15.4.3 Queuing systems

Problem: There are three machines, working in the manufactory, which break down with intensities \( \lambda_{1}, \lambda_{2}, \lambda_{3} \) (per day) respectively. There are two regulators in the staff, eliminating the breakdowns of machines with intensities \( \mu_{1}, \mu_{2} \) (per day) respectively. It is required to plot the graph of this queuing system and find the fraction of time, both regulators are busy with work. \begin{tabular}{|c|c|c|c|c|} \hline\( \lambda_{1} \) & \( \lambda_{2} \) & \( \lambda_{3} \) & \( \mu_{1} \) & \( \mu_{2} \) \\ \hline 0,4 & 0,15 & 0,15 & 0,4 & 0,1 \\ \hline \end{tabular}