An alternative approach in finding the stationary queue length distribution of a queueing system with negative customers

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 con...

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Bibliographic Details
Published inITM Web of Conferences Vol. 36; p. 4001
Main Authors Koh, Siew Khew, Chin, Ching Herny, Tan, Yi Fei, Ng, Tan Ching
Format Journal Article Conference Proceeding
LanguageEnglish
Published Les Ulis EDP Sciences 2021
Subjects
Customers
Queuing theory
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Summary: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.
ISSN:2271-2097
2431-7578
2271-2097
DOI:10.1051/itmconf/20213604001