Approximate uniformization for continuous-time Markov chains with an application to performability analysis

SERIE RESEHRCH mEmORBnDH APPROXIMATE UNIFORMIZATION FOR CONTINUOUS-TIME MARKOV CHAINS WITH AN APPLICATION TO PERFORMABILITY ANALYSIS

An approximate version of the Standard uniformization technique is introduced for application to continuous-time Markov chains with unbounded jump rates. This technique is shown to be asymptotically exact and an error bound for the order of its accuracy is provided. An illustrative queueing application is included.

Approximate Symbolic Model Checking of Continuous-Time Markov Chains

This paper presents a symbolic model checking algorithm for continuous-time Markov chains for an extension of the continuous stochastic logic CSL of Aziz et al 1]. The considered logic contains a time-bounded until-operator and a novel operator to express steady-state probabilities. We show that the model checking problem for this logic reduces to a system of linear equations (for unbounded unt...

Continuous Time Markov Chains

Discrete-time Markov chains are useful in simulation, since updating algorithms are easier to construct in discrete steps. They can also be useful as crude models of physical, biological, and social processes. However, in the physical and biological worlds time runs continuously, and so discrete-time mathematical models are not always appropriate. This is especially true in population biology –...

Continuous-time Markov Chains

Bayesian analysis of continuous time Markov chains with application to phylogenetic modelling

Bayesian analysis of continuous time, discrete state space time series is an important and challenging problem, where incomplete observation and large parameter sets call for user-defined priors based on known properties of the process. Generalized linear models have a largely unexplored potential to construct such prior distributions. We show that an important challenge with Bayesian generaliz...