Markovian Queueing System with Discouraged Arrivals and Self-Regulatory Servers

K. V. Abdul Rasheed and M. Manoharan

Advances in Operations Research, 2016, vol. 2016, 1-11

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.

Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaor:2456135

DOI: 10.1155/2016/2456135

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