It is well known that various characteristics in risk and queuing process can be formulated as Markov Renewal function. We study the max-position of finitely many Markov Renewal Reward process with countable state space. We define Markov Renewal equation associated with max-posed process. The solutions of the Markov Renewal Reward equation are derived and the asymptotic behaviors of the equatio...

Model checking has been introduced as an automated technique to verify whether functional properties, expressed in a formal logic like computational tree logic (CTL), do hold in a formally-specified system. In recent years, we have extended CTL such that it allows for the specification of properties over finite-state continuous-time Markov chains (CTMCs). Computational techniques for model chec...

Supermarket models with different servers become a key in modeling resource management of stochastic networks, such as, computer networks, manufacturing systems and transportation networks. While these different servers always make analysis of such a supermarket model more interesting, difficult and challenging. This paper provides a new novel method for analyzing the supermarket model with dif...

There are effective numerical methods for the analysis of Markov reward models (MRMs) without or with complete reward loss, but the analysis of MRMs with partial reward loss is more complex. This paper presents the analytical description of the distribution and the moments of the accumulated reward of partial increment loss reward models and an effective numerical method to evaluate these measu...

State-based systems with discrete or continuous time are often modelled with the help of Markov chains. In order to specify performance measures for such systems, one can define a reward structure over the Markov chain, leading to the Markov Reward Model (MRM) formalism. Typical examples of performance measures that can be defined in this way are time-based measures (e.g. mean time to failure),...

Numerical methods for solving Markov chains are in general inefficient if the state space of the chain is very large (or infinite) and lacking a simple repeating structure. One alternative to solving such chains is to construct models that are simple to analyze and that provide bounds for a reward function of interest. We present a new bounding method for Markov chains inspired by Markov reward...

Solving Markov chains is in general difficult if the state space of the chain is very large (or infinite) and lacking a simple repeating structure. One alternative to solving such chains is to construct models that are simple to analyze and provide bounds for a reward function of interest. We present a new bounding method for Markov chains inspired by Markov reward theory: Our method constructs...

There have always been tremendous efforts to make acceptable and suitable models for telecommunication networks. The goal is usually to calculate some Quality of Service parameters: mostly throughput, blocking probability, average response time. But these models always have (and will have) their limitations. My goal is to extend the limits of usability in some cases, and to introduce a new appr...

Continuous Stochastic Logic (CSL) which lets to express real-time probabilistic properties on Continuous-Time Markov Chains (CTMC) has been augmented by reward structures to check also performability measures. Thus Continuous Stochastic Reward Logic (CSRL) defined on Markov Reward Models (MRM) provides a framework to verify performancerelated and as well as dependability-related measures. Proba...

  In this paper Semi-Markov models are used to forecast the triple dimensions of next earthquake occurrences. Each earthquake can be investigated in three dimensions including temporal, spatial and magnitude. Semi-Markov models can be used for earthquake forecasting in each arbitrary area and each area can be divided into several zones. In Semi-Markov models each zone can be considered as a sta...