Fractional Queues with Catastrophes and Their Transient Behaviour
AbstractStarting 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. View Full-Text
Share & Cite This Article
Ascione, G.; Leonenko, N.; Pirozzi, E. Fractional Queues with Catastrophes and Their Transient Behaviour. Mathematics 2018, 6, 159.
Ascione G, Leonenko N, Pirozzi E. Fractional Queues with Catastrophes and Their Transient Behaviour. Mathematics. 2018; 6(9):159.Chicago/Turabian Style
Ascione, Giacomo; Leonenko, Nikolai; Pirozzi, Enrica. 2018. "Fractional Queues with Catastrophes and Their Transient Behaviour." Mathematics 6, no. 9: 159.
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.