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Time-utility Function
A Time/Utility Function (''TUF''), née ''Time/Value Function'', specifies the application-specific ''utility'' that an ''action'' (e.g., computational task, mechanical movement) yields depending on its completion time. TUFs and their utility interpretations (semantics), scales, and values are derived from application domain-specific subject matter knowledge. An example (but not the only) interpretation of utility is an action's relative ''importance,'' which otherwise is independent of its ''timeliness''. The traditional deadline represented as a TUF is a special case—a downward step of utility from 1 to 0 at the deadline time—e.g., timeliness without importance. A TUF is more general—it has a ''critical time,'' with application-specific shapes and utility values on each side, after which it does not increase. The various researcher and practitioner definitions of ''firm'' and ''soft'' real-time can also be represented as special cases of the TUF model. The optimality criteri ...
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Scheduling
A schedule (, ) or a timetable, as a basic time-management tool, consists of a list of times at which possible tasks, events, or actions are intended to take place, or of a sequence of events in the chronological order in which such things are intended to take place. The process of creating a schedule — deciding how to order these tasks and how to commit resources between the variety of possible tasks — is called scheduling,Ofer Zwikael, John Smyrk, ''Project Management for the Creation of Organisational Value'' (2011), p. 196: "The process is called scheduling, the output from which is a timetable of some form". and a person responsible for making a particular schedule may be called a scheduler. Making and following schedules is an ancient human activity. Some scenarios associate this kind of planning with learning life skills. Schedules are necessary, or at least useful, in situations where individuals need to know what time they must be at a specific location to rece ...
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Concave Function
In mathematics, a concave function is one for which the function value at any convex combination of elements in the domain is greater than or equal to that convex combination of those domain elements. Equivalently, a concave function is any function for which the hypograph is convex. The class of concave functions is in a sense the opposite of the class of convex functions. A concave function is also synonymously called concave downwards, concave down, convex upwards, convex cap, or upper convex. Definition A real-valued function f on an interval (or, more generally, a convex set in vector space) is said to be ''concave'' if, for any x and y in the interval and for any \alpha \in ,1/math>, :f((1-\alpha )x+\alpha y)\geq (1-\alpha ) f(x)+\alpha f(y) A function is called ''strictly concave'' if :f((1-\alpha )x+\alpha y) > (1-\alpha ) f(x)+\alpha f(y) for any \alpha \in (0,1) and x \neq y. For a function f: \mathbb \to \mathbb, this second definition merely states that for ev ...
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Constant Function
In mathematics, a constant function is a function whose (output) value is the same for every input value. Basic properties As a real-valued function of a real-valued argument, a constant function has the general form or just For example, the function is the specific constant function where the output value is . The domain of this function is the set of all real numbers. The image of this function is the singleton set . The independent variable does not appear on the right side of the function expression and so its value is "vacuously substituted"; namely , , , and so on. No matter what value of is input, the output is . The graph of the constant function is a ''horizontal line'' in the plane that passes through the point . In the context of a polynomial in one variable , the constant function is called ''non-zero constant function'' because it is a polynomial of degree 0, and its general form is , where is nonzero. This function has no intersection point with the a ...
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Tardiness
Tardiness is the habit of being late or delaying arrival. Being late as a form of misconduct may be formally punishable in various arrangements, such as workplace, school, etc. An opposite personality trait is punctuality. Workplace tardiness United States Workplace tardiness is one attendance issue, along with the absence from work and failure to properly notify about absence or being late. To be at work on time is an implied obligation unless stated otherwise. It is a legal reason for discharge in cases when it is a demonstrable disregard of duty: repeated tardiness without compelling reasons, tardiness associated with other misconduct, and single inexcusable tardiness resulted in grave loss of employer's interests. If tardiness is minor or without interference with employer's operations, it is not to be legally considered as misconduct. Characteristics of tardy people Diana DeLonzor in her book ''Never Be Late Again: 7 Cures for the Punctually Challenged'' classified h ...
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Imprecise Probability
Imprecise probability generalizes probability theory to allow for partial probability specifications, and is applicable when information is scarce, vague, or conflicting, in which case a unique probability distribution may be hard to identify. Thereby, the theory aims to represent the available knowledge more accurately. Imprecision is useful for dealing with expert elicitation, because: * People have a limited ability to determine their own subjective probabilities and might find that they can only provide an interval. * As an interval is compatible with a range of opinions, the analysis ought to be more convincing to a range of different people. Introduction Uncertainty is traditionally modelled by a probability theory, probability distribution, as developed by Andrey Kolmogorov, Kolmogorov, Pierre-Simon Laplace, Laplace, Bruno de Finetti, de Finetti, Frank P. Ramsey, Ramsey, Richard Threlkeld Cox, Cox, Dennis Lindley, Lindley, and many others. However, this has not been unani ...
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Real-time Computing
Real-time computing (RTC) is the computer science term for Computer hardware, hardware and software systems subject to a "real-time constraint", for example from Event (synchronization primitive), event to Event (computing), system response. Real-time programs must guarantee response within specified time constraints, often referred to as "deadlines".Mordechai Ben-Ari, Ben-Ari, Mordechai; "Principles of Concurrent and Distributed Programming", ch. 16, Prentice Hall, 1990, , p. 164 The term "real-time" is also used in Computer simulation, simulation to mean that the simulation's clock runs at the same speed as a real clock. Real-time responses are often understood to be in the order of milliseconds, and sometimes microseconds. A system not specified as operating in real time cannot usually ''guarantee'' a response within any timeframe, although ''typical'' or ''expected'' response times may be given. Real-time processing ''fails'' if not completed within a specified deadline rela ...
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Utility Accrual Scheduling
In economics, utility is a measure of a certain person's satisfaction from a certain state of the world. Over time, the term has been used with at least two meanings. * In a normative context, utility refers to a goal or objective that we wish to maximize, i.e., an objective function. This kind of utility bears a closer resemblance to the original utilitarian concept, developed by moral philosophers such as Jeremy Bentham and John Stuart Mill. * In a descriptive context, the term refers to an ''apparent'' objective function; such a function is revealed by a person's behavior, and specifically by their preferences over lotteries, which can be any quantified choice. The relationship between these two kinds of utility functions has been a source of controversy among both economists and ethicists, with most maintaining that the two are distinct but generally related. Utility function Consider a set of alternatives among which a person has a preference ordering. A utility functi ...
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Real-time Computing
Real-time computing (RTC) is the computer science term for Computer hardware, hardware and software systems subject to a "real-time constraint", for example from Event (synchronization primitive), event to Event (computing), system response. Real-time programs must guarantee response within specified time constraints, often referred to as "deadlines".Mordechai Ben-Ari, Ben-Ari, Mordechai; "Principles of Concurrent and Distributed Programming", ch. 16, Prentice Hall, 1990, , p. 164 The term "real-time" is also used in Computer simulation, simulation to mean that the simulation's clock runs at the same speed as a real clock. Real-time responses are often understood to be in the order of milliseconds, and sometimes microseconds. A system not specified as operating in real time cannot usually ''guarantee'' a response within any timeframe, although ''typical'' or ''expected'' response times may be given. Real-time processing ''fails'' if not completed within a specified deadline rela ...
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Optimal Scheduling
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. Optimization problems Optimization problems can be divided into two categories, depending on whether the variables ...
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Quality Of Service
Quality of service (QoS) is the description or measurement of the overall performance of a service, such as a telephony or computer network, or a cloud computing service, particularly the performance seen by the users of the network. To quantitatively measure quality of service, several related aspects of the network service are often considered, such as packet loss, bit rate, throughput, transmission delay, availability, jitter, etc. In the field of computer networking and other packet-switched telecommunication networks, quality of service refers to traffic prioritization and resource reservation control mechanisms rather than the achieved service quality. Quality of service is the ability to provide different priorities to different applications, users, or data Traffic flow (computer networking), flows, or to guarantee a certain level of performance to a data flow. Quality of service is particularly important for the transport of traffic with special requirements. In particula ...
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