## Efficient solutions of a PEPA model of key distribution centre with a cost function

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### Abstract

In this paper we explore the trade-off between security and performance in considering a model of a key distribution centre. The model is specified using the Markovian process algebra PEPA. The basic model suffers from the commonly encountered state space explosion problem, and so we apply some approximate techniques to solve it. First, model reduction techniques and approximation to give a form of the model(in fact, a closed queueing network model) which is more scalable. The approximated model is analysed numerically and results derived from the approximation are compared with a discrete event simulation. We, then, consider the use of a fluid flow approximation based on ordinary differential equations (ODEs) derived from a form of simplified model. The results derived from solving the ODEs are compared with previous closed queueing network approximation. Those results have been found are the same as the asymptotic bounds solution for the queueing network approximation which demonstrates that ODEs gives a alternative solvent of asymptotic bounds, only having been proved, in this circumstance. Base on those techniques above, we, finally, evaluate a cost function of this secure key exchange model. Three questions have been proposed; how many clients can a given KDC configure support? how much service capacity must we provide at a KDC to satisfy a given number of clients? and what is the maximum rate at which keys can be refreshed before the KDC performance begins to degrade in a given demand on a given system? Answers of these three questions are illustrated through numerical examples.

### Publication metadata

**Author(s): **Zhao Y, Thomas N

**Publication type: **Report

**Series Title: **School of Computing Science Technical Report Series

**Year: **2008

**Pages: **30

**Source Publication Date: **July 2008

**Report Number: **1112

**Institution: **School of Computing Science, University of Newcastle upon Tyne

**Place Published: **Newcastle upon Tyne

**URL: **http://www.cs.ncl.ac.uk/publications/trs/papers/1112.pdf

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