In this paper a two-state Markovian maintenance process where the true state is unknown will be considered. The operating cost per period is a continuous random variable which depends on the state of the process. If investigation cost is incurred at the beginning of any period, the system wit I be returned to the "in-control" state instantaneously. This problem is solved using the average crite...

Several Markovian process calculi have been proposed in the literature, which differ from each other for various aspects. With regard to the action representation, we distinguish between integrated-time Markovian process calculi, in which every action has an exponentially distributed duration associated with it, and orthogonal-time Markovian process calculi, in which action execution is separat...

Since a real epidemic process is not necessarily Markovian, the epidemic threshold obtained under the Markovian assumption may be not realistic. To understand general non-Markovian epidemic processes on networks, we study the Weibullian SIS process in which the infection process is a renewal process with a Weibull time distribution. We find that, if the infection rate exceeds 1/ ln(λ1 + 1), whe...

Since a real epidemic process is not necessarily Markovian, the epidemic threshold obtained under the Markovian assumption may be not realistic. To understand general non-Markovian epidemic processes on networks, we study the Weibullian susceptible-infected-susceptible (SIS) process in which the infection process is a renewal process with a Weibull time distribution. We find that, if the infect...

Process algebras extended by a concept to present timing behaviour have been very recently proposed as a good modelling tool for the combined analysis of qualitative and quantitative system behaviour. We introduce a a process algebra including exponentially distributed time delays and a systematic approach to compute the underlying labelled transition system and continuous time Markov process. ...