Finite-capacity M/M/۲ machine repair model with impatient customers, triadic discipline, and two working vacation policies

In this paper, we model and analyze a machine repair system characterized as an M/M/۲ queue with finite source L, operating under the triadic policy (۰,Q,N,M), considering impatience, and both multiple and single working vacations. The two servers can be active, on working vacation, or dormant depending on the number of failed machines in the system, following the triadic policy (۰,Q,N,M). We analyze the system's steady-state using the matrix-geometric method. Various performance measures are numerically presented and accurately interpreted. Finally, the Quadratic Fit Search method is employed to determine the optimal service rate \mu_{v}^{*} and the optimal expected cost. Additionally, the effect of system parameters on the cost function is investigated. This study offers a comprehensive analytical framework for complex queueing environments, informing decision-making and operational efficiency across various industrial sectors.

کلیدواژه ها:

Queueing system ، servers vacation ، impatience ، matrix-geometric method ، Optimization