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.

Fractional Erlang queues

Ascione Giacomo;Pirozzi Enrica
2020

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/764472
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