This paper reports on the implementation and the experiments with symbolic model checking of continuous-time Markov chains using multi-terminal binary decision diagrams (MTBDDs). Properties are expressed in Continuous Stochastic Logic (CSL) [7] which includes the means to express both transient and steady-state performance measures. We show that all CSL operators can be treated using standard o...

We consider continuous time Markov chains (CTMCs) where there are costs and rewards associated with each state. For such a CTMC the objective usually is to calculate either the long-run average costs incurred per unit time or the total discounted cost incurred over an infinite horizon. We illustrate the calculations using several examples and conclude with applications to system performance ana...

CTMC (continuous-time Markov chains) are a commonly used formalism for modeling fault-tolerant systems. One of the major drawbacks of CTMC is the well-known state-space explosion problem. This work develops and analyzes a method (SC-BM) to compute bounds for the reliability of non-repairable fault-tolerant systems in which only a portion of the state space of the CTMC is generated. SC-BM uses t...

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...

Markov chains are widely used to determine system performance and reliability characteristics. The vast majority of applications considers continuous-time Markov chains (CTMCs). This note motivates how concurrency theory can be extended (as opposed to twisted) to CTMCs. We provide the core motivation for the algebraic setup of Interactive Markov Chains. Therefore, this note should have better b...

Quantitative analysis of computer systems has become very important as they are being used to handle various mission critical and performance intensive applications. In this independent study I studied methods to model computer systems for analyzing them for reliability, availability, and performance metrics. The techniques that were covered include modeling using Discrete Time Markov Chains (D...

In order to avoid the state space explosion problem encountered in the quantitative analysis of large scale PEPA models, a fluid approximation approach has recently been proposed, which results in a set of ordinary differential equations (ODEs) to approximate the underlying continuous time Markov chain (CTMC). This paper presents a mapping semantics from PEPA to ODEs based on a numerical repres...

In the present work‎, ‎a new stochastic algorithm is proposed to solve multiple dimensional Fredholm integral equations of the second kind‎. ‎The solution of the‎ integral equation is described by the Neumann series expansion‎. ‎Each term of this expansion can be considered as an expectation which is approximated by a continuous Markov chain Monte Carlo method‎. ‎An algorithm is proposed to sim...

We consider weak lumpability of denumerable discrete or continuous time Markov chains. Firstly, we are concerned with irreducible recurrent positive and R-positive Markov chains evolving in discrete time. We study the properties of the set of all initial distributions of the starting chain leading to an aggregated homogeneous Markov chain with respect to a partition of the state space. In parti...