On a fractional queueing model with catastrophes
Probability
2021-07-13 v3 Statistics Theory
Statistics Theory
Abstract
A queue with catastrophes is a modified queue model for which, according to the times of a Poisson process, catastrophes occur leaving the system empty. In this work, we study a fractional queue with catastrophes, which is formulated by considering fractional derivatives in the Kolmogorov's Forward Equations of the original Markov process. For the resulting fractional process, we obtain the state probabilities, the mean and the variance for the number of customers at any time. In addition, we discuss the estimation of parameters.
Keywords
Cite
@article{arxiv.2012.09317,
title = {On a fractional queueing model with catastrophes},
author = {Matheus de Oliveira Souza and Pablo Martin Rodriguez},
journal= {arXiv preprint arXiv:2012.09317},
year = {2021}
}
Comments
Revised version accepted for publication at Applied Mathematics and Computation