Modeling and optimizing an AMS with DV policy, waiting servers, impatient customers, and failures: A queueing analysis

Abstract

In this paper, we analyze an automated manufacturing system modeled as a queueing system with multiple servers, differentiated vacation (DV) policy, customer impatience, and server failures. We consider the waiting servers policy, where the servers wait for a random duration before leaving for a vacation once the system gets empty. Upon their return, if no customers are waiting, the servers may leave for a second type-2 vacation of shorter duration. The system may experience breakdowns and require immediate repair. During the repair period, customers are served at a lower rate, and they become impatient during busy, vacation, and repair periods, abandoning the queue if their timer expires. Further, based on the queue length, arriving customers may either join the system or balk with some probability. We use the matrix analytic method to derive the steady-state probability of the system and several performance measures. Moreover, we illustrate the effect of different system parameters on various performance measures. Additionally, we develop a cost model and optimize the system capacity, number of servers, and service rates such that cost per unit time is minimized. Finally, we analyze the impact of system parameters on the cost through numerical examples.