Stochastic (Markovian) process algebra extend classical process algebra with probabilistic exponentially distributed time durations denoted by rates (the parameter of the exponential distribution). Defining a semantics for such an algebra, so to derive Continuous Time Markov Chains from system specifications, requires dealing with transitions labeled by rates. With respect to standard process a...

In this paper, finite phase semi-Markov processes are introduced. By introducing variables and a simple transformation, every finite phase semi-Markov process can be transformed to a finite Markov chain which is called its associated Markov chain. A consequence of this is that every phase semi-Markovian switching system may be equivalently expressed as its associated Markovian switching system....

We introduce a novel stochastic process algebra, called PHASE, which directly supports phase-type distributions, useful for approximating the dynamics of non-Markovian HCI systems. In order to encourage the effective use of PHASE, we give a step by step account of how PHASE processes can be implemented in PRISM, one of the most powerful and popular probabilistic model checkers currently availab...

We derive novel upper and lower finite length bounds of the error probability in joint source-channel coding when the source is distributed according to an ergodic Markov process and the channel is a Markovian additive channel or a Markovian conditional additive channel. We show that these bounds are tight in the moderate deviations regime and for a certain interval of rates, also in the large ...

We study nonstationary non-Markovian processes defined by Langevin-type stochastic differential equations with an Ornstein-Uhlenbeck driving force. We concentrate on the long time limit of the dynamical evolution. We derive an approximate equation for the correlation function of a nonlinear nonstationary non-Markovian process, and we discuss its consequences. Non-Markovicity can introduce a dep...

Setting signals at traffic intersections to reduce congestion is one of the most challenging problems in traffic management. To find the optimal control strategy, specific information of the traffic flows passing through intersections, such as vehicle arrival rates (number of vehicles per hour), must be provided in advance. In most control approaches, this parameter is assumed to be a known con...

We consider the maintenance of a mission-based system that is designed to perform missions consisting of a random sequence of phases or stages with random durations. A …nite state Markov process describes the mission process. The age or deterioration process of the system is described by another …nite state Markov process whose generator depends on the phases of the mission. We discuss optimal ...

Providing probabilistic analysis of queueing models can be difficult when the input distributions are non-Markovian. In response, a plethora of methods have been developed to approximate a general renewal process by a process with the time between renewals being distributed as a phase type random variable, which allows the resulting queueing models to become analytically or numerically tractabl...

A rigorous formalism for the extraction of state-to-state transition functions from a Boltzmann-weighted ensemble of microcanonical molecular dynamics simulations has been developed as a way to study the kinetics of protein folding in the context of a Markov chain. Analysis of these transition functions for signatures of Markovian behavior is described. The method has been applied to an example...

The National Bridge Stock of Iran consists of about 330,000 bridges, of which around 50% are older than 30 years. Since 2010, Iran Road Maintenance & Transportation Organization has started implementing a comprehensive Bridge Management System in order to manage this aged stock efficiently. To predict future conditions of bridge stock, a heuristic numerical method is presented. This methodology...