Fractional Erlang queues

Ascione, Giacomo, Leonenko, Nikolai ORCID: https://orcid.org/0000-0003-1932-4091 and Pirozzi, Enrica 2020. Fractional Erlang queues. Stochastic Processes and their Applications 130 (6) , pp. 3249-3276. 10.1016/j.spa.2019.09.012

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Abstract

We introduce a fractional generalization of the Erlang Queues M∕Ek∕1 . Such process is obtained through a time-change via inverse stable subordinator of the classical queue process. We first exploit the (fractional) Kolmogorov forward equation for such process, then we use such equation to obtain an interpretation of this process in the queuing theory context. Then we also exploit the transient state probabilities and some features of this fractional queue model, such as the mean queue length, the distribution of the busy periods and some conditional distributions of the waiting times. Finally, we provide some algorithms to simulate their sample paths. M∕Ek∕1 . Such process is obtained through a time-change via inverse stable subordinator of the classical queue process. We first exploit the (fractional) Kolmogorov forward equation for such process, then we use such equation to obtain an interpretation of this process in the queuing theory context. Then we also exploit the transient state probabilities and some features of this fractional queue model, such as the mean queue length, the distribution of the busy periods and some conditional distributions of the waiting times. Finally, we provide some algorithms to simulate their sample paths.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Elsevier
ISSN:	0304-4149
Date of First Compliant Deposit:	27 September 2019
Date of Acceptance:	25 September 2019
Last Modified:	06 Nov 2023 20:04
URI:	https://orca.cardiff.ac.uk/id/eprint/125715

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