Abstract:
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.
