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...

Markovian processes have long been used to model stochastic environments. Reinforcement learning has emerged as a framework to solve sequential planning and decision-making problems in such environments. In recent years, attempts were made to apply methods from reinforcement learning to construct decision support systems for action selection in Markovian environments. Although conventional meth...

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. ...

We present GSMPA, a stochastically timed process algebra that enhances the expressiveness of the stochastically timed process algebra EMPA by allowing arbitrarily distributed durations to be directly modeled through the adoption of the mechanism of action identification as well as the adoption of the preselection policy for alternative actions. GSMPA is introduced together with the definition o...

This paper consideres an optimal ordering and replacement problem of a continuous time Markovian degradation system. An optimal policy minimizes the expected cost per unit time in an infinite time horizon. The problem is formulated by semi-Markov decision process and the optimality of an (n,N)-policy is shown. Further, the expected cost rate of the system operated under an (n,N)-policy is obtai...