Abstract
We analyse a priority queueing system with a normal queue (high priority) and an orbit (low priority). Only the first customer in orbit can retry during times that the queue and server are empty (constant retrial policy). In contrast with existing literature, we assume different service time distributions for the high- and low-priority customers. We obtain closed-form expressions for the probability generating function of the number of customers in queue and orbit, in steady state, and for the Laplace Stieltjes transforms of the stationary waiting times of both type of customers.
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Notes
- 1.
- 2.
Note from Eq. (24) that \(P_2(0,z_1,z_2)\) is independent of \(z_1\).
- 3.
The effective retrial time of class-2 customer starts when the customer is for the first time the head of the orbit and ends when he enters the server.
- 4.
The coefficient of variation of a distribution is defined as the ratio of the standard deviation to the mean.
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Acknowledgments
The authors wish to thank Tuan Phung-Duc and Dieter Claeys for preliminary discussions about the model in this paper.
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Devos, A., Walraevens, J., Bruneel, H. (2018). A Priority Retrial Queue with Constant Retrial Policy. In: Takahashi, Y., Phung-Duc, T., Wittevrongel, S., Yue, W. (eds) Queueing Theory and Network Applications. QTNA 2018. Lecture Notes in Computer Science(), vol 10932. Springer, Cham. https://doi.org/10.1007/978-3-319-93736-6_1
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