Computational and Mathematical Methods in Medicine
Volume 2012 (2012), Article ID 154038, 11 pages
Review Article

Asymptotic Identity in Min-Plus Algebra: A Report on CPNS

1School of Information Science & Technology, East China Normal University, No. 500 Dong-Chuan Road, Shanghai 200241, China
2Department of Computer and Information Science, University of Macau, Avenue Padre Tomas Pereira, Taipa, Macau

Received 23 March 2011; Accepted 20 April 2011

Academic Editor: Carlo Cattani

Copyright © 2012 Ming Li and Wei Zhao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Network calculus is a theory initiated primarily in computer communication networks, especially in the aspect of real-time communications, where min-plus algebra plays a role. Cyber-physical networking systems (CPNSs) are recently developing fast and models in data flows as well as systems in CPNS are, accordingly, greatly desired. Though min-plus algebra may be a promising tool to linearize any node in CPNS as can be seen from its applications to the Internet computing, there are tough problems remaining unsolved in this regard. The identity in min-plus algebra is one problem we shall address. We shall point out the confusions about the conventional identity in the min-plus algebra and present an analytical expression of the asymptotic identity that may not cause confusions.