Fractional queues with catastrophes and their transient behaviour

Ascione, G, Leonenko, Nikolai ORCID: https://orcid.org/0000-0003-1932-4091 and Pirozzi, E 2018. Fractional queues with catastrophes and their transient behaviour. Mathematics 6 (9) , 159. 10.3390/math6090159

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Abstract

Starting from the definition of fractional M/M/1 queue given in the reference by Cahoy et al. in 2015 and M/M/1 queue with catastrophes given in the reference by Di Crescenzo et al. in 2003, we define and study a fractional M/M/1 queue with catastrophes. In particular, we focus our attention on the transient behaviour, in which the time-change plays a key role. We first specify the conditions for the global uniqueness of solutions of the corresponding linear fractional differential problem. Then, we provide an alternative expression for the transient distribution of the fractional M/M/1 model, the state probabilities for the fractional queue with catastrophes, the distributions of the busy period for fractional queues without and with catastrophes and, finally, the distribution of the time of the first occurrence of a catastrophe.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	MDPI
ISSN:	2227-7390
Date of First Compliant Deposit:	31 August 2018
Date of Acceptance:	31 August 2018
Last Modified:	19 Nov 2024 07:00
URI:	https://orca.cardiff.ac.uk/id/eprint/114527

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