Markov chains are an application of stochastic models in operation research, helping the analysis and optimization of processes with random events and transitions. The method that will be deployed to obtain the transient solution to a Markov chain problem is an important part of this process. The present paper introduces a novel Ordinary Differential Equation (ODE) approach to solve the Markov chain problem. The probability distribution of a continuous-time Markov chain with an infinitesimal generator at a given time is considered, which is a resulting solution of the Chapman-Kolmogorov differential equation. This study presents a one-step second-derivative method with better accuracy in solving the first-order Initial Value Problems (IVPs) compared to other approaches found in the literature, which is verified by the obtained solutions. The determination of the transient solutions for Markov chains is presented using the proposed method. The results show better accuracy in solving the transient distribution in Markov chains, which implies that there is an improved assurance in adopting this approach in future studies of the Markov chain modeling process for predicting future events based on the current state of a process. Future studies on Markov chain modeling could adopt the introduced method to predict future events based on the current state of a process.
Receipt date:3/13/2021 accepted date:5/26/2021 Publication date:12/31/2021
This work is licensed under a Creative Commons Attribution 4.0 International License.
energy is one of the strategic resources within international politics, and this is through the existing competition between the international powers on it, and the global powers have begun to rely on interest in new areas, such as import, depending on new projects an
... Show MoreThe present study aims at knowing the reasons of the student of secondary school abstention from participation in the theatrical activity, and to know the reasons that resulted in this abstention. In addition to that, the study aims at knowing the differences according to variables (gender, scholastic stage, and major of study). The sample of the study was chosen from the secondary schools in Baghdad in the random manner from Al-Karakh and Al-Rusafa districts of (147) students. The questionnaire was used to collected data.
The result showed that all the items are intense, the item of (Students do not know how to use their leisure time) obtained the hi
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... Show MoreHighlighting the role of the movement and its dramatic dimensions, as an artistic product, whether at the level of cinema or television in general, and the stages of its influence within the structure of the cinematographic scene in particular, had an effective role in the continuation of the structure of the event according to its dramatic and aesthetic process, and from this the research problem crystallized in the following question: What is How the kinetic diversity of the camera in the structure of the cinematographic scene is achieved to achieve the maximum possible benefit by extrapolating all opinions in line with the objectives of the research, the research presented and two topics and the introduction were divided, which
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... Show MoreThe research deals with the important and modern two subjects, strategic leadership which have six demotions and knowledge management
(four demotions') . the gools & the research is to know the relation & the effect them in the oil ministry (project department) , the sample was (50) persons who works in the department the questionnaire was the tool of data gathering .
The research divided to four parties, the first to the theotical review of the research variables, the second to the research methrology, the third to analysis and discoed the empirical results the last to the conclusions and recommendations .
This research aims to identify the effective role of self-managed teams in the quality of service performance in the directorate of Ramadi municipality. The problematic nature of our research involves this main question of the effective role of self-managed teams in the Municipality of Ramadi in improving the services of performance quality to the beneficiaries from the Directorate service. The importance of this study lies in the role played by the work teams in the organizations that excel in their field, the attendant of the changes in the leadership, administrative roles of the institutions, and teams leaders, will be achieved by the self-managed teams in improving the quality of the service provided by the institution to whi
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