Analysis of Non-Steady Queue-Length Distribution in a Finite-Buffer Model with Group Arrivals and Power Saving Mechanism with Setups

Wojciech M. Kempa () and Dariusz Kurzyk
Additional contact information
Wojciech M. Kempa: Department of Mathematics Applications and Methods for Artificial Intelligence, Faculty of Applied Mathematics, Silesian University of Technology, 23 Kaszubska Str., 44-100 Gliwice, Poland
Dariusz Kurzyk: Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, 5 Bałtycka Str., 44-100 Gliwice, Poland

Energies, 2022, vol. 15, issue 22, 1-15

Abstract: In the manuscript, a probability distribution of the queue length is studied in a model with group Markov arrivals, arbitrarily distributed service times and finite waiting room. After the period of suspension of service due to lack of packets, each new busy period is preceded by a random setup time. Integral equations for time-dependent queue-length distribution are derived by identifying renewal moments in the operation of the system and by applying total probability law. The representation for the solution of the system is found in terms of Laplace transforms. Computational examples illustrating the impact of system parameters on the queue-length distribution are included.

Keywords: finite buffer; integral equations; queue-size distribution; setup time; transient state (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/1996-1073/15/22/8471/pdf (application/pdf)
https://www.mdpi.com/1996-1073/15/22/8471/ (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:jeners:v:15:y:2022:i:22:p:8471-:d:971215

Access Statistics for this article

Energies is currently edited by Ms. Agatha Cao

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