A feedback queue with additional optional batch service

R. Kalayanaraman, S. Sumathy


A single server infinite capacity queuing system with Poisson arrival process along with Bernoulli feedback decision process is considered wherein the server provides two types of service. The first essential service is rendered one by one to all the customers and second optional service is given in batches of fixed size b. For this model the steady state probability generating function for the queue length process has been obtained and average queue length has been found explicitly. Results for particular cases are obtained and some numerical results are presented to test the feasibility of the queuing model.


Bernoulli process; Queue length distribution; Feedback;

Full Text:



G.R. D’ Avignon and R.L. Disney, Management Sciences, Vol.24, No. 2, (1976)168 – 180.

R. Kalyanaraman, N. Thillai Govindan and G. Ayyappan, Octogon, Vol.10, No.2, (2002)583-591.

L. Kleinrock, Queuing Systems, Vol.I : Theory, Wiley, New York, 1975.

K.C. Madan, J.Appl. Prob., Vol.12, (1975)195-200.

K.C. Madan, IAPQR Transactions, Vol. 17, No.1, 1992.

L. Takacs, Bell Systems Technical Journal, Vol.42, (1963)509-519.

DOI: https://doi.org/10.11113/mjfas.v6n2.194


  • There are currently no refbacks.

Copyright (c) 2014 R. Kalayanaraman, S. Sumathy

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Copyright © 2005-2019 Penerbit UTM Press, Universiti Teknologi Malaysia. Disclaimer: This website has been updated to the best of our knowledge to be accurate. However, Universiti Teknologi Malaysia shall not be liable for any loss or damage caused by the usage of any information obtained from this website.