TITLE:
Alternative Approaches of Convolution within Network Calculus
AUTHORS:
Ulrich Klehmet, Rüdiger Berndt
KEYWORDS:
Network Calculus, Min-Plus Convolution, Algebraic Laws, Convex Analysis
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.2 No.11,
October
28,
2014
ABSTRACT: Network Calculus is a powerful mathematical
theory for the performance evaluation of communication systems; among others it
allows to determine worst-case performance measures. This is why it is often
used to appoint Quality of Service guarantees in packet-switched systems like
the internet. The main mathematical operation within this deterministic queuing
theory is the min- plus convolution of two functions. For example the
convolution of the arrival and service curve of a system which reflects the
data’s departure. Considering Quality of Service measures and performance evaluation,
the convolution operation plays a considerable important role, similar to
classical system theory. Up to the present day, in many cases it is not
practical and simple to perform this operation. In this article we describe
approaches to simplify the min-plus convolution and, accordingly, facilitate
the corresponding calculations.