Ross's Conjecture

	Ross's Conjecture In queueing theory, a discipline within the mathematical theory of probability, Ross's conjecture gives a lower bound for the average waiting-time experienced by a customer when arrivals to the queue do not follow the simplest model for random arrivals. It was proposed by Sheldon M. Ross in 1978 and proved in 1981 by Tomasz Rolski. Equality can be obtained in the bound; and the bound does not hold for finite buffer queues. Bound Ross's conjecture is a bound for the mean delay in a queue where arrivals are governed by a doubly stochastic Poisson process. or by a non-stationary Poisson process 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 ...... The conjecture states that the average amount of time that a customer spends waiting in a queue is greater than or equal to ::\frac where ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	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]
	Sheldon M Sheldon may refer to: * Sheldon (name), a given name and a surname, and a list of people with the name Places Australia Sheldon, Queensland Sheldon Forest, New South Wales United Kingdom Sheldon, Derbyshire, England Sheldon, Devon, England Sheldon, West Midlands, England Sheldon Stone Circle, Aberdeenshire, Scotland Sheldon Manor, Chippenham, Wiltshire United States Sheldon, Illinois * Sheldon, Iowa * Sheldon, Minnesota * Sheldon, Missouri * Sheldon, New York * Sheldon, North Dakota * Sheldon, South Carolina * Sheldon, Texas * Sheldon, Vermont * Sheldon, Monroe County, Wisconsin * Sheldon, Rusk County, Wisconsin Other uses * Sheldon coin grading scale * Sheldon School, Chippenham, Wiltshire, England * Sheldon High School, several schools * The Sheldon, concert hall and art galleries in St. Louis, Missouri * ''Sheldon'' (webcomic), created by Dave Kellett * ''Young Sheldon'', created by Chuck Lorre and Steven Molaro * Sheldon, a character from the video game ''Splato ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Doubly Stochastic Poisson Process In probability theory, a Cox process, also known as a doubly stochastic Poisson process is a point process which is a generalization of a Poisson process where the intensity that varies across the underlying mathematical space (often space or time) is itself a stochastic process. The process is named after the statistician David Cox, who first published the model in 1955. Cox processes are used to generate simulations of spike trains (the sequence of action potentials generated by a neuron), and also in financial mathematics where they produce a "useful framework for modeling prices of financial instruments in which credit risk is a significant factor." Definition Let \xi be a random measure. A random measure \eta is called a Cox process directed by \xi , if \mathcal L(\eta \mid \xi=\mu) is a Poisson process with intensity measure \mu . Here, \mathcal L(\eta \mid \xi=\mu) is the conditional distribution of \eta , given \ . Laplace transform If \eta is a Cox p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Poisson Process 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]
picture info	Probabilistic Inequalities Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th Ed, (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', (Vol 1), 3rd Ed, (1968), Wiley, . The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%). These conc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]