Fractional Erlang queues

Giacomo Ascione, Nikolai Leonenko and Enrica Pirozzi

Stochastic Processes and their Applications, 2020, vol. 130, issue 6, 3249-3276

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.

Keywords: Stable subordinator; Caputo fractional derivative; Mittag-Leffler function; Time-changed process; Continuous time Markov chain (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:130:y:2020:i:6:p:3249-3276

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DOI: 10.1016/j.spa.2019.09.012

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