[Tip: Study the MC, QT, and Little's law lectures together: CTMC (MC lecture), M/M/1 queue (QT lecture), Little's law lecture (when deriving the mean response time from mean number of customers), DTMC (MC lecture), M/M/1 queue derivation using DTMC analysis, derive distribution of response time in M/M/1 queue (QT lecture), relation between Markov property and mem-oryless property (MC lecture), ...

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 ...

It is often the case in modeling biological phenomena that the structure and the effect of the involved interactions are known but the rates of the interactions are neither known nor can easily be determined by experiments. This paper deals with the estimation of the rate parameters of reaction networks in a general and abstract context. In particular, we consider the case in which the phenomen...

Weibull distributions can be used to accurately model failure behaviours of a wide range of critical systems such as on-orbit satellite subsystems. Markov chains have been used extensively to model reliability and performance of engineering systems or applications. However, the exponentially distributed sojourn time of Continuous-Time Markov Chains (CTMCs) can sometimes be unrealistic for satel...

We investigate the behaviour of population models written in Stochastic Concurrent ConstraintProgramming (sCCP), a stochastic extension of Concurrent Constraint Programming. In particular,we focus on models from which we can define a semantics of sCCP both in terms of ContinuousTime Markov Chains (CTMC) and in terms of Stochastic Hybrid Systems, in which some populationsare appr...

Dynamic Fault Trees in Reliability Engineering. Reliability and availability measures, such as system failure probability during a given mission time and system meantime-between-failures, are often important measures to assess in embedded systems design. There exist several techniques and formalisms for reliability/availability assessment. One such formalism is dynamic fault trees (DFT) [6]. DF...

State based analysis of stochasticmodels for performance and dependability often requires the computation of the stationary distribution of a multidimensional continuous-time Markov chain (CTMC). The infinitesimal generator underlying a multidimensional CTMC with a large reachable state space can be represented compactly in the form of a block matrix in which each nonzero block is expressed as ...

Solving sparse systems of linear equations is at the heart of scientific computing. Large sparse systems often arise in science and engineering problems. One such problem we consider in this paper is the steadystate analysis of Continuous Time Markov Chains (CTMCs). CTMCs are a widely used formalism for the performance analysis of computer and communication systems. A large variety of useful pe...

We study properties and parameter estimation of finite-state homogeneous continuous-time bivariate Markov chains. Only one of the two processes of the bivariate Markov chain is observable. The general form of the bivariate Markov chain studied here makes no assumptions on the structure of the generator of the chain, and hence, neither the underlying process nor the observable process is necessa...

We consider the following problem: For a real-time probabilistic system S consisting of two submodules M1 and M2, the specification of the global system S is given, as well as part of the specification of M1 and part of the specification of M2 (the possible traces are known but not their probabilities nor their timing delays). We need to fully determine of M1 and M2 in a way to “best approximat...