We ascertain the diffusively scaled limit of a periodic Lorentz process in a strip with an almost reflecting wall at the origin. Here, almost reflecting means that the wall contains a small hole waning in time. The limiting process is a quasi-reflected Brownian motion, which is Markovian, but not strong Markovian. Local time results for the periodic Lorentz process, having independent interest,...

This paper focuses on an infinite-server queue modulated by an independently evolving finite-state Markovian background process, with transition rate matrix Q ≡ (qij)i,j=1. Both arrival rates and service rates are depending on the state of the background process. The main contribution concerns the derivation of central limit theorems for the number of customers in the system at time t ≥ 0, in t...

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...

The purpose of this note is to show that it possible establish a many-server functional strong law large numbers (FSLLN) for the fraction occupied servers (i.e., scaled number-in-system) without explicitly tracking through measure valued process either age or residual service times jobs in non-Markovian, non-stationary loss model. This considerable analytical simplification achieved by exploiti...

Future mobile systems are expected to offer users flexible access to information and services using a combination of different end-user devices in a Personal Distributed Environment (PDE). With PDEs able to operate over multiple air interfaces and heterogeneous networks, requiring seamless and rapid service provision, a flexible and fair trading of communication services is required. For this r...

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...