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

Journal of Industrial Engineering International

دوره 9، شماره 1، اسفند 2013   

نویسندگان

Madhu Jain¹؛ Richa Sharma^{* 2}؛ Gokul Chandra Sharma³

¹Department of Mathematics, IIT, Roorkee, 247667, India

²Department of Mathematics, JK Lakshmipat University, Jaipur, 302026, India

³Department of Mathematics, I.B.S., Khandari, Agra, 282002, India

چکیده

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.

کلیدواژه‌ها

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