MATEC Web Conf.
Volume 189, 20182018 2nd International Conference on Material Engineering and Advanced Manufacturing Technology (MEAMT 2018)
|Number of page(s)||8|
|Published online||10 August 2018|
Stationary queue length of a single-server queue with negative arrivals and nonexponential service time distributions
Universiti Tunku Abdul Rahman, Jalan Sungai Long, Bandar Sungai Long, 43000 Kajang, Selangor, Malaysia
2 Multimedia University, Persiaran Multimedia, 63100 Cyberjaya, Selangor, Malaysia
3 Sunway University, Jalan Universiti, Bandar Sunway, 47500 Subang Jaya, Selangor, Malaysia
Corresponding author : firstname.lastname@example.org
In this paper, a single-server queue with negative customers is considered. The arrival of a negative customer will remove one positive customer that is being served, if any is present. An alternative approach will be introduced to derive a set of equations which will be solved to obtain the stationary queue length distribution. We assume that the service time distribution tends to a constant asymptotic rate when time t goes to infinity. This assumption will allow for finding the stationary queue length of queueing systems with non-exponential service time distributions. Numerical examples for gamma distributed service time with fractional value of shape parameter will be presented in which the steady-state distribution of queue length with such service time distributions may not be easily computed by most of the existing analytical methods.
© The Authors, published by EDP Sciences, 2018
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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