Fluid Queue controlled by Markovian Queue with Matrix Approach

This study aims to analyze a fluid queue with infinite capacity controlled by Markovian queue with the matrix approach. The Markovian queue is an M/M/1/N queue, where customers arrive and get service with constant rates. After that, customers inflow to the fluid queue buffer with net effective input constant rates. For this scenario, we could develop a mathematical model and obtain closed-form formulas. Further, numerical illustration is shown the effectiveness and accuracy of the results and the proposed approach.