http://ir.haramaya.edu.et//hru/handle/123456789/117 2026-05-22T19:26:42Z 2026-05-22T19:26:42Z LAMORE ADE, TSEGAYE Demie (PhD), Seleshi t Alemayehu (PhD), Getine http://ir.haramaya.edu.et//hru/handle/123456789/8421 2026-05-20T07:41:53Z 2025-01-01T00:00:00Z

A FLUID QUEUE DRIVEN BY SINGLE SERVER MARKOVIAN QUEUE WITH VARIANT WORKING VACATIONS LAMORE ADE, TSEGAYE; Demie (PhD), Seleshi; t Alemayehu (PhD), Getine In this thesis a fluid queue driven by single server Markovian queue with variant working vacation was investigated. Queuing theory is a mathematical approach that studies and models waiting lines. A fluid Queue is an input output system the customers are modeled as a continuous fluid that enters and leaves a storage device, called Buffer, Where the background process is governed by a single server Markovian queue. Fluid queues are powerfully applied across diverse fields to model systems where a continuous workload accumulates and depletes under rates controlled by a random environment, typically a Markov chain. In telecommunications, they model data buffers in routers and wireless networks with fluctuating traffic and channel capacity. In manufacturing, they represent continuous-flow production lines subject to machine breakdowns, while in finance, they analyze cash reserves in insurance and dam-based company models. The study focuses on formulating governing equations for background process model and fluid model, the closed-form solutions for steady state probabilities of the system were obtained by applying probability generating functions methods. Various performance measures of the system such as buffer content distribution, mean buffer content, server utilization were obtained. The model captures the dynamics of the system under working vacation polices, where the server operates at a reduced rate rather than being completely idle. Numerical computations were performed by MATLAB software to validate the theoretical results and analyze the system performance under various parameter settings. The findings provide insights into the behavior of fluid queues influenced by Markovian driven vacation polices, contributing to the broader understanding of queuing systems with server vacations. 47

2025-01-01T00:00:00Z Bizuayehu Seyoum Zalale (PhD) Getachew Teshome (PhD) Melisew Tesfera http://ir.haramaya.edu.et//hru/handle/123456789/8384 2025-05-07T07:18:16Z 2024-12-01T00:00:00Z

MODELING AND ANALYZING DIARRHEAL DISEASE DYNAMICS USING CONTROL MEASURES Bizuayehu Seyoum Zalale; (PhD) Getachew Teshome; (PhD) Melisew Tesfera In this study, a mathematical model to analyze the dynamics of a chronic water-borne disease known as diarrhea is developed. To achieve the objectives of this study work, secondary data on the population under five years of age from Bishoftu General Hospital between 2020 and March 2024 is collected. These populations were categorized as newborn, vaccinated, infected, and treated. Based on the epidemiological behavior of the diarrhea disease, a deterministic model is formulated by dividing the total population into seven classes. This model accounts for preventive interventions through vaccination and control measures through treatment. Since diarrhea is caused by pathogens that can survive and reproduce in water at specific temperatures and salinities, so we considered the pathogens as a compartment in the model. Our findings revealed that this water-borne disease can lead to serious infections. The qualitative behavior of the models, including the existence of equilibrium points, basic reproductive number of the model, and stability analysis of equilibrium points were analyzed. Using the collected data, some parameters value were estimated while value some others parameters were received from related publications, and based on the behavior of these disease the values left parameters where assumed. To determine the effect of parameters on the dynamics of the disease, a numerical simulation was performed and displayed the results in a graph using MATLAB 2019 computer software. The results show that increasing the rate of vaccination and treatment plays a crucial role in controlling the dynamics of diarrhea. Therefore, in order to eliminate diarrhea in the community, it is essential for stakeholders to consider these prevention strategies and control measures 62p.

2024-12-01T00:00:00Z MURAD MUMMEDIMER Dr, Seleshi Demie (PhD) Dr. Melisew Tefera (PhD) http://ir.haramaya.edu.et//hru/handle/123456789/8309 2025-03-14T06:11:49Z 2024-06-01T00:00:00Z

MULTI SERVER MARKOVIAN QUEUE WITH MULTIPLE WORKING VACATIONS, WAITING SERVER, FEEDBACK, RENEGING AND RETENTION OF RENEGED CUSTOMERS MURAD MUMMEDIMER; Dr, Seleshi Demie (PhD); Dr. Melisew Tefera (PhD) In this thesis an infinite capacity Multi server Markovian queuing system with multiple working vacations, waiting server, feedback, reneging and retention of reneged customers is examined. If all active servers finish service and these is no customer in the system, the server wait for a duration of time before begin a synchronous WV (waiting server). During WV after completion of each service, customer can either leave the system satisfactorily with probability β or rejoin the queue to get service with feedback com plementary probability 1− β, where 0 ≤ β ≤ 1. The servers serve the customers at a slower rate than the normal busy period during a working vacation and this becomes the cause of customer’s impatience and this impatient customers may remain in the system with probability by employing certain convincing mechanisms. The inter-arrival times, the waiting server times, the feedback times, the service times, the impatient times and the vacation times are taken to be independent and exponentially distributed. The steady state probabilities when the server is in a regular busy period and in a working vacation periods are obtained by using recursive and probability generating function approach, also the steady state probabilities of the system being in any particular state were ob tained by using probability generating function. Various performance measures of the model such as the expected system size during normal busy periods, the expected system size during working vacations periods, the expected system size, the expected number of customer served, the proportion of customers served and the average of reneging and retention rate are obtained by using probability generating function approach. At the end, we have presented some numerical examples to demonstrate the effects of system parameters on some performance measures. 61

2024-06-01T00:00:00Z Tajudin Shafi (PhD) Melisew Tefera (PhD) Getachow Teshome http://ir.haramaya.edu.et//hru/handle/123456789/8290 2025-03-07T12:25:04Z 2024-10-01T00:00:00Z

A METHOD BASED ON BERNSTEIN POLYNOMIAL FOR SOLVING NONLINEAR VOLOTERRA-FREDHOLM INTEGRAL EQUATIONS OF SECOND Tajudin Shafi; (PhD) Melisew Tefera; (PhD) Getachow Teshome In this thesis, we discussed numerical solutions of nonlinear Volterra-Fredholm integral equations by using Bernstein polynomial collocation method. Nonlinear Volterra-Fredholm integral equations which cannot be easily evaluated analytically. This thesis was concerned with numerical method (Bernstein polynomial collocation method). Bernstein polynomial collocation method were utilized to convert the Nonlinear Volterra-Fredholm integral equation into a system of nonlinear algebraic equations and the resulting nonlinear algebraic equations were solved by using newton iteration technique to compute the Bernstein coefficients. The presented concept and method was verified by different examples, where theoretical results are numerically confirmed. The numerical results of six test problems, for which the exact solutions are known, are considered to verify the accuracy and the efficiency of the proposed method. The numerical results were compared with the exact solutions and with other method used for solving nonlinear VFIE based on absolute error. Finally the numerical results were demonstrated by table, in order to show the reliability of proposed method. From the results of the study as the values of the degree n, increases and the error were decreasing and computational costs were increases to obtain more accurate results. Lastly from the result, we have seen that BPCM is converge to exact solution as number of degree is increased. This thesis can be extended to solve nonlinear volterra-fredholm integro differential equation and also can be extended for the numerical solutions of two dimensional nonlinear volterra-fredholm equations using these methods. 74p.

2024-10-01T00:00:00Z