1 Description of the Model In this test case, we consider the dependability of a fault-tolerant workstation cluster [5]. Notably, we consider a finite-state model leading to finite CTMCs. Taking into account different aspects of the model, we can consider it either as a Continuous-Time Markov Chain (CTMC) [5] or as a Continuous-Time Markov Decision Process (CTMDP) [7]. We can handle the CTMC ve...

We consider a continuous-time Markov chain (CTMC) whose state space is partitioned into aggregates, and each aggregate is assigned a probability measure. A sufficient condition for defining a CTMC over the aggregates is presented as a variant of weak lumpability, which also characterizes that the measure over the original process can be recovered from that of the aggregated one. We show how the...

In this chapter, we will describe, in a tutorial style, recent work on the use of fluid approximation techniques in the context of stochastic model checking. We will discuss the theoretical background and the algorithms working out an example. This approach is designed for population models, in which a (large) number of individual agents interact, which give rise to continuous time Markov chain...

This paper describes the tool CASPA, a new performance evaluation tool which is based on a Markovian stochastic process algebra. CASPA uses multi-terminal binary decision diagrams (MTBDD) to represent the labelled continuous time Markov chain (CTMC) underlying a given process algebraic specification. All phases of modelling, from model construction to numerical analysis and measure computation,...

Markov regenerative processes (MRGPs) constitute a more general class of stochastic processes than traditional Markov processes. Markovian dependency, the first-order dependency, is the simplest and most important dependency in stochastic processes. Past history of a Markov chain is summarized in the current state and the behavior of the system thereafter only depends on the current state. Sojo...

We consider a single stage production-inventory system whose production and demand rates are modulated by an environment process modeled as a finite state Continuous Time Markov Chain (CTMC). When the inventory level reaches zero, an order is placed from an external supplier, and it arrives instantaneously. We derive an Economic Order Quantity (EOQ ) policy that minimizes the long-run average c...

We consider the problem of constructing a physical system that evolves according to some specified conditional distribution. We restrict attention to physical systems that can be modeled as a timeinhomogeneous continuous-time Markov chain (CTMC) over a finite state space, which includes many of the systems considered in stochastic thermodynamics. Examples range from constructing a logical gate ...

While the Internet and the World-Wide-Web (WWW)-based online services expand at an unprecedented pace, the Web users are still experiencing a high level of unavailability. Paralleling the effort of identifying the failure-recovery behaviors of the underlying supporting infrastructure, attention has also been paid to Web users’ behaviors. However, a link between the two research directions seems...

Jackson queueing networks (JQNs) are a very general class of queueing networks that find their application in a variety of settings. The state space of the continuous-time Markov chain (CTMC) that underlies such a JQN, is highly structured, however, of infinite size in as many dimensions as there are queues. We present CSL model checking algorithms for labeled JQNs. To do so, we rely on well-kn...

We present CCMC (Conditional CSL Model Checker), a model checker for continuous-time Markov chains (CTMCs) with respect to formulas specified in continuoustime stochastic logic (CSL). Existing CTMC model checkers such as PRISM or MRMC handle only binary CSL until path formulas. CCMC is the first tool that supports algorithms for analyzing multiple until path formulas. Moreover, CCMC supports a ...