Order Relations in the Set of Probability Distribution Functions and Their Applications in Queueing Theory PDF Download

Author: Tomasz Rolski
Publisher:
ISBN:
Category : Distribution (Probability theory).
Languages : en
Pages : 58

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Author: Tomasz Rolski
Publisher:
ISBN:
Category :
Languages : en
Pages : 52

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Book Description

Author: Tomasz Rolski
Publisher:
ISBN:
Category : Distribution (Probability theory)
Languages : en
Pages : 52

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Author: Karl Mosler
Publisher: Springer Science & Business Media
ISBN: 3642499724
Category : Mathematics
Languages : en
Pages : 385

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A bibliography on stochastic orderings. Was there a real need for it? In a time of reference databases as the MathSci or the Science Citation Index or the Social Science Citation Index the answer seems to be negative. The reason we think that this bibliog raphy might be of some use stems from the frustration that we, as workers in the field, have often experienced by finding similar results being discovered and proved over and over in different journals of different disciplines with different levels of mathematical so phistication and accuracy and most of the times without cross references. Of course it would be very unfair to blame an economist, say, for not knowing a result in mathematical physics, or vice versa, especially when the problems and the languages are so far apart that it is often difficult to recognize the analogies even after further scrutiny. We hope that collecting the references on this topic, regardless of the area of application, will be of some help, at least to pinpoint the problem. We use the term stochastic ordering in a broad sense to denote any ordering relation on a space of probability measures. Questions that can be related to the idea of stochastic orderings are as old as probability itself. Think for instance of the problem of comparing two gambles in order to decide which one is more favorable.

Author: Gordon Frank Newell
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 170

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Fluid approximations; Simple queueing systems; Stochastic models; Equilibrium distributions; Diffusion approximations; Time-dependent queues; Neglected subjects.

Author: C. Newell
Publisher: Springer Science & Business Media
ISBN: 9400959702
Category : Science
Languages : en
Pages : 314

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Book Description
The literature on queueing theory is already very large. It contains more than a dozen books and about a thousand papers devoted exclusively to the subject; plus many other books on probability theory or operations research in which queueing theory is discussed. Despite this tremendous activity, queueing theory, as a tool for analysis of practical problems, remains in a primitive state; perhaps mostly because the theory has been motivated only superficially by its potential applications. People have devoted great efforts to solving the 'wrong problems. ' Queueing theory originated as a very practical subject. Much ofthe early work was motivated by problems concerning telephone traffic. Erlang, in particular, made many important contributions to the subject in the early part of this century. Telephone traffic remained one of the principle applications until about 1950. After World War II, activity in the fields of operations research and probability theory grew rapidly. Queueing theory became very popular, particularly in the late 1950s, but its popularity did not center so much around its applications as around its mathematical aspects. With the refine ment of some clever mathematical tricks, it became clear that exact solutions could be found for a large number of mathematical problems associated with models of queueing phenomena. The literature grew from 'solutions looking for a problem' rather than from 'problems looking for a solution.

Author: R. Szekli
Publisher: Springer Science & Business Media
ISBN: 1461225280
Category : Mathematics
Languages : en
Pages : 204

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This book is an introductionary course in stochastic ordering and dependence in the field of applied probability for readers with some background in mathematics. It is based on lectures and senlinars I have been giving for students at Mathematical Institute of Wroclaw University, and on a graduate course a.t Industrial Engineering Department of Texas A&M University, College Station, and addressed to a reader willing to use for example Lebesgue measure, conditional expectations with respect to sigma fields, martingales, or compensators as a common language in this field. In Chapter 1 a selection of one dimensional orderings is presented together with applications in the theory of queues, some parts of this selection are based on the recent literature (not older than five years). In Chapter 2 the material is centered around the strong stochastic ordering in many dimen sional spaces and functional spaces. Necessary facts about conditioning, Markov processes an"d point processes are introduced together with some classical results such as the product formula and Poissonian departure theorem for Jackson networks, or monotonicity results for some re newal processes, then results on stochastic ordering of networks, re~~ment policies and single server queues connected with Markov renewal processes are given. Chapter 3 is devoted to dependence and relations between dependence and ordering, exem plified by results on queueing networks and point processes among others.

Author: Moshe Shaked
Publisher: Springer Science & Business Media
ISBN: 0387346759
Category : Mathematics
Languages : en
Pages : 482

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Book Description
This reference text presents comprehensive coverage of the various notions of stochastic orderings, their closure properties, and their applications. Some of these orderings are routinely used in many applications in economics, finance, insurance, management science, operations research, statistics, and various other fields. And the value of the other notions of stochastic orderings needs further exploration. This book is an ideal reference for those interested in decision making under uncertainty and interested in the analysis of complex stochastic systems. It is suitable as a text for advanced graduate course on stochastic ordering and applications.

Author: K Gunavathi
Publisher: S. Chand Publishing
ISBN: 8121923565
Category : Mathematics
Languages : en
Pages : 571

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Common to CSE and IT for all Anna Universities

Author: H. M. Srivastava
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 328

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