Stochastic convexity for multidimensional processes and its applications

Author

Chang, Cheng-Shang ; Chao, Xiuli ; Pinedo, Michael ; Shanthikumar, J. George

Author_Institution

IBM Thomas J. Watson Res. Center, Yorktown Heights, NY, USA

Volume

36

Issue

12

fYear

1991

fDate

12/1/1991 12:00:00 AM

Firstpage

1347

Lastpage

1355

Abstract

A multidimensional stochastic process is considered which is a function of a parametric process. The parametric process may be multidimensional as well. Two such processes are compared that differ only in their parametric processes. Known stochastic convexity results for one-dimensional stochastic processes are extended to multidimensional processes. These results are used to obtain comparison results for various queuing systems that are subject to different parametric processes, which may be the arrival processes, service processes, etc. Based on these comparison results it is shown how the performances of queueing systems can be affected by the variability of parametric processes

Keywords

queueing theory; stochastic processes; arrival processes; multidimensional processes; one-dimensional process; parametric process; queuing systems; service processes; stochastic convexity; stochastic process; Chaos; Engineering management; Industrial engineering; Length measurement; Loss measurement; Multidimensional systems; Random variables; Stochastic processes; Technology management; Time measurement;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.106151

Filename

106151