Jñānābha‎, Vol. 50 (2) (2020), (9-20)

AN UNRELIABLE BATCH ARRIVAL G-QUEUE WITH WORKING VACATION, VACATION INTERRUPTION AND MULTI-OPTIONAL SERVICES


By

 ^*Shweta Upadhyaya and Geetika Malik

Amity Institute of Applied Sciences, Amity University, Noida-201303, Uttar Pradesh, India

Email: shwetau28@gmail.com, malikgeetika21@gmail.com

(Received: October 03, 2019; Revised : June 03, 2020; Final Form : December 18, 2020)

 

 

 This paper predicts the performance of an unreliable Mx/G/1 G-queue with delayed repair. The negative customers stop functioning of the server and force the server to undergo repair. The failed server takes a random amount of time called delay time before going for repair. It is assumed that the positive customers arrive in batches and negative customers arrive singly, according to Poisson process. The server provides first phase of regular service to all arriving customers whereas it provides l types of optional services to only those who demand the same. The working vacation period of the server starts either if queue becomes empty or repairing of the server finishes. Numerical experiments are provided to show the effects of various critical system parameters on performance measures.

 

2010 Mathematics Subject Classifications: 68M20, 60K25.

Keywords and phrases: Batch arrival, G-queue, Server breakdown, Two phase service, Working Vacation, Delayed repair.