Generalised Stochastic Petri Nets (GSPNs) are a popular modelling formalism for performance and dependability analysis. Their semantics is traditionally associated to continuous-time Markov chains (CTMCs), enabling the use of standard CTMC analysis algorithms and software tools. Due to ambiguities in the semantic interpretation of confused GSPNs, this analysis strand is however restricted to ne...

Stochastic process algebras such as PEPA allow complex stochastic models to be described in a compositional way, but this leads to state space explosion problems. To combat this, there has been a great deal of work in developing techniques for abstracting Markov chains. In particular, abstract — or interval — Markov chains allow us to aggregate states in such a way as to safely bound transient ...

Continuous-time Markov chain (CTMC) models have become a central tool for understanding the dynamics of complex reaction networks and the importance of stochasticity in the underlying biochemical processes. When such models are employed to answer questions in applications, in order to ensure that the model provides a sufficiently accurate representation of the real system, it is of vital import...

This paper reconsiders Bernardo’s T-lumpability on continuous-time Markov chains (CTMCs). This notion allows for a more aggressive state-level aggregation than ordinary lumpability. We provide a novel structural definition of (what we refer to as) weighted lumpability, prove some elementary properties, and investigate its compatibility with linear real-time objectives. The main result is that t...

Formal verification methods, such as Model Checking, have been used for addressing performance/dependability analysis of systems. Such formal methods have several advantages over traditional techniques aiming at performance/dependability analysis such as the use of a single computational technique for evaluation of any measure and all complex numerical computation steps are hidden to the user. ...

Continuous Time Markov Chains (CTMC) have been used extensively to model reliability of storage systems. While the exponentially distributed sojourn time of Markov models is widely known to be unrealistic (and it is necessary to consider Weibull-type models for components such as disks), recent work has also highlighted some additional infirmities with the CTMC model, such as the ability to han...

A. A stochastic process is a collection of random variables {X t , t ∈ T }. B. A sample path or realization of a stochastic process is the collection of values assumed by the random variables in one realization of the random process, e.g. C. The state space is the collection of all possible values the random variables can take on, i.e. it is the sample space of the random variables. For example...

T paper is concerned with the computation of the interval availability (proportion of time in a time interval in which the system is up) distribution of a fault-tolerant system modeled by a finite (homogeneous) continuous-time Markov chain (CTMC). General-purpose methods for performing that computation tend to be very expensive when the CTMC and the time interval are large. Based on a previousl...

This paper presents IM-SPDL, a stochastic extension of the modal logic PDL, which supports the specification of complex performance and dependability requirements. The logic is interpreted over extended stochastic labelled transition systems (ESLTS), i.e. transition systems containing both immediate and Markovian transitions. We define the syntax and semantics of the new logic and show that IM-...

Large multimedia document archives hold most of their data in near-line tertiary storage libraries for cost reasons. This paper develops an integrated approach to the vertical data migration between the tertiary and secondary storage in that it reconciles speculative preloading, to mask the high latency of the tertiary storage, with the replacement policy of the secondary storage. In addition, ...