Analysis of unreliable bulk queue with statedependent arrivals

Subject Areas : Mathematical Optimization

Charan Jeet Singh ¹ , Madhu Jain ² , Binay Kumar ³

1 - Department of Mathematics, Guru Nanak Dev University, Amritsar, 143005, India
2 - Department of Mathematics, Indian Institute of Technology, Roorkee, 247667, India
3 - Department of Mathematics, M.L.U. DAV College, Phagwara, 144402, India

Received: 2020-10-01 Accepted : 2020-10-01 Published : 2013-12-01

Keywords: Supplementary variable, Breakdown, Arbitrary service time, Bulk queue, Queue size,

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.