Bulk Arrival Two Phase Retrial Queue with Two Types Service and Extended Bernoulli Vacation

J. Ebenesar Anna Bagyam; Dr. K. Udaya Chandrika

doi:https://doi.org/10.14445/22315373/IJMTT-V4I7P2

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 4 | Issue 7 | Year 2013 | Article Id. IJMTT-V4I7P2 | DOI : https://doi.org/10.14445/22315373/IJMTT-V4I7P2

Bulk Arrival Two Phase Retrial Queue with Two Types Service and Extended Bernoulli Vacation

J. Ebenesar Anna Bagyam, Dr. K. Udaya Chandrika

Abstract

This paper is concerned with the analysis of a single server batch arrival retrial queueing system with optional extended server vacation. Server provides two stages of heterogeneous service in succession. Each phase has two types of service and the customer has the option to choice any one of the two types at the time of service. After completion of the second phase service, the server takes Bernoulli vacation. After the vacation completion the server has the option to extend the vacation. The steady state distributions of the server state and the number of customers in the orbit are obtained along with other system characteristics. A general decomposition law for the model is established. Numerical results are calculated.

Keywords

Retrial, Bernoulli vacation, Extended server vacation, Stochastic decomposition

References

[1] Arivudainambi, D. and Godhandaraman, P., A Batch Arrival Retrial Queue with Two Phases of Service, Feedback and K Optional Vacations, Applied Mathematical Sciences, 6, 22, 1071 – 1087, 2012.
[2] Baruah, M., Madan, K.C. and Eldabi, T., Balking and Re-service in a Vacation Queue with Batch Arrival and Two Types of Heterogeneous Service, Journal of Mathematics Research, 4, 4, 114-124, 2012.
[3] Ebenesar Annabagyam, J. and Udayachandrika, K., Non – Persistent Retrial Queueing System with two Types of Heterogeneous Service, Global Journal of Theoretical and Mathematical Sciences, 1, 2, 157 – 164, 2011.
[4] Madan, K.C., Steady State Analysis of an MX /1 Queue with Restricted Admissibility of Arriving Batches and Modified Bernoulli Schedule Server Vacations Based on a Single Vacation Policy, Applied Mathematical Sciences, 4, 46, 2271-2292, 2010.

Citation :

J. Ebenesar Anna Bagyam, Dr. K. Udaya Chandrika, "Bulk Arrival Two Phase Retrial Queue with Two Types Service and Extended Bernoulli Vacation," International Journal of Mathematics Trends and Technology (IJMTT), vol. 4, no. 7, pp. 116-124, 2013. Crossref, https://doi.org/10.14445/22315373/IJMTT-V4I7P2