Abstract
In this paper, we investigate a single-server Poisson input queueing model, wherein arrivals of units are in bulk. The arrival rate of the units is state dependent, and service time is arbitrary distributed. It is also assumed that the system is subject to breakdown, and the failed server immediately joins the repair facility which takes constant duration to repair the server. By using supplementary variable technique, we obtain the probability generating function of the number of units in the system which is further used to establish some performance indices such as the mean number of units in the system, mean waiting time, etc. Special cases are also discussed. In order to obtain approximate values of system state probabilities, the principle of maximum entropy is employed. Numerical results are also presented to validate the analytical formulae.
Highlights
In many congestion problems of the queueing systems, it is a common phenomenon that the server is always available in the service station without any interruption and the service system never fails
Many other examples are available in the area of computer communication networks and flexible manufacturing systems where the performance of such systems may be affected by service station breakdown
Our model reduces to M/G/1 queue with uniform arrival rates with time-homogeneous breakdowns and deterministic repair times [see Madan (2003)]
Summary
In many congestion problems of the queueing systems, it is a common phenomenon that the server is always available in the service station without any interruption and the service system never fails. Rn(t): The probability of n units in the queue at time t when the broken down server is under repair. Pq(z): The probability generating function of the queue length, whether the server is in operating state or in breakdown state.
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