Quantitative analysis of computer systems is often based on Markovian models. Among the formalisms that are used in practice, Markovian process algebras have found many applications, also thanks to their compositional nature that allows one to specify systems as interacting individual automata that carry out actions. Nevertheless, as with all state-based modelling techniques, Markovian process ...

We study behavioural relations for process algebra with a fluid semantics given in terms of a system of ordinary differential equations (ODEs). We introduce label equivalence, a relation which is shown to induce an exactly lumped fluid model, a potentially smaller ODE system which can be exactly related to the original one. We show that, in general, for two processes that are related in the flu...

Markovian Process Algebra (MPA) is a process algebra enhanced with exponential timing which allows the mapping of speciications on continuous time Markov chains (CTMCs). This paper introduces a compositional approach to compute the generator matrix of the CTMC underlying a MPA speciication which consists of the parallel composition of nite state agents. Furthermore two diierent equivalence rela...

We introduce a stochastic process algebra, PEPA, as a high-level modelling paradigm for continuous time Markov chains (CTMC). Process algebras are mathematical theories which model concurrent systems by their algebra and provide apparatus for reasoning about the structure and behaviour of the model. Recent extensions of these algebras, associating random variables with actions, make the models ...

Product-form solutions in Markovian process algebra (MPA) are constructed using properties of reversed processes. The compositionality of MPAs is directly exploited, allowing a large class of hierarchically constructed systems to be solved for their state probabilities at equilibrium. The paper contains new results on both reversed stationary Markov processes as well as MPA itself and includes ...

Stochastic process algebras have become an accepted part of performance modelling over recent years. Because of the advantages of compositionality and exibility they are increasingly being used to model larger and more complex systems. Therefore tools which support the evaluation of models expressed using stochastic process algebra must be able to utilise the full range of decomposition and sol...

In this paper we establish asymptotics for the basic steady-state distributions in a large class of single-server queues. We consider the waiting time, the workload (virtual waiting time) and the steady-state queue lengths at an arbitrary time, just before an arrival and just after a departure. We start by establishing asymptotics for steady-state distributions of Markov chains of M/GI/1 type. ...

Stochastic Process Algebras (SPA) are process algebras in which the duration of each activity is given by a random variable. If the stochastic aspect is restricted to Markovian, i.e. exponentially distributed durations, nice algebraic foundations are available. They include a formal semantics and an equational theory for Markovian bisimulation , a congruence that can be seen as a stochastic cou...

We introduce immediate transitions as an extension of Stochastic Process Algebras (SPA). We distinguish two diierent classes of immediate transitions: probabilistic branching and management activities. We discuss both approaches and develop a theory for the probabilistic branching case. Although we use TIPP as a sample language within this paper, the theory can easily be adapted to other Stocha...

Extended Markovian Process Algebra (EMPA) is a process algebra suitable for expressing functional and performance aspects of concurrent systems. It is equipped with an operational interleaving semantics, a functional semantics, a Markovian semantics and an operational net semantics. In this paper we apply an integrated approach based on EMPA for mod-eling and analyzing concurrent systems to the...