Abstract
Calculation of the delay distribution of (low-priority) customers in priority queues is difficult, especially when the arrival process is correlated. In this paper, we find the generating functions of the delays of high- and low-priority customers in a discrete-time queue where the arrivals are generated by a superposition of two processes, an independent one and a correlated one that can bring an extra customer in the buffer during a slot. The latter process can be seen as a simplified model for the output process of another priority queue. As a consequence, our results can be used to estimate the delay in the second stage of a tandem queueing system with an extra exogenous arrival process. A tandem priority queue is not of product-form type and its analysis is known to be a hard problem. This paper can lead to a first approximate analysis that can later be extended to incorporate the correlation in the output process of a priority queue more accurately.
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Notes
Note that other orders within an arrival slot are possible which would change \(F_1^{(1)}(z)\), but the rest of the analysis would remain the same.
We have opted for mean buffer contents instead of mean packet delays for validation. With Little’s law, these can easily be transformed to mean packet delays.
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The authors wish to thank two reviewers for their suggestions on how to improve presentation of the paper.
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De Clercq, S., Walraevens, J. Delay analysis of a two-class priority queue with external arrivals and correlated arrivals from another node. Ann Oper Res 293, 57–72 (2020). https://doi.org/10.1007/s10479-020-03548-1
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DOI: https://doi.org/10.1007/s10479-020-03548-1