Journal
PERFORMANCE EVALUATION
Volume 163, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.peva.2023.102383
Keywords
Laplace -Stieltjes transform; Phase -type distribution; Inter -departure time distribution; PH/PH / c queue; Correlation
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This paper introduces the Laplace-Stieltjes transform (LST) and the two-dimensional joint LST for the inter-departure time distribution in a PH/PH/c queue. These LSTs are constructed using the properties of phase-type (PH) random variables and the steady-state distribution of the continuous-time Markov chain. Numerical examples are provided to validate the approach, and the correlation between consecutive inter-departure times in various queues is analyzed.
In this paper, we introduce the Laplace-Stieltjes transform (LST) of the inter-departure time distribution in a PH/PH/c queue, and the two-dimensional joint LST of two consecutive inter -departure times to construct their correlation structure. We exploit the properties of phase-type (PH) random variables, as well as the steady-state distribution of the underlying continuous -time Markov chain in a PH/PH/c queue to construct these LSTs. We demonstrate our approach through numerical examples, while validating the results. Later, we analyze the correlation be-tween two consecutive inter-departure times for various PH/PH/c queues. We observe that, if the fundamental elements of the queue have high (low) variability, then the correlation is positive (negative).
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