Author: Reginald A. Banez
Publisher: Springer Nature
ISBN: 3030869059
Category : Computers
Languages : en
Pages : 184
Book Description
This book covers the basic theory of mean field game (MFG) and its applications in wireless networks. It starts with an overview of the current and future state-of-the-art in 5G and 6G wireless networks. Then, a tutorial is presented for MFG, mean-field-type game (MFTG), and prerequisite fields of study such as optimal control theory and differential games. This book also includes a literature survey of MFG-based research in wireless network technologies such as ultra-dense networks (UDNs), device-to-device (D2D) communications, internet-of-things (IoT), unmanned aerial vehicles (UAVs), and mobile edge networks (MENs). Several applications of MFG and MFTG in UDNs, social networks, and multi-access edge computing networks (MECNs) are introduced as well. Applications of MFG covered in this book are divided in three parts. The first part covers three single-population MFG research works or case studies in UDNs including ultra-dense D2D networks, ultra-dense UAV networks, and dense-user MECNs. The second part centers on a multiple-population MFG (MPMFG) modeling of belief and opinion evolution in social networks. It focuses on a recently developed MPMFG framework and its application in analyzing the behavior of users in a multiple-population social network. Finally, the last part concentrates on an MFTG approach to computation offloading in MECN. The computation offloading algorithms are designed for energy- and time-efficient offloading of computation-intensive tasks in an MECN. This book targets advanced-level students, professors, researchers, scientists, and engineers in the fields of communications and networks. Industry managers and government employees working in these same fields will also find this book useful.
Mean Field Game and its Applications in Wireless Networks
Author: Reginald A. Banez
Publisher: Springer Nature
ISBN: 3030869059
Category : Computers
Languages : en
Pages : 184
Book Description
This book covers the basic theory of mean field game (MFG) and its applications in wireless networks. It starts with an overview of the current and future state-of-the-art in 5G and 6G wireless networks. Then, a tutorial is presented for MFG, mean-field-type game (MFTG), and prerequisite fields of study such as optimal control theory and differential games. This book also includes a literature survey of MFG-based research in wireless network technologies such as ultra-dense networks (UDNs), device-to-device (D2D) communications, internet-of-things (IoT), unmanned aerial vehicles (UAVs), and mobile edge networks (MENs). Several applications of MFG and MFTG in UDNs, social networks, and multi-access edge computing networks (MECNs) are introduced as well. Applications of MFG covered in this book are divided in three parts. The first part covers three single-population MFG research works or case studies in UDNs including ultra-dense D2D networks, ultra-dense UAV networks, and dense-user MECNs. The second part centers on a multiple-population MFG (MPMFG) modeling of belief and opinion evolution in social networks. It focuses on a recently developed MPMFG framework and its application in analyzing the behavior of users in a multiple-population social network. Finally, the last part concentrates on an MFTG approach to computation offloading in MECN. The computation offloading algorithms are designed for energy- and time-efficient offloading of computation-intensive tasks in an MECN. This book targets advanced-level students, professors, researchers, scientists, and engineers in the fields of communications and networks. Industry managers and government employees working in these same fields will also find this book useful.
Publisher: Springer Nature
ISBN: 3030869059
Category : Computers
Languages : en
Pages : 184
Book Description
This book covers the basic theory of mean field game (MFG) and its applications in wireless networks. It starts with an overview of the current and future state-of-the-art in 5G and 6G wireless networks. Then, a tutorial is presented for MFG, mean-field-type game (MFTG), and prerequisite fields of study such as optimal control theory and differential games. This book also includes a literature survey of MFG-based research in wireless network technologies such as ultra-dense networks (UDNs), device-to-device (D2D) communications, internet-of-things (IoT), unmanned aerial vehicles (UAVs), and mobile edge networks (MENs). Several applications of MFG and MFTG in UDNs, social networks, and multi-access edge computing networks (MECNs) are introduced as well. Applications of MFG covered in this book are divided in three parts. The first part covers three single-population MFG research works or case studies in UDNs including ultra-dense D2D networks, ultra-dense UAV networks, and dense-user MECNs. The second part centers on a multiple-population MFG (MPMFG) modeling of belief and opinion evolution in social networks. It focuses on a recently developed MPMFG framework and its application in analyzing the behavior of users in a multiple-population social network. Finally, the last part concentrates on an MFTG approach to computation offloading in MECN. The computation offloading algorithms are designed for energy- and time-efficient offloading of computation-intensive tasks in an MECN. This book targets advanced-level students, professors, researchers, scientists, and engineers in the fields of communications and networks. Industry managers and government employees working in these same fields will also find this book useful.
Mean-Field-Type Games for Engineers
Author: Julian Barreiro-Gomez
Publisher: CRC Press
ISBN: 1000473538
Category : Technology & Engineering
Languages : en
Pages : 526
Book Description
The contents of this book comprise an appropriate background to start working and doing research on mean-field-type control and game theory. To make the exposition and explanation even easier, we first study the deterministic optimal control and differential linear-quadratic games. Then, we progressively add complexity step-by-step and little-by-little to the problem settings until we finally study and analyze mean-field-type control and game problems incorporating several stochastic processes, e.g., Brownian motions, Poisson jumps, and random coefficients. We go beyond the Nash equilibrium, which provides a solution for non- cooperative games, by analyzing other game-theoretical concepts such as the Berge, Stackelberg, adversarial/robust, and co-opetitive equilibria. For the mean-field-type game analysis, we provide several numerical examples using a Matlab-based user-friendly toolbox that is available for the free use to the readers of this book. We present several engineering applications in both continuous and discrete time. Among these applications we find the following: water distribution systems, micro-grid energy storage, stirred tank reactor, mechanism design for evolutionary dynamics, multi-level building evacuation problem, and the COVID-19 propagation control. Julian Barreiro-Gomez Hamidou Tembine With such a demand from engineering audiences, this book is very timely and provides a thorough study of mean-field-type game theory. The strenuous protagonist of this book is to bridge between the theoretical findings and engineering solutions. The book introduces the basics first, and then mathematical frameworks are elaborately explained. The engineering application examples are shown in detail, and the popular learning approaches are also investigated. Those advantageous characteristics will make this book a comprehensive handbook of many engineering fields for many years, and I will buy one when it gets published. Zhu Han
Publisher: CRC Press
ISBN: 1000473538
Category : Technology & Engineering
Languages : en
Pages : 526
Book Description
The contents of this book comprise an appropriate background to start working and doing research on mean-field-type control and game theory. To make the exposition and explanation even easier, we first study the deterministic optimal control and differential linear-quadratic games. Then, we progressively add complexity step-by-step and little-by-little to the problem settings until we finally study and analyze mean-field-type control and game problems incorporating several stochastic processes, e.g., Brownian motions, Poisson jumps, and random coefficients. We go beyond the Nash equilibrium, which provides a solution for non- cooperative games, by analyzing other game-theoretical concepts such as the Berge, Stackelberg, adversarial/robust, and co-opetitive equilibria. For the mean-field-type game analysis, we provide several numerical examples using a Matlab-based user-friendly toolbox that is available for the free use to the readers of this book. We present several engineering applications in both continuous and discrete time. Among these applications we find the following: water distribution systems, micro-grid energy storage, stirred tank reactor, mechanism design for evolutionary dynamics, multi-level building evacuation problem, and the COVID-19 propagation control. Julian Barreiro-Gomez Hamidou Tembine With such a demand from engineering audiences, this book is very timely and provides a thorough study of mean-field-type game theory. The strenuous protagonist of this book is to bridge between the theoretical findings and engineering solutions. The book introduces the basics first, and then mathematical frameworks are elaborately explained. The engineering application examples are shown in detail, and the popular learning approaches are also investigated. Those advantageous characteristics will make this book a comprehensive handbook of many engineering fields for many years, and I will buy one when it gets published. Zhu Han
Game Theory and Learning for Wireless Networks
Author: Samson Lasaulce
Publisher:
ISBN: 9787519296766
Category : Game theory
Languages : en
Pages : 0
Book Description
Publisher:
ISBN: 9787519296766
Category : Game theory
Languages : en
Pages : 0
Book Description
Game Theory in Wireless and Communication Networks
Author: Zhu Han
Publisher: Cambridge University Press
ISBN: 0521196965
Category : Business & Economics
Languages : en
Pages : 555
Book Description
This unified 2001 treatment of game theory focuses on finding state-of-the-art solutions to issues surrounding the next generation of wireless and communications networks. The key results and tools of game theory are covered, as are various real-world technologies and a wide range of techniques for modeling, design and analysis.
Publisher: Cambridge University Press
ISBN: 0521196965
Category : Business & Economics
Languages : en
Pages : 555
Book Description
This unified 2001 treatment of game theory focuses on finding state-of-the-art solutions to issues surrounding the next generation of wireless and communications networks. The key results and tools of game theory are covered, as are various real-world technologies and a wide range of techniques for modeling, design and analysis.
Ultra-Dense Networks for 5G and Beyond
Author: Trung Q. Duong
Publisher: John Wiley & Sons
ISBN: 1119473691
Category : Technology & Engineering
Languages : en
Pages : 312
Book Description
Offers comprehensive insight into the theory, models, and techniques of ultra-dense networks and applications in 5G and other emerging wireless networks The need for speed—and power—in wireless communications is growing exponentially. Data rates are projected to increase by a factor of ten every five years—and with the emerging Internet of Things (IoT) predicted to wirelessly connect trillions of devices across the globe, future mobile networks (5G) will grind to a halt unless more capacity is created. This book presents new research related to the theory and practice of all aspects of ultra-dense networks, covering recent advances in ultra-dense networks for 5G networks and beyond, including cognitive radio networks, massive multiple-input multiple-output (MIMO), device-to-device (D2D) communications, millimeter-wave communications, and energy harvesting communications. Clear and concise throughout, Ultra-Dense Networks for 5G and Beyond - Modelling, Analysis, and Applications offers a comprehensive coverage on such topics as network optimization; mobility, handoff control, and interference management; and load balancing schemes and energy saving techniques. It delves into the backhaul traffic aspects in ultra-dense networks and studies transceiver hardware impairments and power consumption models in ultra-dense networks. The book also examines new IoT, smart-grid, and smart-city applications, as well as novel modulation, coding, and waveform designs. One of the first books to focus solely on ultra-dense networks for 5G in a complete presentation Covers advanced architectures, self-organizing protocols, resource allocation, user-base station association, synchronization, and signaling Examines the current state of cell-free massive MIMO, distributed massive MIMO, and heterogeneous small cell architectures Offers network measurements, implementations, and demos Looks at wireless caching techniques, physical layer security, cognitive radio, energy harvesting, and D2D communications in ultra-dense networks Ultra-Dense Networks for 5G and Beyond - Modelling, Analysis, and Applications is an ideal reference for those who want to design high-speed, high-capacity communications in advanced networks, and will appeal to postgraduate students, researchers, and engineers in the field.
Publisher: John Wiley & Sons
ISBN: 1119473691
Category : Technology & Engineering
Languages : en
Pages : 312
Book Description
Offers comprehensive insight into the theory, models, and techniques of ultra-dense networks and applications in 5G and other emerging wireless networks The need for speed—and power—in wireless communications is growing exponentially. Data rates are projected to increase by a factor of ten every five years—and with the emerging Internet of Things (IoT) predicted to wirelessly connect trillions of devices across the globe, future mobile networks (5G) will grind to a halt unless more capacity is created. This book presents new research related to the theory and practice of all aspects of ultra-dense networks, covering recent advances in ultra-dense networks for 5G networks and beyond, including cognitive radio networks, massive multiple-input multiple-output (MIMO), device-to-device (D2D) communications, millimeter-wave communications, and energy harvesting communications. Clear and concise throughout, Ultra-Dense Networks for 5G and Beyond - Modelling, Analysis, and Applications offers a comprehensive coverage on such topics as network optimization; mobility, handoff control, and interference management; and load balancing schemes and energy saving techniques. It delves into the backhaul traffic aspects in ultra-dense networks and studies transceiver hardware impairments and power consumption models in ultra-dense networks. The book also examines new IoT, smart-grid, and smart-city applications, as well as novel modulation, coding, and waveform designs. One of the first books to focus solely on ultra-dense networks for 5G in a complete presentation Covers advanced architectures, self-organizing protocols, resource allocation, user-base station association, synchronization, and signaling Examines the current state of cell-free massive MIMO, distributed massive MIMO, and heterogeneous small cell architectures Offers network measurements, implementations, and demos Looks at wireless caching techniques, physical layer security, cognitive radio, energy harvesting, and D2D communications in ultra-dense networks Ultra-Dense Networks for 5G and Beyond - Modelling, Analysis, and Applications is an ideal reference for those who want to design high-speed, high-capacity communications in advanced networks, and will appeal to postgraduate students, researchers, and engineers in the field.
Game Theory for Next Generation Wireless and Communication Networks
Author: Zhu Han
Publisher: Cambridge University Press
ISBN: 1108417337
Category : Computers
Languages : en
Pages : 509
Book Description
A unified treatment of the latest game theoretic approaches for designing, modeling, and optimizing emerging wireless communication networks. Covering theory, analytical tools, and applications, it is ideal for researchers and graduate students in academia and industry designing efficient, scalable and robust protocols for future wireless networks.
Publisher: Cambridge University Press
ISBN: 1108417337
Category : Computers
Languages : en
Pages : 509
Book Description
A unified treatment of the latest game theoretic approaches for designing, modeling, and optimizing emerging wireless communication networks. Covering theory, analytical tools, and applications, it is ideal for researchers and graduate students in academia and industry designing efficient, scalable and robust protocols for future wireless networks.
Distributed Strategic Learning for Wireless Engineers
Author: Hamidou Tembine
Publisher: CRC Press
ISBN: 1439876371
Category : Mathematics
Languages : en
Pages : 498
Book Description
Although valued for its ability to allow teams to collaborate and foster coalitional behaviors among the participants, game theory’s application to networking systems is not without challenges. Distributed Strategic Learning for Wireless Engineers illuminates the promise of learning in dynamic games as a tool for analyzing network evolution and underlines the potential pitfalls and difficulties likely to be encountered. Establishing the link between several theories, this book demonstrates what is needed to learn strategic interaction in wireless networks under uncertainty, randomness, and time delays. It addresses questions such as: How much information is enough for effective distributed decision making? Is having more information always useful in terms of system performance? What are the individual learning performance bounds under outdated and imperfect measurement? What are the possible dynamics and outcomes if the players adopt different learning patterns? If convergence occurs, what is the convergence time of heterogeneous learning? What are the issues of hybrid learning? How can one develop fast and efficient learning schemes in scenarios where some players have more information than the others? What is the impact of risk-sensitivity in strategic learning systems? How can one construct learning schemes in a dynamic environment in which one of the players do not observe a numerical value of its own-payoffs but only a signal of it? How can one learn "unstable" equilibria and global optima in a fully distributed manner? The book provides an explicit description of how players attempt to learn over time about the game and about the behavior of others. It focuses on finite and infinite systems, where the interplay among the individual adjustments undertaken by the different players generates different learning dynamics, heterogeneous learning, risk-sensitive learning, and hybrid dynamics.
Publisher: CRC Press
ISBN: 1439876371
Category : Mathematics
Languages : en
Pages : 498
Book Description
Although valued for its ability to allow teams to collaborate and foster coalitional behaviors among the participants, game theory’s application to networking systems is not without challenges. Distributed Strategic Learning for Wireless Engineers illuminates the promise of learning in dynamic games as a tool for analyzing network evolution and underlines the potential pitfalls and difficulties likely to be encountered. Establishing the link between several theories, this book demonstrates what is needed to learn strategic interaction in wireless networks under uncertainty, randomness, and time delays. It addresses questions such as: How much information is enough for effective distributed decision making? Is having more information always useful in terms of system performance? What are the individual learning performance bounds under outdated and imperfect measurement? What are the possible dynamics and outcomes if the players adopt different learning patterns? If convergence occurs, what is the convergence time of heterogeneous learning? What are the issues of hybrid learning? How can one develop fast and efficient learning schemes in scenarios where some players have more information than the others? What is the impact of risk-sensitivity in strategic learning systems? How can one construct learning schemes in a dynamic environment in which one of the players do not observe a numerical value of its own-payoffs but only a signal of it? How can one learn "unstable" equilibria and global optima in a fully distributed manner? The book provides an explicit description of how players attempt to learn over time about the game and about the behavior of others. It focuses on finite and infinite systems, where the interplay among the individual adjustments undertaken by the different players generates different learning dynamics, heterogeneous learning, risk-sensitive learning, and hybrid dynamics.
Intelligent Robotics and Applications
Author: Haibin Yu
Publisher: Springer
ISBN: 3030275388
Category : Computers
Languages : en
Pages : 741
Book Description
The volume set LNAI 11740 until LNAI 11745 constitutes the proceedings of the 12th International Conference on Intelligent Robotics and Applications, ICIRA 2019, held in Shenyang, China, in August 2019. The total of 378 full and 25 short papers presented in these proceedings was carefully reviewed and selected from 522 submissions. The papers are organized in topical sections as follows: Part I: collective and social robots; human biomechanics and human-centered robotics; robotics for cell manipulation and characterization; field robots; compliant mechanisms; robotic grasping and manipulation with incomplete information and strong disturbance; human-centered robotics; development of high-performance joint drive for robots; modular robots and other mechatronic systems; compliant manipulation learning and control for lightweight robot. Part II: power-assisted system and control; bio-inspired wall climbing robot; underwater acoustic and optical signal processing for environmental cognition; piezoelectric actuators and micro-nano manipulations; robot vision and scene understanding; visual and motional learning in robotics; signal processing and underwater bionic robots; soft locomotion robot; teleoperation robot; autonomous control of unmanned aircraft systems. Part III: marine bio-inspired robotics and soft robotics: materials, mechanisms, modelling, and control; robot intelligence technologies and system integration; continuum mechanisms and robots; unmanned underwater vehicles; intelligent robots for environment detection or fine manipulation; parallel robotics; human-robot collaboration; swarm intelligence and multi-robot cooperation; adaptive and learning control system; wearable and assistive devices and robots for healthcare; nonlinear systems and control. Part IV: swarm intelligence unmanned system; computational intelligence inspired robot navigation and SLAM; fuzzy modelling for automation, control, and robotics; development of ultra-thin-film, flexible sensors, and tactile sensation; robotic technology for deep space exploration; wearable sensing based limb motor function rehabilitation; pattern recognition and machine learning; navigation/localization. Part V: robot legged locomotion; advanced measurement and machine vision system; man-machine interactions; fault detection, testing and diagnosis; estimation and identification; mobile robots and intelligent autonomous systems; robotic vision, recognition and reconstruction; robot mechanism and design. Part VI: robot motion analysis and planning; robot design, development and control; medical robot; robot intelligence, learning and linguistics; motion control; computer integrated manufacturing; robot cooperation; virtual and augmented reality; education in mechatronics engineering; robotic drilling and sampling technology; automotive systems; mechatronics in energy systems; human-robot interaction.
Publisher: Springer
ISBN: 3030275388
Category : Computers
Languages : en
Pages : 741
Book Description
The volume set LNAI 11740 until LNAI 11745 constitutes the proceedings of the 12th International Conference on Intelligent Robotics and Applications, ICIRA 2019, held in Shenyang, China, in August 2019. The total of 378 full and 25 short papers presented in these proceedings was carefully reviewed and selected from 522 submissions. The papers are organized in topical sections as follows: Part I: collective and social robots; human biomechanics and human-centered robotics; robotics for cell manipulation and characterization; field robots; compliant mechanisms; robotic grasping and manipulation with incomplete information and strong disturbance; human-centered robotics; development of high-performance joint drive for robots; modular robots and other mechatronic systems; compliant manipulation learning and control for lightweight robot. Part II: power-assisted system and control; bio-inspired wall climbing robot; underwater acoustic and optical signal processing for environmental cognition; piezoelectric actuators and micro-nano manipulations; robot vision and scene understanding; visual and motional learning in robotics; signal processing and underwater bionic robots; soft locomotion robot; teleoperation robot; autonomous control of unmanned aircraft systems. Part III: marine bio-inspired robotics and soft robotics: materials, mechanisms, modelling, and control; robot intelligence technologies and system integration; continuum mechanisms and robots; unmanned underwater vehicles; intelligent robots for environment detection or fine manipulation; parallel robotics; human-robot collaboration; swarm intelligence and multi-robot cooperation; adaptive and learning control system; wearable and assistive devices and robots for healthcare; nonlinear systems and control. Part IV: swarm intelligence unmanned system; computational intelligence inspired robot navigation and SLAM; fuzzy modelling for automation, control, and robotics; development of ultra-thin-film, flexible sensors, and tactile sensation; robotic technology for deep space exploration; wearable sensing based limb motor function rehabilitation; pattern recognition and machine learning; navigation/localization. Part V: robot legged locomotion; advanced measurement and machine vision system; man-machine interactions; fault detection, testing and diagnosis; estimation and identification; mobile robots and intelligent autonomous systems; robotic vision, recognition and reconstruction; robot mechanism and design. Part VI: robot motion analysis and planning; robot design, development and control; medical robot; robot intelligence, learning and linguistics; motion control; computer integrated manufacturing; robot cooperation; virtual and augmented reality; education in mechatronics engineering; robotic drilling and sampling technology; automotive systems; mechatronics in energy systems; human-robot interaction.
Mechanisms and Games for Dynamic Spectrum Allocation
Author: Tansu Alpcan
Publisher: Cambridge University Press
ISBN: 1107034124
Category : Computers
Languages : en
Pages : 604
Book Description
An innovative and comprehensive book presenting state-of-the-art research into wireless spectrum allocation based on game theory and mechanism design.
Publisher: Cambridge University Press
ISBN: 1107034124
Category : Computers
Languages : en
Pages : 604
Book Description
An innovative and comprehensive book presenting state-of-the-art research into wireless spectrum allocation based on game theory and mechanism design.
Game Theory and Learning for Wireless Networks
Author: Samson Lasaulce
Publisher: Academic Press
ISBN: 0123846994
Category : Technology & Engineering
Languages : en
Pages : 346
Book Description
Written by leading experts in the field, Game Theory and Learning for Wireless Networks Covers how theory can be used to solve prevalent problems in wireless networks such as power control, resource allocation or medium access control. With the emphasis now on promoting 'green' solutions in the wireless field where power consumption is minimized, there is an added focus on developing network solutions that maximizes the use of the spectrum available. With the growth of distributed wireless networks such as Wi-Fi and the Internet; the push to develop ad hoc and cognitive networks has led to a considerable interest in applying game theory to wireless communication systems. Game Theory and Learning for Wireless Networks is the first comprehensive resource of its kind, and is ideal for wireless communications R&D engineers and graduate students. Samson Lasaulce is a senior CNRS researcher at the Laboratory of Signals and Systems (LSS) at Supélec, Gif-sur-Yvette, France. He is also a part-time professor in the Department of Physics at École Polytechnique, Palaiseau, France. Hamidou Tembine is a professor in the Department of Telecommunications at Supélec, Gif-sur-Yvette, France. Merouane Debbah is a professor at Supélec, Gif-sur-Yvette, France. He is the holder of the Alcatel-Lucent chair in flexible radio since 2007. - The first tutorial style book that gives all the relevant theory, at the right level of rigour, for the wireless communications engineer - Bridges the gap between theory and practice by giving examples and case studies showing how game theory can solve real world resource allocation problems - Contains algorithms and techniques to implement game theory in wireless terminals
Publisher: Academic Press
ISBN: 0123846994
Category : Technology & Engineering
Languages : en
Pages : 346
Book Description
Written by leading experts in the field, Game Theory and Learning for Wireless Networks Covers how theory can be used to solve prevalent problems in wireless networks such as power control, resource allocation or medium access control. With the emphasis now on promoting 'green' solutions in the wireless field where power consumption is minimized, there is an added focus on developing network solutions that maximizes the use of the spectrum available. With the growth of distributed wireless networks such as Wi-Fi and the Internet; the push to develop ad hoc and cognitive networks has led to a considerable interest in applying game theory to wireless communication systems. Game Theory and Learning for Wireless Networks is the first comprehensive resource of its kind, and is ideal for wireless communications R&D engineers and graduate students. Samson Lasaulce is a senior CNRS researcher at the Laboratory of Signals and Systems (LSS) at Supélec, Gif-sur-Yvette, France. He is also a part-time professor in the Department of Physics at École Polytechnique, Palaiseau, France. Hamidou Tembine is a professor in the Department of Telecommunications at Supélec, Gif-sur-Yvette, France. Merouane Debbah is a professor at Supélec, Gif-sur-Yvette, France. He is the holder of the Alcatel-Lucent chair in flexible radio since 2007. - The first tutorial style book that gives all the relevant theory, at the right level of rigour, for the wireless communications engineer - Bridges the gap between theory and practice by giving examples and case studies showing how game theory can solve real world resource allocation problems - Contains algorithms and techniques to implement game theory in wireless terminals