University of Sussex
Browse
- No file added yet -

Queuing models with Mittag-Leffler inter-event times

Download (1.04 MB)
journal contribution
posted on 2023-06-10, 06:54 authored by Jacob Stephen ButtJacob Stephen Butt, Nicos GeorgiouNicos Georgiou, Enrico Scalas
We study three non-equivalent queueing models in continuous time that each generalise the classical M/M/1 queue in a different way. Inter-event times in all models are Mittag-Leffler distributed, which is a heavy tail distribution with no moments. For each of the models we answer the question of the queue being at zero infinitely often (the ‘recurrence’ regime) or not (the transient regime). Aside from this question, the different analytical properties of each models allow us to answer a number of questions such as existence and description of equilibrium distributions, mixing times, asymptotic behaviour of return probabilities and moments and functional limit theorems.

History

Publication status

  • Published

File Version

  • Published version

Journal

Journal of Fractional Calculus and Applied Analysis

ISSN

1311-0454

Publisher

Springer

Volume

26

Page range

1465–1503

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Probability and Statistics Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2023-04-26

First Open Access (FOA) Date

2023-05-22

First Compliant Deposit (FCD) Date

2023-04-25

Usage metrics

    University of Sussex (Publications)

    Categories

    No categories selected

    Licence

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC