The major goal of this study was to create a continuous time Markov chain (CTMC) models of voltage gating of gap junction (GJ) channels formed of connexin protein. This goal was achieved by using the Piece Linear Aggregate (PLA) formalism to describe the function of GJs and transforming PLA into Markov process. Infinitesimal generator of CTMC was used to automate construction of Markov chain mo...

This deliverable describes the first year results of the QUASIMODO project on analysing quantitative systems. Keyword list: Markov chain, Markov decision process, probabilistic bisimulation, probabilistic simulations; probabilistic timed automata; priced probabilistic timed automata; Continuous Time Markov Chains, inhomogeneous CTMC, Infinite state CTMC, counter-example guided abstractionrefine...

The quality of an architectural design of a software system has a great influence on achieving non-functional requirements of a system. A regular software development project is often influenced by non-functional factors such as the customers' expectations about the performance and reliability of the software as well as the reduction of underlying risks. The evaluation of non-functional paramet...

In this note we explore an aspect of the relationship between the notion of equilibrium of a continuous time Markov chain (CTMC) and that of the traditional concept of termination in rewriting systems. Unlike in deterministic dynamical systems, a Markov chain equilibrium is not a definite state, but rather a probability over the state space which is invariant under the Markov semigroup, and sat...

A novel method is presented for estimating the parameters of a parametric diffusion process. The approach based on closed-form Maximum Likelihood estimator an approximating Continuous Time Markov Chain (CTMC) Unlike typical time discretization approaches, such as pseudo-likelihood approximations with Shoji-Ozaki or Kessler's method, CTMC approximation introduces no time-discretization error dur...

We present a reduction of the Post correspondence problem (PCP) to the question of whether a continuous-time Markov chain (CTMC) presented as a set graph-rewriting rules has an equilibrium. It follows that the question of whether a computable CTMC is dissipative (ie does not have an equilibrium) is undecidable. The encoding uses the Kappa language and is presented in details for a simple PCP in...

A solution method for solving Markov chains for a class of stochastic process algebra terms is presented. The solution technique is based on a reformulation of the underlying continuous-time Markov chain (CTMC) in terms of semi-Markov processes. For the reformulation only local information about the processes running in parallel is needed, and it is therefore never necessary to generate the com...

Abstract We develop a continuous-time Markov chain (CTMC) approximation of one-dimensional diffusions with sticky boundary or interior points. Approximate solutions to the action Feynman–Kac operator associated diffusion and first passage probabilities are obtained using matrix exponentials. show how compute exponentials efficiently prove that carefully designed scheme achieves second-order con...

In this paper, a new variant of the multilevel algorithm for computing the steady-state solution of a continuous-time Markov chain is proposed. The method is integrated into a symbolic framework, where the CTMC is represented in a compact way using multi-terminal binary decision diagrams (MTBDD). It is shown how to represent the original CTMC and several aggregated chains within the same decisi...

the problem we investigate deals with the optimal assignment of resources to the activities of a stochastic project network. we seek to minimize the expected cost of the project include sum of resource utilization costs and lateness costs. we assume that the work content required by the activities follows an exponential distribution. the decision variables of the model are the allocated resourc...