A Lévy-Driven Stochastic Queueing System with Server Breakdowns and Vacations

Yi Peng and Jinbiao Wu
Additional contact information
Yi Peng: School of Mathematical Science, Changsha Normal University, Changsha 410100, China
Jinbiao Wu: School of Mathematics and Statistics, Central South University, Changsha 410083, China

Mathematics, 2020, vol. 8, issue 8, 1-12

Abstract: Motivated by modelling the data transmission in computer communication networks, we study a Lévy-driven stochastic fluid queueing system where the server may subject to breakdowns and repairs. In addition, the server will leave for a vacation each time when the system is empty. We cast the workload process as a Lévy process modified to have random jumps at two classes of stopping times. By using the properties of Lévy processes and Kella–Whitt martingale method, we derive the limiting distribution of the workload process. Moreover, we investigate the busy period and the correlation structure. Finally, we prove that the stochastic decomposition properties also hold for fluid queues with Lévy input.

Keywords: fluid queueing systems; Lévy processes; martingales; queues with Lévy input; server breakdowns and vacations; stochastic decomposition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/8/1239/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/8/1239/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:8:p:1239-:d:391568

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().