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...

Stochastic (Markovian) process algebra extend classical process algebra with probabilistic exponentially distributed time durations denoted by rates (the parameter of the exponential distribution). Defining a semantics for such an algebra, so to derive Continuous Time Markov Chains from system specifications, requires dealing with transitions labeled by rates. With respect to standard process a...

In this paper, finite phase semi-Markov processes are introduced. By introducing variables and a simple transformation, every finite phase semi-Markov process can be transformed to a finite Markov chain which is called its associated Markov chain. A consequence of this is that every phase semi-Markovian switching system may be equivalently expressed as its associated Markovian switching system....

We introduce a novel stochastic process algebra, called PHASE, which directly supports phase-type distributions, useful for approximating the dynamics of non-Markovian HCI systems. In order to encourage the effective use of PHASE, we give a step by step account of how PHASE processes can be implemented in PRISM, one of the most powerful and popular probabilistic model checkers currently availab...

We derive novel upper and lower finite length bounds of the error probability in joint source-channel coding when the source is distributed according to an ergodic Markov process and the channel is a Markovian additive channel or a Markovian conditional additive channel. We show that these bounds are tight in the moderate deviations regime and for a certain interval of rates, also in the large ...

We study nonstationary non-Markovian processes defined by Langevin-type stochastic differential equations with an Ornstein-Uhlenbeck driving force. We concentrate on the long time limit of the dynamical evolution. We derive an approximate equation for the correlation function of a nonlinear nonstationary non-Markovian process, and we discuss its consequences. Non-Markovicity can introduce a dep...