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Annals of Operations Research

, Volume 9, Issue 1, pp 531–543 | Cite as

Majorization and arrangement orderings in open queueing networks

  • D. D. Yao
Real World Issues in Probability Modeling

Abstract

Consider an open Jackson network of queues. Majorization and arrangement orderings are studied to order, respectively, various loading and server-assignment policies. It is shown that under these order relations, stochastic and likelihood ratio orderings can be established for the maximum and the minimum queue lengths and for the total number of jobs in the network. Stochastic majorization and stochastic orderings are also established, respectively, for the queue-length vector and the associated order-statistic vector. Implications of the results on loading and assignment decisions are discussed.

Keywords and phrases

Jackson network majorization arrangement ordering stochastic ordering likelihood ratio ordering 

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Copyright information

© J.C. Baltzer A.G., Scientific Publishing Company 1987

Authors and Affiliations

  • D. D. Yao
    • 1
  1. 1.Department of Industrial Engineering and Operations ResearchColumbia UniversityNew YorkUSA

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