PEPA Queues: Capturing Customer Behaviour in Queueing Networks

Ashok Argent-Katwala, Jeremy T. Bradley
2007 Electronical Notes in Theoretical Computer Science  
Queueing network formalisms are very good at describing the spatial movement of customers, but typically poor at describing how customers change as they move through the network. We present the PEPA Queues formalism, which uses the popular stochastic process algebra PEPA to represent the individual state and behaviour of customers and servers. We offer a formal semantics for PEPA Queues, plus a direct translation to PEPA, allowing access to the existing tools for analysing PEPA models. Finally,
more » ... we use the ipc/DNAmaca tool-chain to provide passage-time analysis of a dual Web server example. Open access under CC BY-NC-ND license. found in [11]. A brief discussion of the basic PEPA operators is given below: Prefix The basic mechanism for describing the behaviour of a system with a PEPA model is to give a component a designated first action using the prefix combinator, denoted by a full stop. As explained above, (α, r).P carries out an α action with rate r, and it subsequently behaves as P . Choice The component P +Q represents a system which may behave either as P or as Q. The activities of both P and Q are enabled. The first activity to complete distinguishes one of them: the other is discarded. The system will behave as the derivative resulting from the evolution of the chosen component. Constant It is convenient to be able to assign names to patterns of behaviour associated with components. Constants are components whose meaning is given by a defining equation. The notation for this is X def = E. The name X is in scope in the expression on the right hand side meaning that, for example, X def = (α, r).X performs α at rate r forever. Hiding The possibility to abstract away some aspects of a component's behaviour is provided by the hiding operator, denoted P/L. Here, the set L identifies those activities which are to be considered internal or private to the component and which will appear as the distinguished unknown type τ . Cooperation We write P £ ¡
doi:10.1016/j.entcs.2007.07.002 fatcat:7gqpcipfefey5m6l73sscwjp7u