In this paper algorithms for model checking CSL (continuous stochastic logic) against infinite-state continuous-time Markov chains of so-called quasi birth-death type are developed. In doing so we extend the applicability of CSL model checking beyond the recently proposed case for finite-state continuous-time Markov chains, to an important class of infinite-state Markov chains. We present synta...

Abstract Nature is never at a steady state. Natural history generated by ever-new and ever-interacting forces that produce continuous changes. At virtually all timescales, the geological record shows these changes do not cancel each other out and, thus, state utopic. However, we need of equilibrium as starting point for modelling Nature, steady-state condition widely used reference in idealisat...

Performance evaluation of modern complex systems has become compulsory in order to understand a system's behavior before it is constructed or implemented. Usually either Simulation of Analytical approaches are used to obtain such understanding. However, the system must, somehow, be represented. The paper describes PerformCharts, a tool to analytically obtain performance evaluation of a system s...

The paper presents the theoretical evaluation of the complexity of an algorithm, based on embedded Markov chains, for computing steady state probabilities. Experimental research with different infinitesimal generator matrices was performed to support theoretical evaluations. Results showed that modified algorithm can be more effective for sparse matrices. An example of a queuing system is prese...

A general model for describing, evaluation and control of most common reliability characteristics of multi-stage systems with gradual failures and repairs of the whole system is proposed. The steady state probabilities and the Laplace transform of the reliability function are calculated.

This paper draws attention to the risk of rounding error in the numerical evaluation of steady-state probabilities for the M/M family of queues. A method for avoiding the risk is presented which is easy to program for calculation in practice.