Temporal stochastic convexity and concavity
TLDR
In this article, the authors define temporal convexity and concavity for continuous time stochastic processes and apply it to reliability theory, queueing theory, branching processes and record values.About:
This article is published in Stochastic Processes and their Applications.The article was published on 1987-01-01 and is currently open access. It has received 37 citations till now. The article focuses on the topics: Concave function & Logarithmically concave function.read more
Citations
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Queueing theory in manufacturing: A survey
Manish K. Govil,Michael C. Fu +1 more
TL;DR: The survey classifies the contributions into two groups: descriptive (performance analysis) and generative (design, planning, and control) and software based on analytical models in queueing theory, as applied to manufacturing.
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Design of manufacturing systems using queueing models
TL;DR: It is shown how the structural properties that are recently derived for single and multiple stage queueing systems can be used effectively in the solution of certain design optimization problems.
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Parametric stochastic convexity and concavity of stochastic processes
TL;DR: In this article, a notion of directional convexity (concavity) is introduced and its stochastic analog is studied, and a sufficient condition on the transition matrix of a discrete time Markov process is found.
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Regularity of Stochastic Processes: A Theory Based on Directional Convexity
TL;DR: In this paper, the authors define a notion of regularity ordering among stochastic processes called directionally convex (dcx) ordering and give examples of doubly-stochastic Poisson and Markov renewal processes where such ordering is prevalent.
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Rearrangement, majorization and stochastic scheduling
Cheng-Shang Chang,David D. Yao +1 more
TL;DR: Stochastic versions of Day's Inequality are developed, over both unrestricted and restricted permutations, which are applied to solve the stochastic version of several classical deterministic scheduling problems.
References
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Book
Inequalities: Theory of Majorization and Its Applications
TL;DR: In this paper, Doubly Stochastic Matrices and Schur-Convex Functions are used to represent matrix functions in the context of matrix factorizations, compounds, direct products and M-matrices.
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Comparison methods for queues and other stochastic models
TL;DR: Comparison properties of random variables and stochastic processes are given and are illustrated by application to various queueing models and questions in experimental design, renewal and reliability theory, PERT networks and branching processes.
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Shock Models and Wear Processes
J. D. Esary,A. W. Marshall +1 more
TL;DR: In this article, the life distribution of a device subject to shocks governed by a Poisson process is considered as a function of the probabilities of not surviving the first $k$ shocks.