Cost function analysis of a single-server queueing system with Poisson input stream and Erlang-k service time

Stefan Mirchevski and Verica Bakeva

Applied Mathematics and Computation, 2024, vol. 475, issue C

Abstract: In this paper, the cost function of a single-server queueing system with Poisson input stream and Erlang-k service time will be analyzed. Treated as a function of the traffic intensity ρ, with respect to some known constants, we will show that its stationary points are solutions of a fourth-degree polynomial equation with real coefficients. Moreover, an explicit form of these solutions is given and it is shown the function reaches a minimum value at some of these points. For illustration, a numerical analysis of the cost function is carried out by changing the values of the costs, which are changed according to the principle of arithmetic progression. Also, a statistical analysis of the relationship between optimal solutions ρ⁎ and Φ(ρ⁎) is done.

Keywords: Poisson input stream; Erlang-k service time; Cost function; Numerical analysis; Statistical analysis (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300324002017
Full text for ScienceDirect subscribers only

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:eee:apmaco:v:475:y:2024:i:c:s0096300324002017

DOI: 10.1016/j.amc.2024.128729

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().