A Continuous State Space Approximation for PEPA Queues Ashok Argent-Katwala Jeremy T. Bradley * Abstract PEPA Queues is a formalism that augments queueing networks with customers that have behavioural characteristics, as defined by PEPA com- ponents. PEPA Queues suffer from the traditional state-space explosion that affects both closed queueing networks and PEPA models. We dis- cuss a possible solution to this with a continuous state-space approxima- tion that allows us to derive an underlying mathematical model based on ordinary differential equations from a PEPA Queues model. 1 Introduction PEPA Queues [1] is a behavioural extension of closed queueing networks. In PEPA Queues, the customers and servers are modelled as PEPA components and the servers can interact with queueing customers to determine how they are routed to other queues in the system. 2 A Rough Outline In Hillston’s original continuous state-space approximation of PEPA models [2], components which are grouped into self-synchronising sets: P || P || ··· || P || P are represented by a tuple which counts the number of P components that are in a given derivative state, that is: (N (P ),N (P 1 ),N (P 2 ),...,N (P n )) where P has (n + 1) derivative states (including itself). A set of ordinary differential equations (ODEs) can then be generated to show how the quantities N (P i ) vary over time. * Department of Computing, Imperial College London. Email: {ashok,jb}@doc.ic.ac.uk