We study some features of the transient probability distribution of a fractional M/ M/ ∞ queueing system. Such model is constructed as a suitable time-changed birth-death process. The fractional differential-difference problem is studied for the corresponding probability distribution and a fractional partial differential equation is obtained for the generating function. Finally, the interpretation of the system as an actual M/ M/ ∞ queue and as a M/M/1 queue with responsive server is given and some conditioned virtual waiting times are studied.
On the Transient Behaviour of Fractional M/ M/ ∞ Queues / Ascione, G.; Leonenko, N.; Pirozzi, E.. - 26:(2021), pp. 1-22. [10.1007/978-3-030-69236-0_1]
On the Transient Behaviour of Fractional M/ M/ ∞ Queues
Ascione G.;Pirozzi E.
2021
Abstract
We study some features of the transient probability distribution of a fractional M/ M/ ∞ queueing system. Such model is constructed as a suitable time-changed birth-death process. The fractional differential-difference problem is studied for the corresponding probability distribution and a fractional partial differential equation is obtained for the generating function. Finally, the interpretation of the system as an actual M/ M/ ∞ queue and as a M/M/1 queue with responsive server is given and some conditioned virtual waiting times are studied.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
