42 research outputs found
Model Checking CSL for Markov Population Models
Markov population models (MPMs) are a widely used modelling formalism in the
area of computational biology and related areas. The semantics of a MPM is an
infinite-state continuous-time Markov chain. In this paper, we use the
established continuous stochastic logic (CSL) to express properties of Markov
population models. This allows us to express important measures of biological
systems, such as probabilistic reachability, survivability, oscillations,
switching times between attractor regions, and various others. Because of the
infinite state space, available analysis techniques only apply to a very
restricted subset of CSL properties. We present a full algorithm for model
checking CSL for MPMs, and provide experimental evidence showing that our
method is effective.Comment: In Proceedings QAPL 2014, arXiv:1406.156
Two approaches to the construction of perturbation bounds for continuous-time Markov chains
The paper is largely of a review nature. It considers two main methods used
to study stability and obtain appropriate quantitative estimates of
perturbations of (inhomogeneous) Markov chains with continuous time and a
finite or countable state space. An approach is described to the construction
of perturbation estimates for the main five classes of such chains associated
with queuing models. Several specific models are considered for which the limit
characteristics and perturbation bounds for admissible "perturbed" processes
are calculated
Stationary distributions of continuous-time Markov chains: a review of theory and truncation-based approximations
Computing the stationary distributions of a continuous-time Markov chain involves solving a set of linear equations. In most cases of interest, the number of equations is infinite or too large, and cannot be solved analytically or numerically. Several approximation schemes overcome this issue by truncating the state space to a manageable size. In this review, we first give a comprehensive theoretical account of the stationary distributions and their relation to the long-term behaviour of the Markov chain, which is readily accessible to non-experts and free of irreducibility assumptions made in standard texts. We then review truncation-based approximation schemes paying particular attention to their convergence and to the errors they introduce, and we illustrate their performance with an example of a stochastic reaction network of relevance in biology and chemistry. We conclude by elaborating on computational trade-offs associated with error control and some open questions
A new general-purpose method for the computation of the interval availability distribution
We develop a new randomization-based general-purpose method for the computation of the interval availability
distribution of systems modeled by continuous-time Markov chains (CTMCs). The basic idea of
the new method is the use of a randomization construct with different randomization rates for up and down
states. The new method is numerically stable and computes the measure with well-controlled truncation error.
In addition, for large CTMC models, when the maximum output rates from up and down states are significantly
different, and when the interval availability has to be guaranteed to have a level close to one, the new
method is significantly or moderately less costly in terms of CPU time than a previous randomization-based
state-of-the-art method, depending on whether the maximum output rate from down states is larger than the
maximum output rate from up states, or vice versa. Otherwise, the new method can be more costly, but a relatively
inexpensive for large models switch of reasonable quality can be easily developed to choose the fastest
method. Along the way, we show the correctness of a generalized randomization construct, in which arbitrarily
different randomization rates can be associated with different states, for both finite CTMCs with infinitesimal
generator and uniformizable CTMCs with denumerable state space.Preprin