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Pepa Roldán
Performance Evaluation Process Algebra (PEPA) is a stochastic process algebra designed for modelling computer and communication systems introduced by Jane Hillston in the 1990s. The language extends classical process algebras such as Milner's CCS and Hoare's CSP by introducing probabilistic branching and timing of transitions. Rates are drawn from the exponential distribution and PEPA models are finite-state and so give rise to a stochastic process, specifically a continuous-time Markov process (CTMC). Thus the language can be used to study quantitative properties of models of computer and communication systems such as throughput, utilisation and response time as well as qualitative properties such as freedom from deadlock. The language is formally defined using a structured operational semantics in the style invented by Gordon Plotkin. As with most process algebras, PEPA is a parsimonious language. It has only four combinators, ''prefix'', ''choice'', ''co-operatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic
Stochastic (, ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselves, these two terms are often used synonymously. Furthermore, in probability theory, the formal concept of a ''stochastic process'' is also referred to as a ''random process''. Stochasticity is used in many different fields, including the natural sciences such as biology, chemistry, ecology, neuroscience, and physics, as well as technology and engineering fields such as image processing, signal processing, information theory, computer science, cryptography, and telecommunications. It is also used in finance, due to seemingly random changes in financial markets as well as in medicine, linguistics, music, media, colour theory, botany, manufacturing, and geomorphology. Etymology The word ''stochastic'' in English was originally used as a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Response Time (technology)
In technology, response time is the time a system or functional unit takes to react to a given input. Computing Response time is the total amount of time it takes to respond to a request for service. That service can be anything from a memory fetch, to a disk IO, to a complex database query, or loading a full web page. Ignoring transmission time for a moment, the response time is the sum of the service time and wait time. The service time is the time it takes to do the work you requested. For a given request the service time varies little as the workload increases – to do X amount of work it always takes X amount of time. The wait time is how long the request had to wait in a queue before being serviced and it varies from zero, when no waiting is required, to a large multiple of the service time, as many requests are already in the queue and have to be serviced first. With basic queueing theory math you can calculate how the average wait time increases as the device providing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eclipse (software)
Eclipse is an integrated development environment (IDE) used in computer programming. It contains a base workspace and an extensible plug-in (computing), plug-in system for customizing the environment. It is the second-most-popular IDE for Java (programming language), Java development, and, until 2016, was the most popular. Eclipse is written mostly in Java and its primary use is for developing Java applications, but it may also be used to develop applications in other programming languages via plug-ins, including Ada (programming language), Ada, ABAP, C (programming language), C, C++, C Sharp (programming language), C#, Clojure, COBOL, D (programming language), D, Erlang (programming language), Erlang, Fortran, Groovy (programming language), Groovy, Haskell (programming language), Haskell, JavaScript, Julia (programming language), Julia, Lasso (programming language), Lasso, Lua (programming language), Lua, Software AG, NATURAL, Perl, PHP, Prolog, Python (programming language), Py ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Product Form Stationary Distribution
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 que ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reversed Compound Agent Theorem
In probability theory, the reversed compound agent theorem (RCAT) is a set of sufficient conditions for a stochastic process In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used as mathematical models of systems and phenomena that appea ... expressed in any formalism to have a product form stationary distribution (assuming that the process is stationary). The theorem shows that product form solutions in Jackson's theorem, the BCMP theorem and G-networks are based on the same fundamental mechanisms. The theorem identifies a reversed process using Kelly's lemma, from which the stationary distribution can be computed. Notes References * ::A short introduction to RCAT. Probability theorems {{Probability-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gordon Plotkin
Gordon David Plotkin, (born 9 September 1946) is a theoretical computer scientist in the School of Informatics at the University of Edinburgh. Plotkin is probably best known for his introduction of structural operational semantics (SOS) and his work on denotational semantics. In particular, his notes on ''A Structural Approach to Operational Semantics'' were very influential. He has contributed to many other areas of computer science. Education Plotkin was educated at the University of Glasgow and the University of Edinburgh, gaining his Bachelor of Science degree in 1967 and PhD in 1972 supervised by Rod Burstall. Career and research Plotkin has remained at Edinburgh, and was, with Burstall and Robin Milner, a co-founder of the Laboratory for Foundations of Computer Science (LFCS). His former doctoral students include Luca Cardelli, Philippa Gardner, Doug Gurr, Eugenio Moggi, and Lǐ Wèi. Awards and honours Plotkin was elected a Fellow of the Royal Society (FRS) in 19 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operational Semantics
Operational semantics is a category of formal programming language semantics in which certain desired properties of a program, such as correctness, safety or security, are verified by constructing proofs from logical statements about its execution and procedures, rather than by attaching mathematical meanings to its terms (denotational semantics). Operational semantics are classified in two categories: structural operational semantics (or small-step semantics) formally describe how the ''individual steps'' of a computation take place in a computer-based system; by opposition natural semantics (or big-step semantics) describe how the ''overall results'' of the executions are obtained. Other approaches to providing a formal semantics of programming languages include axiomatic semantics and denotational semantics. The operational semantics for a programming language describes how a valid program is interpreted as sequences of computational steps. These sequences then ''are'' the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deadlock
In concurrent computing, deadlock is any situation in which no member of some group of entities can proceed because each waits for another member, including itself, to take action, such as sending a message or, more commonly, releasing a lock. Deadlocks are a common problem in multiprocessing systems, parallel computing, and distributed systems, because in these contexts systems often use software or hardware locks to arbitrate shared resources and implement process synchronization. In an operating system, a deadlock occurs when a process or thread enters a waiting state because a requested system resource is held by another waiting process, which in turn is waiting for another resource held by another waiting process. If a process remains indefinitely unable to change its state because resources requested by it are being used by another process that itself is waiting, then the system is said to be in a deadlock. In a communications system, deadlocks occur mainly due t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Throughput
Network throughput (or just throughput, when in context) refers to the rate of message delivery over a communication channel, such as Ethernet or packet radio, in a communication network. The data that these messages contain may be delivered over physical or logical links, or through network nodes. Throughput is usually measured in bits per second (bit/s or bps), and sometimes in data packets per second (p/s or pps) or data packets per time slot. The system throughput or aggregate throughput is the sum of the data rates that are delivered to all terminals in a network. Throughput is essentially synonymous to digital bandwidth consumption; it can be determined numerically by applying the queueing theory, where the load in packets per time unit is denoted as the arrival rate (), and the drop in packets per unit time is denoted as the departure rate (). The throughput of a communication system may be affected by various factors, including the limitations of the underlying analog ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Process Algebra
In computer science, the process calculi (or process algebras) are a diverse family of related approaches for formally modelling concurrent systems. Process calculi provide a tool for the high-level description of interactions, communications, and synchronizations between a collection of independent agents or processes. They also provide algebraic laws that allow process descriptions to be manipulated and analyzed, and permit formal reasoning about equivalences between processes (e.g., using bisimulation). Leading examples of process calculi include CSP, CCS, ACP, and LOTOS. More recent additions to the family include the π-calculus, the ambient calculus, PEPA, the fusion calculus and the join-calculus. Essential features While the variety of existing process calculi is very large (including variants that incorporate stochastic behaviour, timing information, and specializations for studying molecular interactions), there are several features that all process calculi h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuous-time Markov Process
A continuous-time Markov chain (CTMC) is a continuous stochastic process in which, for each state, the process will change state according to an exponential random variable and then move to a different state as specified by the probabilities of a stochastic matrix. An equivalent formulation describes the process as changing state according to the least value of a set of exponential random variables, one for each possible state it can move to, with the parameters determined by the current state. An example of a CTMC with three states \ is as follows: the process makes a transition after the amount of time specified by the holding time—an exponential random variable E_i, where ''i'' is its current state. Each random variable is independent and such that E_0\sim \text(6), E_1\sim \text(12) and E_2\sim \text(18). When a transition is to be made, the process moves according to the jump chain, a discrete-time Markov chain with stochastic matrix: :\begin 0 & \frac & \frac \\ \frac & ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
