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Advances in Operations Research
Volume 2016, Article ID 2456135, 11 pages
http://dx.doi.org/10.1155/2016/2456135
Research Article

Markovian Queueing System with Discouraged Arrivals and Self-Regulatory Servers

Department of Statistics, University of Calicut, Kerala 673 635, India

Received 28 September 2015; Revised 1 February 2016; Accepted 28 March 2016

Academic Editor: Ahmed Ghoniem

Copyright © 2016 K. V. Abdul Rasheed and M. Manoharan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider discouraged arrival of Markovian queueing systems whose service speed is regulated according to the number of customers in the system. We will reduce the congestion in two ways. First we attempt to reduce the congestion by discouraging the arrivals of customers from joining the queue. Secondly we reduce the congestion by introducing the concept of service switches. First we consider a model in which multiple servers have three service rates , , and (), say, slow, medium, and fast rates, respectively. If the number of customers in the system exceeds a particular point or , the server switches to the medium or fast rate, respectively. For this adaptive queueing system the steady state probabilities are derived and some performance measures such as expected number in the system/queue and expected waiting time in the system/queue are obtained. Multiple server discouraged arrival model having one service switch and single server discouraged arrival model having one and two service switches are obtained as special cases. A Matlab program of the model is presented and numerical illustrations are given.