Economic application in a Bernoulli F-policy queueing system with server breakdown

For maintaining the service quality of working place, some kinds of arriving customers control policy are needed. This paper investigates a randomised arriving control policy of finite capacity queuing system with an unreliable server. In the investigated system, when the number of customers reaches the systems capacity, further arriving customers are not allowed to enter the system. As the queue length decreases to a predefined threshold value, customers may either be allowed entering the system with an exponential startup time or the customers are still unable to enter the system. For such a system, we develop the steady-state solutions and some important system characteristics, such as the probability that the server is busy, effective arrival rate, expected waiting time in the system, etc. We also develop a cost model to determine the optimal control policy at a minimum cost. A sensitivity analysis is also conducted to investigate the effects of changes in the system parameters on the expected cost function. Finally, we present some managerial insights through an application example of the printed circuit boards manufacturing system. © 2013 Taylor and Francis.