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Table Of Integrals Series And Products

Praise for the Third Edition: "This is one of the best books available. Its excellent organizational structure allows quick reference to specific models and its clear presentation . . . solidifies the understanding of the concepts being presented."IIE Transactions on Operations EngineeringThoroughly revised and expanded to reflect the latest developments in the field, Fundamentals of Queueing Theory, Fourth Edition continues to present the basic statistical principles that are necessary to analyze the probabilistic nature of queues. Rather than presenting a narrow focus on the subject, this update illustrates the wide-reaching, fundamental concepts in queueing theory and its applications to diverse areas such as computer science, engineering, business, and operations research.This update takes a numerical approach to understanding and making probable estimations relating to queues, with a comprehensive outline of simple and more advanced queueing models. Newly featured topics of the Fourth Edition include:Retrial queuesApproximations for queueing networksNumerical inversion of transformsDetermining the appropriate number of servers to balance quality and cost of serviceEach chapter provides a self-contained presentation of key concepts and formulae, allowing readers to work with each section independently, while a summary table at the end of the book outlines the types of queues that have been discussed and their results. In addition, two new appendices have been added, discussing transforms and generating functions as well as the fundamentals of differential and difference equations. New examples are now included along with problems that incorporate QtsPlus software, which is freely available via the book's related Web site.With its accessible style and wealth of real-world examples, Fundamentals of Queueing Theory, Fourth Edition is an ideal book for courses on queueing theory at the upper-undergraduate and graduate levels. It is also a valuable resource for researchers and practitioners who analyze congestion in the fields of telecommunications, transportation, aviation, and management science.

Fundamentals of Queueing Theory

Wireless networks are fundamentally limited by the intensity of the received signals and by their interference. Since both of these quantities depend on the spatial location of the nodes, mathematical techniques have been developed in the last decade to provide communication-theoretic results accounting for the networks geometrical configuration. Often, the location of the nodes in the network can be modeled as random, following for example a Poisson point process. In this case, different techniques based on stochastic geometry and the theory of random geometric graphs -including point process theory, percolation theory, and probabilistic combinatorics-have led to results on the connectivity, the capacity, the outage probability, and other fundamental limits of wireless networks. This tutorial article surveys some of these techniques, discusses their application to model wireless networks, and presents some of the main results that have appeared in the literature. It also serves as an introduction to the field for the other papers in this special issue.

/pdf/stochastic-geometry-and-random-graphs-for-the-analysis-and-1e671n4af3.pdf

Stochastic geometry and random graphs for the analysis and design of wireless networks

Are Power Line Communications (PLC) a good candidate for Smart Grid applications? The objective of this paper is to address this important question. To do so, we provide an overview of what PLC can deliver today by surveying its history and describing the most recent technological advances in the area. We then address Smart Grid applications as instances of sensor networking and network control problems and discuss the main conclusions one can draw from the literature on these subjects. The application scenario of PLC within the Smart Grid is then analyzed in detail. Because a necessary ingredient of network planning is modeling, we also discuss two aspects of engineering modeling that relate to our question. The first aspect is modeling the PLC channel through fading models. The second aspect we review is the Smart Grid control and traffic modeling problem which allows us to achieve a better understanding of the communications requirements. Finally, this paper reports recent studies on the electrical and topological properties of a sample power distribution network. Power grid topological studies are very important for PLC networking as the power grid is not only the information source but also the information delivery system-a unique feature when PLC is used for the Smart Grid.

/pdf/for-the-grid-and-through-the-grid-the-role-of-power-line-u1a0j36lkc.pdf

For the Grid and Through the Grid: The Role of Power Line Communications in the Smart Grid

Multiple-input-multiple-output (MIMO) wireless systems use multiple antenna elements at transmit and receive to offer improved capacity over single antenna topologies in multipath channels In such systems, the antenna properties as well as the multipath channel characteristics play a key role in determining communication performance This paper reviews recent research findings concerning antennas and propagation in MIMO systems Issues considered include channel capacity computation, channel measurement and modeling approaches, and the impact of antenna element properties and array configuration on system performance Throughout the discussion, outstanding research questions in these areas are highlighted

/pdf/a-review-of-antennas-and-propagation-for-mimo-wireless-1xbqo9fzkp.pdf

A review of antennas and propagation for MIMO wireless communications

A simple, novel, and general method is presented in this paper for approximating the sum of independent or arbitrarily correlated lognormal random variables (RV) by a single lognormal RV. The method is also shown to be applicable for approximating the sum of lognormal-Rice and Suzuki RVs by a single lognormal RV. A sum consisting of a mixture of the above distributions can also be easily handled. The method uses the moment generating function (MGF) as a tool in the approximation and does so without the extremely precise numerical computations at a large number of points that were required by the previously proposed methods in the literature. Unlike popular approximation methods such as the Fenton-Wilkinson method and the Schwartz-Yeh method, which have their own respective short-comings, the proposed method provides the parametric flexibility to accurately approximate different portions of the lognormal sum distribution. The accuracy of the method is measured both visually, as has been done in the literature, as well as quantitatively, using curve-fitting metrics. An upper bound on the sensitivity of the method is also provided.

Approximating a Sum of Random Variables with a Lognormal

Providing reliable broadband wireless communications in high mobility environments, such as high-speed railway systems, remains one of the main challenges faced by the development of the next generation wireless systems. This paper provides a systematic review of high mobility communications. We first summarize a list of key challenges and opportunities in high mobility communication systems, then provide comprehensive reviews of techniques that can address these challenges and utilize the unique opportunities. The review covers a wide spectrum of communication operations, including the accurate modeling of high mobility channels, the transceiver structures that can exploit the properties of high mobility environments, the signal processing techniques that can harvest the benefits (e.g., Doppler diversity) and mitigate the impairments (e.g., carrier frequency offset, intercarrier interference, channel estimation errors) in high mobility systems, and the mobility management and network architectures that are designed specifically for high mobility systems. The survey focuses primarily on physical layer operations, which are affected the most by the mobile environment, with some additional discussions on higher layer operations, such as handover management and control-plane/user-plane decoupling, which are essential to high mobility operations. Future research directions on high mobility communications are summarized at the end of this paper.

A Survey on High Mobility Wireless Communications: Challenges, Opportunities and Solutions

In this paper, we consider a scenario where an energy harvesting sensor continuously monitors a system and sends time-stamped status updates to a destination. The destination keeps track of the system status through the received updates. We use the metric Age of Information (AoI), the time that has elapsed since the last received update was generated, to measure the “freshness” of the status information available at the destination. Our objective is to design optimal online status update policies to minimize the long-term average AoI, subject to the energy causality constraint at the sensor. We consider three scenarios, i.e., the battery size is infinite, finite, and one unit only, respectively. For the infinite battery scenario, we adopt a best-effort uniform status update policy and show that it minimizes the long-term average AoI. For the finite battery scenario, we adopt an energy-aware adaptive status update policy, and prove that it is asymptotically optimal when the battery size goes to infinity. For the last scenario where the battery size is one, we first show that within a broadly defined class of online policies, the optimal policy should have a renewal structure. We then focus on a renewal interval, and prove that the optimal policy should have a threshold structure, i.e., if the AoI in the system is below a threshold when an energy arrival enters an empty battery, the sensor should store the energy first and then update when the AoI reaches the threshold; otherwise, it updates the status immediately. Simulation results corroborate the theoretical bounds.

Optimal Status Update for Age of Information Minimization With an Energy Harvesting Source

In this paper, we consider a scenario where an energy harvesting sensor continuously monitors a system and sends time-stamped status updates to a destination. The destination keeps track of the system status through the received updates. We use the metric Age of Information (AoI), the time that has elapsed since the last received update was generated, to measure the "freshness" of the status information available at the destination. We assume energy arrives randomly at the sensor according to a Poisson process, and each status update consumes one unit of energy. Our objective is to design optimal online status update policies to minimize the long-term average AoI, subject to the energy causality constraint at the sensor. We consider three scenarios, i.e., the battery size is infinite, finite, and one unit only, respectively. 
For the infinite battery scenario, we adopt a best-effort uniform status update policy and show that it minimizes the long-term average AoI. For the finite battery scenario, we adopt an energy-aware adaptive status update policy, and prove that it is asymptotically optimal when the battery size goes to infinity. For the last scenario where the battery size is one, we first show that within a broadly defined class of online policies, the optimal policy should have a renewal structure, i.e., the status update epochs form a renewal process, and the length of each renewal interval depends on the first energy arrival over that interval only. We then focus on a renewal interval, and prove that if the AoI in the system is below a threshold when the first energy arrives, the sensor should store the energy and hold status update until the AoI reaches the threshold, otherwise, it updates the status immediately. We analytically characterize the long-term average AoI under such a threshold-based policy, and explicitly identify the optimal threshold.

Optimal Status Update for Age of Information Minimization with an Energy Harvesting Source

A statistical discrete-time model is proposed for simulating wideband multiple-input multiple-output (MIMO) fading channels which are triply selective due to angle spread, Doppler spread, and delay spread. The new discrete-time MIMO channel model includes the combined effects of the transmit filter, physical MIMO multipath channel fading, and receive filter, and it has the same sampling period as that of the MIMO receiver. This leads to very efficient simulation of physical continuous-time MIMO channels. A new method is also presented to efficiently generate the MIMO channel stochastic coefficients. The statistical accuracy of the discrete-time MIMO channel model is rigorously verified through theoretical analysis and extensive simulations in different conditions. The high computational efficiency of the discrete-time MIMO channel model is illustrated by comparing it to that of the continuous-time MIMO channel model. The new model is further employed to evaluate the channel capacity of MIMO systems in a triply selective Rayleigh fading environment. The simulation results reveal some interesting effects of spatial correlations, multipaths, and number of antennas on the MIMO channel capacity.

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Jingxian Wu

Papers

Approximating a Sum of Random Variables with a Lognormal

A Survey on High Mobility Wireless Communications: Challenges, Opportunities and Solutions

Optimal Status Update for Age of Information Minimization With an Energy Harvesting Source

Optimal Status Update for Age of Information Minimization with an Energy Harvesting Source

A discrete-time model for triply selective MIMO Rayleigh fading channels