Unreliable server M/G/1 queue with multi-optional services and multi-optional vacations. (1st January 2013)

• Record Type: Journal Article
• Authors: Jain, Madhu; Sharma, G.C.; Sharma, Richa
• Is Part Of: International journal of mathematics in operational research. Volume 5:Number 2(2013)
• Page Start: 145
• Page End: 169
• Publication Date: 2013-01-01
• Subjects: multi-optional services -- multi-optional vacations -- unreliable server -- supplementary variables -- queue size -- waiting time -- reliability indices; Operations research -- Mathematical models -- Periodicals; Operations research -- Mathematics -- Periodicals; Decision making -- Mathematical models -- Periodicals; 658.4033
• Languages: English
• ISSNs: 1757-5850

Abstract

This paper deals with an M/G/1 queue with multiple optional services and multiple optional vacations for an unreliable server queue. All arriving customers require a First Essential Service (FES), while only some of them ask for other optional services. The stability and ergodicity condition for the model has been discussed. By introducing supplementary variables and employing the generating function technique, we derive the system size distribution at the random epoch as well as the departure epoch. Waiting time distribution and some other queuing and reliability measures have also been obtained. The sensitivity analysis has been facilitated by taking numerical illustrations to explore the effect of the different parameters on various performance indices.