ITM Web Conf.
Volume 36, 2021The 16th IMT-GT International Conference on Mathematics, Statistics and their Applications (ICMSA 2020)
|Number of page(s)||8|
|Section||Operations Research/Applied Mathematics|
|Published online||26 January 2021|
An alternative approach in finding the stationary queue length distribution of a queueing system with negative customers
Centre for Mathematical Sciences, Universiti Tunku Abdul Rahman, Jalan Sungai Long, Bandar Sungai Long, 43000 Kajang, Selangor, Malaysia
2 Multimedia University, Persiaran Multimedia, 63100 Cyberjaya, Selangor, Malaysia
3 Universiti Tunku Abdul Rahman, Jalan Sungai Long, Bandar Sungai Long, 43000 Kajang, Selangor, Malaysia
* Corresponding author: firstname.lastname@example.org
A single-server queueing system with negative customers is considered in this paper. One positive customer will be removed from the head of the queue if any negative customer is present. The distribution of the interarrival time for the positive customer is assumed to have a rate that tends to a constant as time t tends to infinity. An alternative approach will be proposed to derive a set of equations to find the stationary probabilities. The stationary probabilities will then be used to find the stationary queue length distribution. Numerical examples will be presented and compared to the results found using the analytical method and simulation procedure. The advantage of using the proposed alternative approach will be discussed in this paper.
© The Authors, published by EDP Sciences, 2021
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