Multiple vacation policy for MX/Hk/1 queue with un-reliable server

Subject Areas : Mathematical Optimization

Madhu Jain ¹ , Richa Sharma ² , Gokul Chandra Sharma ³

1 - Department of Mathematics, IIT, Roorkee, 247667, India
2 - Department of Mathematics, JK Lakshmipat University, Jaipur, 302026, India
3 - Department of Mathematics, I.B.S., Khandari, Agra, 282002, India

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

Keywords: Batch arrival, k-type hyper-exponential distribution, State-dependent rates, Maximum entropy principle, Long-run probabilities, Un-reliable server, Queue length,

Abstract :

This paper studies the operating characteristics of an MX/Hk/1 queueing system under multiple vacation policy. It is assumed that the server goes for vacation as soon as the system becomes empty. When he returns from a vacation and there is one or more customers waiting in the queue, he serves these customers until the system becomes empty again, otherwise goes for another vacation. The breakdown and repair times of the server are assumed to follow a negative exponential distribution. By using a generating function, we derive various performance indices. The approximate formulas for the probability distribution of the waiting time of the customers in the system by using the maximum entropy principle (MEP) are obtained. This approach is accurate enough for practical purposes and is a useful method for solving complex queueing systems. The sensitivity analysis is carried out by taking a numerical illustration.