Extension of PRISM by Synthesis of Optimal Timeouts in Fixed-Delay CTMC

We present a practically appealing extension of the probabilistic model checker PRISM rendering it to handle fixed-delay continuous-time Markov chains (fdCTMCs) with rewards, the equivalent formalism to the deterministic and stochastic Petri nets (DSPNs). fdCTMCs allow transitions with fixed-delays (or timeouts) on top of the traditional transitions with exponential rates. Our extension supports an evaluation of expected reward until reaching a given set of target states. The main contribution is that, considering the fixed-delays as parameters, we implemented a synthesis algorithm that computes the epsilon-optimal values of the fixed-delays minimizing the expected reward. We provide a performance evaluation of the synthesis on practical examples

A note on the invariant distribution of a quasi-birth-and-death process

The aim of this paper is to give an explicit formula of the invariant distribution of a quasi-birth-and-death process in terms of the block entries of the transition probability matrix using a matrix-valued orthogonal polynomials approach. We will show that the invariant distribution can be computed using the squared norms of the corresponding matrix-valued orthogonal polynomials, no matter if they are or not diagonal matrices. We will give an example where the squared norms are not diagonal matrices, but nevertheless we can compute its invariant distribution

Decision support system for the environmental impact of e-business

With less than half a century's development, e-business and the Information and Communication Technologies it relies on, have been growing rapidly. With an even shorter history than the technology itself, the study of its impact on the environment and sustainable development in general, is still in its infancy. A review of past literature has revealed that the problem is complex. Both negative and positive impacts have been identified. Traditional systematic approaches have been found to be insufficient for this research topic. To explore the relationship further, a new methodology is proposed in this thesis. In particular the main objective of this PhD study is to demonstrate and develop an Expert Decision Support System at the meso level, to simulate the relationship between e-business and the environment. In pursuit of this aim, results are presented of two surveys that were conducted to collect data and build a knowledge base. Analysis of the data using various techniques was considered, based on data mining technologies and Fuzzy Logic. The development of the Expert Decision Support System is then discussed, adopting a two-way simulation approach. The forward chain of the system is developed based on Decision Support System technology, with the heart of the system built on Neural Networks. Calculation, estimation and prediction of environmental indicator values based e-business indicators are conducted in this part. The backward chain is based on Expert System technology, where conditions and rules are presented to reach certain pre-defined environmental targets. An individual company should then be able to use this system within a certain industry, for example, to simulate its environmental performance by adopting or limiting Information and Communication technologies. A demonstration of how the system can be used and operated on various occasions for different purposes is presented, based on four application scenarios: predictions, simulations, comparisons and solutions. It is claimed that the results from the Expert Decision Support System, which ideally should be integrated into a company's financial system and other information management systems, will provide important information that could be incorporated into a company's strategic plans, action plans and technological reformation. The research presents a pilot study which tries to not only build a quantitative model but also to construct a decision support system to simulate this relationship in the real world. It is claimed that the work both extends research methodologies in this field and endows traditional Neural Network applications with new meanings and challenges.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Optimizing Performance of Continuous-Time Stochastic Systems using Timeout Synthesis

We consider parametric version of fixed-delay continuous-time Markov chains (or equivalently deterministic and stochastic Petri nets, DSPN) where fixed-delay transitions are specified by parameters, rather than concrete values. Our goal is to synthesize values of these parameters that, for a given cost function, minimise expected total cost incurred before reaching a given set of target states. We show that under mild assumptions, optimal values of parameters can be effectively approximated using translation to a Markov decision process (MDP) whose actions correspond to discretized values of these parameters

A discrete MMAP for analysing the behaviour of a multi-state complex dynamic system subject to multiple events.

A complex multi-state system subject to different types of failures, repairable and/or nonrepairable, external shocks and preventive maintenance is modelled by considering a discrete Markovian arrival process with marked arrivals (D-MMAP). The internal performance of the system is composed of several degradation states partitioned into minor and major damage states according to the risk of failure. Random external events can produce failures throughout the system. If an external shock occurs, there may be an aggravation of the internal degradation, cumulative external damage or extreme external failure. The internal performance and the cumulative external damage are observed by random inspection. If major degradation is observed, the unit goes to the repair facility for preventive maintenance. If a repairable failure occurs then the system goes to corrective repair with different time distributions depending on the failure state. Time distributions for corrective repair and preventive maintenance depend on the failure state. Rewards and costs depending on the state at which the device failed or was inspected are introduced. The system is modelled and several measures of interest are built into transient and stationary regimes. A preventive maintenance policy is shown to determine the effectiveness of preventive maintenance and the optimum state of internal and cumulative external damage at which preventive maintenance should be taken into account. A numerical example is presented, revealing the efficacy of the model. Correlations between the numbers of different events over time and in non-overlapping intervals are calculated. The results are expressed in algorithmic-matrix form and are implemented computationally with Matlab.Junta de Andalucía, Spain, under the grant FQM307Ministerio de Economía y Competitividad, España, MTM2017-88708-PEuropean Regional Development Fund (ERDF