In this paper we consider a like-queue production system in which server startup
and breakdowns are possible. The server is turned on (i.e. begins startup)
when N units are accumulated in the system and off when the system is empty.
We model this system by an M[x]/M/1 queue with
server breakdowns and startup time under the N policy. The arrival rate varies according to the server's status:
off, startup, busy, or breakdown.
While the server is working, he is subject to
breakdowns according to a Poisson process. When the server breaks down, he requires repair
at a repair facility, where the repair time follows the negative exponential distribution.
We study the steady-state behaviour of the system size distribution at
stationary point of time as well as the queue size distribution at departure point of time
and obtain some useful results.
The total expected cost function per unit time is developed to determine the optimal operating
policy at a minimum cost. This paper provides the minimum expected cost and the optimal operating
policy based on assumed numerical values of the system parameters. Sensitivity analysis is also provided
