Analysis of $ M^{\times} / G / 1 $ queueing system with setup time, server interruption and multiple vacation

E. Ramesh Kumara,* and N. Saranyab

Analysis of $ M^{\times} / G / 1 $ queueing system with setup time, server interruption and multiple vacation

Authors :

E. Ramesh Kumar^a,*and N. Saranya^b

Author Address :

^a,bDepartment of Mathematics, CMS college of Science and Commerce, Coimbatore-641049, Tamil Nadu, India.

*Corresponding author.

Abstract :

In this paper we analyse an $M^{\times} /G/1$ queue setup time with main server interruptions and a stand-by-server replaces the main server during any potential stop. The main server has six statues in this system where it is either services the customers (active) or it does not work because of some of the reasons original vacation, extended vacation, setup time, when it is broken-down the repairs did not start yet (delay time) and broken-down servers under repairs. The arrivals are assumed to attend the system in bathes.

Here all the distributions of the service, vacation, extended vacation, repairs, Delay and setup times all follow general distributions, while the breakdown times the stand-by-service time and setup time are exponentially distributed.

Keywords :

Server vacation, extended vacation, server breakdown, repair, delay and setup time.

DOI :

Article Info :

Received : May 08, 2015; Accepted : June 19, 2015.