Efficient solutions of a PEPA model of a key distribution centre

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 efficient techniques to solve it. First, we use model reduction techniques and approximation to give a form of the model (in fact, a closed queueing network model) which is more scalable. We then consider the use of a fluid flow approximation based on ordinary differential equations (ODEs) derived from an alternative form of the simplified model. Finally, we evaluate a utility 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 under a given demand on a given system? These questions are explored through numerical examples.