion models that are applied to resource allocation problems in wireless communication system and the numerical analysis for their associated continuous time stochastic control problems. To be specific, the heavy traffic model is a two-dimensional stochastic differential equation with reflection (SDER), and the other model is a second-order Markov modulated diffusion process. With the proliferation of wireless applications having large capacity requirements, such as multimedia, internet, gaming, etc., and the limitations of realizing spectral efficiency gains, wireless queueing systems will be operating a near-capacity levels, so called "Heavy traffic". Under this assumption, SDER has been developed as an approximation model for a multi-buffer and various channel state wireless communication system. Building on the seminal work of Buche and Kushner [13], we study how the reflection process can affect the solution of the SDER and the resource (reserve power) allocation theoretically and numerically. We have shown that Multi-Completely S is a necessary condition for the existence and uniqueness for the SDER instead of the well known Completely S in the wireline system [69]. The whole resource (reserve transmission power) allocation is modeled as a stochastic control problem subject to the SDER. Using Markov Chain Approximation (MCA) method [51], various effects of factors, especially the reflection processes (nominal power reallocation) are studied via numerical experiments. After optimal control policies are obtained via MCA method under an appropriate grid size setting, Monte Carlo and real time simulation experiments are done using heavy traffic policies v.s. heuristic wedge control policies. The performance of heavy traffic policies is better than that of wedge policies under various traffic patterns including aggregated OND FF process (Long Range Dependence & Heavy Tailed) which.
Author: Harold Kushner Publisher: Springer Science & Business Media ISBN: 9780387952642 Category : Mathematics Languages : en Pages : 12
Book Description
One of the first books in the timely and important area of heavy traffic analysis of controlled and uncontrolled stochastics networks, by one of the leading authors in the field. The general theory is developed, with possibly state dependent parameters, and specialized to many different cases of practical interest.
Author: T. P. Bagchi Publisher: Springer ISBN: Category : Mathematics Languages : en Pages : 116
Book Description
Mathematical formulation of the bulk queuing problem; A numerical approach to waiting line problems; Conclusions and directions for further research.
Author: Michael J. Neely Publisher: Morgan & Claypool Publishers ISBN: 160845455X Category : Computers Languages : en Pages : 212
Book Description
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
Author: Agassi Melikov Publisher: Springer ISBN: 3319086693 Category : Computers Languages : en Pages : 201
Book Description
The increasing complexity of telecommunication networks requires us to develop adequate mathematical models. We must find their characteristics, optimize them subject to chosen criteria, and develop the corresponding control algorithms. Multidimensional queueing models are used to design and optimize modern and next-generation networks (NGN). The central problem of the related mathematical theory is to apply multidimensional and large-size queueing models to improve efficiency. In this book new methods are successively developed and applied to solve related problems. The book is recommended for researchers engaged with the mathematical theory of telecommunications traffic.
Author: Attahiru Alfa Publisher: Springer ISBN: 1493934201 Category : Technology & Engineering Languages : en Pages : 400
Book Description
This book introduces the theoretical fundamentals for modeling queues in discrete-time, and the basic procedures for developing queuing models in discrete-time. There is a focus on applications in modern telecommunication systems. It presents how most queueing models in discrete-time can be set up as discrete-time Markov chains. Techniques such as matrix-analytic methods (MAM) that can used to analyze the resulting Markov chains are included. This book covers single node systems, tandem system and queueing networks. It shows how queues with time-varying parameters can be analyzed, and illustrates numerical issues associated with computations for the discrete-time queueing systems. Optimal control of queues is also covered. Applied Discrete-Time Queues targets researchers, advanced-level students and analysts in the field of telecommunication networks. It is suitable as a reference book and can also be used as a secondary text book in computer engineering and computer science. Examples and exercises are included.
Author: Michael Neely Publisher: Springer Nature ISBN: 303179995X Category : Computers Languages : en Pages : 199
Book Description
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
Author: Libin Jiang Publisher: Morgan & Claypool Publishers ISBN: 1608454622 Category : Technology & Engineering Languages : en Pages : 156
Book Description
In this book, we consider the problem of achieving the maximum throughput and utility in a class of networks with resource-sharing constraints. This is a classical problem of great importance. In the context of wireless networks, we first propose a fully distributed scheduling algorithm that achieves the maximum throughput. Inspired by CSMA (Carrier Sense Multiple Access), which is widely deployed in today's wireless networks, our algorithm is simple, asynchronous, and easy to implement. Second, using a novel maximal-entropy technique, we combine the CSMA scheduling algorithm with congestion control to approach the maximum utility. Also, we further show that CSMA scheduling is a modular MAC-layer algorithm that can work with other protocols in the transport layer and network layer. Third, for wireless networks where packet collisions are unavoidable, we establish a general analytical model and extend the above algorithms to that case. Stochastic Processing Networks (SPNs) model manufacturing, communication, and service systems. In manufacturing networks, for example, tasks require parts and resources to produce other parts. SPNs are more general than queueing networks and pose novel challenges to throughput-optimum scheduling. We proposes a "deficit maximum weight" (DMW) algorithm to achieve throughput optimality and maximize the net utility of the production in SPNs. Table of Contents: Introduction / Overview / Scheduling in Wireless Networks / Utility Maximization in Wireless Networks / Distributed CSMA Scheduling with Collisions / Stochastic Processing networks
Author: Harold Kushner Publisher: Springer ISBN: 9781461265412 Category : Mathematics Languages : en Pages : 515
Book Description
One of the first books in the timely and important area of heavy traffic analysis of controlled and uncontrolled stochastics networks, by one of the leading authors in the field. The general theory is developed, with possibly state dependent parameters, and specialized to many different cases of practical interest.
Author: 
Author: 
Author: Chuan Lin
Author: Harold Kushner
Author: T. P. Bagchi
Author: Michael J. Neely
Author: Agassi Melikov
Author: Attahiru Alfa
Author: Michael Neely
Author: Libin Jiang
Author: Harold Kushner