Authors: Madhu Jain; G.C. Sharma; Richa Sharma
Addresses: Department of Mathematics, Indian Institute of Technology, Roorkee 247667, India ' Department of Mathematics, Institute of Basic Science, Khandari, Agra-282002, India ' Department of Mathematics, St. Johns College, Agra 282002, India
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.
Keywords: multi-optional services; multi-optional vacations; unreliable servers; supplementary variables; queue size; waiting times; reliability indices.
International Journal of Mathematics in Operational Research, 2013 Vol.5 No.2, pp.145 - 169
Available online: 05 Mar 2013 *Full-text access for editors Access for subscribers Purchase this article Comment on this article