Stationary queue length distribution of a continuous-time queueing system with negative arrival

This paper studies a continuous-time single-server infinite capacity queueing system with two types of customer: positive and negative customers. Positive customers are ordinary customers that receives service in the server. A negative customer that arrives to the system according to a Poisson proce...

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Bibliographic Details
Published inJournal of physics. Conference series Vol. 1132; no. 1; pp. 12057 - 12064
Main Authors Chin, C H, Koh, S K, Tan, Y F, Pooi, A H, Goh, Y K
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 01.11.2018
Subjects
Continuous time systems
Customer services
Customers
Queuing theory
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Summary:This paper studies a continuous-time single-server infinite capacity queueing system with two types of customer: positive and negative customers. Positive customers are ordinary customers that receives service in the server. A negative customer that arrives to the system according to a Poisson process with rate γ will remove one positive customer at the head upon its arrival. By assuming that the interarrival time and service time distributions tend to a constant when time t goes to infinity, a set of equations will be derived by using an alternative approach to find the stationary queue length distribution. Numerical results obtained by the alternative approach will be compared to those obtained by the existing method and verified by the simulation procedure.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/1132/1/012057