STRONG STOCHASTIC CONVEXITY - CLOSURE-PROPERTIES AND APPLICATIONS

被引:40
作者
SHANTHIKUMAR, JG
YAO, DD
机构
[1] COLUMBIA UNIV,DEPT IND ENGN & OPERAT RES,NEW YORK,NY 10027
[2] HARVARD UNIV,DIV APPL SCI,CAMBRIDGE,MA 02138
关键词
GI/G/1; QUEUES; QUEUING NETWORKS; BOUNDS; CONVEX ORDERING; DESIGN AND OPTIMIZATION OF QUEUING SYSTEMS;
D O I
10.2307/3214746
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
A family of random variables {X(theta)} parameterized by the parameter theta satisfies stochastic convexity (SCX) if and only if for any increasing and convex function f(x), Ef[X(theta)] is convex in theta. This definition, however, has a major drawback for the lack of certain important closure properties. In this paper we establish the notion of strong stochastic convexity (SSCX), which implies SCX. We demonstrate that SSCX is a property enjoyed by a wide range of random variables. We also show that SSCX is preserved under random mixture, random summation, and any increasing and convex operations that are applied to a set of independent random variables. These closure properties greatly facilitate the study of parametric convexity of many stochastic systems. Applications to GI/G/1 queues, tandem and cyclic queues, and tree-like networks are discussed. We also demonstrate the application of SSCX in bounding the performance of certain systems.
引用
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页码:131 / 145
页数:15
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