An M/PH/1 queue with workload-dependent processing speed and vacations

Yutaka Sakuma (), Onno Boxma () and Tuan Phung-Duc ()
Additional contact information
Yutaka Sakuma: National Defense Academy of Japan
Onno Boxma: Eindhoven University of Technology
Tuan Phung-Duc: University of Tsukuba

Queueing Systems: Theory and Applications, 2021, vol. 98, issue 3, No 7, 373-405

Abstract: Abstract Motivated by the trade-off issue between delay performance and energy consumption in modern computer and communication systems, we consider a single-server queue with phase-type service requirements and with the following two special features: Firstly, the service speed is a piecewise constant function of the workload. Secondly, the server switches off when the system becomes empty, only to be activated again when the workload reaches a certain threshold. For this system, we obtain the steady-state workload distribution and its moments of any order. We use this result to choose the activation threshold such that a certain cost function, involving processing costs, activation costs and mean workload, is minimized.

Keywords: Workload-dependent service; Phase-type demand; Matrix exponential solution; Autoscaling; 60K25; 60K05; 90B22 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11134-021-09701-2 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:queues:v:98:y:2021:i:3:d:10.1007_s11134-021-09701-2

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/11134/

DOI: 10.1007/s11134-021-09701-2

Access Statistics for this article

Queueing Systems: Theory and Applications is currently edited by Sergey Foss

More articles in Queueing Systems: Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().