Maintenance of deteriorating non-exponential single server queue / Koh Siew Khew - Koh, Siew Khew (2013)
Consider the single server queue in which the system capacity is infinite and the customers are served on a first come, first served basis. The case of a system without deterioration is first studied. The stationary queue length distribution and the stationary waiting time distribution are derived for the system in which the service time and interarrival time distributions are assumed to have constant asymptotic rates. The results found are verified by using simulation. Next consider a system in which the server would deteriorate due to random shocks and the seriously affected server will be sent for repair. A similar method is applied for deriving the stationary queue length distribution in a system in which the interarrival time distribution (or service time) is assumed to have a constant asymptotic rate while the service time (or interarrival time) remains exponentially distributed. From the stationary queue length distribution, a number of other characteristics can be derived. These include the sojourn time distribution of a customer who arrives when the queue is in a stationary state, and the expected length of the duration between two successive repair completions. From these distributions and expected length, the value of the specified maintenance level is found such that the long run average cost is minimized.