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G-networks
In queueing theory, a discipline within the mathematical theory of probability, a G-network (generalized queueing network, often called a Gelenbe network) is an open network of G-queues first introduced by Erol Gelenbe as a model for queueing systems with specific control functions, such as traffic re-routing or traffic destruction, as well as a model for neural networks. A G-queue is a network of queues with several types of novel and useful customers: *''positive'' customers, which arrive from other queues or arrive externally as Poisson arrivals, and obey standard service and routing disciplines as in conventional network models, *''negative'' customers, which arrive from another queue, or which arrive externally as Poisson arrivals, and remove (or 'kill') customers in a non-empty queue, representing the need to remove traffic when the network is congested, including the removal of "batches" of customers *"triggers", which arrive from other queues or from outside the network, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erol Gelenbe
Sami Erol Gelenbe (born 22 August 1945, in Istanbul, Turkey) is a Turkish and French computer scientist, electronic engineer and applied mathematician who pioneered the field of Computer System and Network Performance in Europe, and is active in many research projects of the European Union. He is Professor in the Institute of Theoretical and Applied Informatics of the Polish Academy of Sciences (2017-), Associate Researcher in the I3S Laboratory (CNRS, University of Côte d'Azur, Nice) and Abraham de Moivre Laboratory (CNRS, Imperial College). He has held Chaired professorships at University of Liège (1974-1979), University Paris-Saclay (1979-1986), University Paris Descartes (1986-2005), Nello L. Teer Professor and ECE Chair at Duke University (1993-1998), University Chair Professor and Director of the School of EECS, University of Central Florida (1998-2003), and Dennis Gabor Professor and Head of Intelligent Systems and Network, Imperial College (2003-2019). He invented the r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Queueing Theory
Queueing theory is the mathematical study of waiting lines, or queues. A queueing model is constructed so that queue lengths and waiting time can be predicted. Queueing theory is generally considered a branch of operations research because the results are often used when making business decisions about the resources needed to provide a service. Queueing theory has its origins in research by Agner Krarup Erlang when he created models to describe the system of Copenhagen Telephone Exchange company, a Danish company. The ideas have since seen applications including telecommunication, traffic engineering, computing and, particularly in industrial engineering, in the design of factories, shops, offices and hospitals, as well as in project management. Spelling The spelling "queueing" over "queuing" is typically encountered in the academic research field. In fact, one of the flagship journals of the field is ''Queueing Systems''. Single queueing nodes A queue, or queueing node ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Product-form Solution
In probability theory, a product-form solution is a particularly efficient form of solution for determining some metric of a system with distinct sub-components, where the metric for the collection of components can be written as a product of the metric across the different components. Using capital Pi notation a product-form solution has algebraic form :\text(x_1,x_2,x_3,\ldots,x_n) = B \prod_^n \text(x_i) where ''B'' is some constant. Solutions of this form are of interest as they are computationally inexpensive to evaluate for large values of ''n''. Such solutions in queueing networks are important for finding performance metrics in models of multiprogrammed and time-shared computer systems. Equilibrium distributions The first product-form solutions were found for equilibrium distributions of Markov chains. Trivially, models composed of two or more independent sub-components exhibit a product-form solution by the definition of independence. Initially the term was used in queu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
First Come First Served
Queueing theory is the mathematical study of waiting lines, or queues. A queueing model is constructed so that queue lengths and waiting time can be predicted. Queueing theory is generally considered a branch of operations research because the results are often used when making business decisions about the resources needed to provide a service. Queueing theory has its origins in research by Agner Krarup Erlang when he created models to describe the system of Copenhagen Telephone Exchange company, a Danish company. The ideas have since seen applications including telecommunication, traffic engineering, computing and, particularly in industrial engineering, in the design of factories, shops, offices and hospitals, as well as in project management. Spelling The spelling "queueing" over "queuing" is typically encountered in the academic research field. In fact, one of the flagship journals of the field is ''Queueing Systems''. Single queueing nodes A queue, or queueing node ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of non-deterministic or uncertain processes or measured quantities that may either be single occurrences or evolve over time in a random fashion). Although it is not possible to perfectly predict random events, much can be said about their behavior. Two major results in probability ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neural Networks
A neural network is a network or circuit of biological neurons, or, in a modern sense, an artificial neural network, composed of artificial neurons or nodes. Thus, a neural network is either a biological neural network, made up of biological neurons, or an artificial neural network, used for solving artificial intelligence (AI) problems. The connections of the biological neuron are modeled in artificial neural networks as weights between nodes. A positive weight reflects an excitatory connection, while negative values mean inhibitory connections. All inputs are modified by a weight and summed. This activity is referred to as a linear combination. Finally, an activation function controls the amplitude of the output. For example, an acceptable range of output is usually between 0 and 1, or it could be −1 and 1. These artificial networks may be used for predictive modeling, adaptive control and applications where they can be trained via a dataset. Self-learning resulting from e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neural Computation
Neural computation is the information processing performed by networks of neurons. Neural computation is affiliated with the philosophical tradition known as Computational theory of mind, also referred to as computationalism, which advances the thesis that neural computation explains cognition. The first persons to propose an account of neural activity as being computational was Warren McCullock and Walter Pitts in their seminal 1943 paper, A Logical Calculus of the Ideas Immanent in Nervous Activity. There are three general branches of computationalism, including classicism, connectionism, and computational neuroscience. All three branches agree that cognition is computation, however, they disagree on what sorts of computations constitute cognition. The classicism tradition believes that computation in the brain is digital, analogous to digital computing. Both connectionism and computational neuroscience do not require that the computations that realize cognition are necessarily d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Computer Journal
''The Computer Journal'' is a peer-reviewed scientific journal covering computer science and information systems. Established in 1958, it is one of the oldest computer science research journals. It is published by Oxford University Press on behalf of BCS, The Chartered Institute for IT. The authors of the best paper in each annual volume receive the Wilkes Award from BCS, The Chartered Institute for IT. Editors-in-chief The following people have been editor-in-chief: * 1958–1969 Eric N. Mutch * 1969–1992 Peter Hammersley * 1993–2000 C. J. van Rijsbergen * 2000–2008 Fionn Murtagh * 2008–2012 Erol Gelenbe Sami Erol Gelenbe (born 22 August 1945, in Istanbul, Turkey) is a Turkish and French computer scientist, electronic engineer and applied mathematician who pioneered the field of Computer System and Network Performance in Europe, and is active ... * 2012–2016 Fionn Murtagh * 2016–2020 Steve Furber * 2021–present Tom Crick References External links Offici ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jackson's Theorem (queueing Theory)
In queueing theory, a discipline within the mathematical theory of probability, a Jackson network (sometimes Jacksonian network) is a class of queueing network where the equilibrium distribution is particularly simple to compute as the network has a product-form solution. It was the first significant development in the theory of networks of queues, and generalising and applying the ideas of the theorem to search for similar product-form solutions in other networks has been the subject of much research, including ideas used in the development of the Internet. The networks were first identified by James R. Jackson A version from January 1963 is available at http://www.dtic.mil/dtic/tr/fulltext/u2/296776.pdf and his paper was re-printed in the journal ''Management Science’s'' ‘Ten Most Influential Titles of Management Sciences First Fifty Years.’ Jackson was inspired by the work of Burke and Reich, though Jean Walrand notes "product-form results … rea much less immediate res ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poisson Processes
In probability, statistics and related fields, a Poisson point process is a type of random mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one another. The Poisson point process is often called simply the Poisson process, but it is also called a Poisson random measure, Poisson random point field or Poisson point field. This point process has convenient mathematical properties, which has led to its being frequently defined in Euclidean space and used as a mathematical model for seemingly random processes in numerous disciplines such as astronomy,G. J. Babu and E. D. Feigelson. Spatial point processes in astronomy. ''Journal of statistical planning and inference'', 50(3):311–326, 1996. biology,H. G. Othmer, S. R. Dunbar, and W. Alt. Models of dispersal in biological systems. ''Journal of mathematical biology'', 26(3):263–298, 1988. ecology,H. Thompson. Spatial point processes, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Balance Equation
In probability theory, a balance equation is an equation that describes the probability flux associated with a Markov chain in and out of states or set of states. Global balance The global balance equations (also known as full balance equations) are a set of equations that characterize the equilibrium distribution (or any stationary distribution) of a Markov chain, when such a distribution exists. For a continuous time Markov chain with state space \mathcal, transition rate from state i to j given by q_ and equilibrium distribution given by \pi, the global balance equations are given by ::\pi_i = \sum_ \pi_j q_, or equivalently :: \pi_i \sum_ q_ = \sum_ \pi_j q_. for all i \in S. Here \pi_i q_ represents the probability flux from state i to state j. So the left-hand side represents the total flow from out of state ''i'' into states other than ''i'', while the right-hand side represents the total flow out of all states j \neq i into state i. In general it is computationa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laplace Transform
In mathematics, the Laplace transform, named after its discoverer Pierre-Simon Laplace (), is an integral transform In mathematics, an integral transform maps a function from its original function space into another function space via integration, where some of the properties of the original function might be more easily characterized and manipulated than in ... that converts a Function (mathematics), function of a Real number, real Variable (mathematics), variable (usually t, in the ''time domain'') to a function of a Complex number, complex variable s (in the complex frequency domain, also known as ''s''-domain, or s-plane). The transform has many applications in science and engineering because it is a tool for solving differential equations. In particular, it transforms ordinary differential equations into algebraic equations and convolution into multiplication. For suitable functions ''f'', the Laplace transform is the integral \mathcal\(s) = \int_0^\infty f(t)e^ \, dt. H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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