Skip to content
DraconiticResearch
Search Sources API
203,948 studies31 sourcesUpdated just now
Peer-reviewedCC BY 4.0Mathematics

Improved Bounds on the Rate of Convergence to Stationarity of the M/M/N Queue as Both the Number of Servers and the Arrival Rate Grow Large

  • Alexander Zeifman1,2
  • Yacov Satin1
  • Rostislav Razumchik2
  1. 1Department of Applied Mathematics, Vologda State University, 160000 Vologda, Russia
  2. 2Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 44-2 Vavilov Str., 119133 Moscow, Russia
Open at sourceDOICite

Abstract

Consideration is given to the stable M/M/N/∞ queueing system as both the arrival rate and the number of servers tend to infinity, including the Halflin–Whitt regime. One is interested in the asymptotic behavior of the rate of convergence to stationarity of the total number of customers in the system. Bounds for the rate of convergence are provided, which improve upon those available in the literature. The derivations, simpler than those available in the literature, are based on the well-known logarithmic norm method. It is also shown that the obtained results can be adopted to M/M/N/N+R queues as well.

Related

  1. Ordinary Nonconvex SGD under Distance-Dependent Moments: Finite-Horizon Stationarity and Nagaev Bounds
    Wei Biao Wu
    arXivPreprintarXiv licenceFull textStatisticsarXiv
  2. Second-Order Stationarity with Common Random Losses: Matching Tolerance Bounds
    Wendao Wu, Haihan Zhang, Chenheng Zhang +5
    arXivPreprintarXiv licenceFull textOptimisation & controlarXiv
  3. Improved convergence radius of the Fer expansion for Hermitian generators
    Lorenzo Bagnasacco, Vittorio Giovannetti
    arXivPreprintCC BY 4.0Full textMathematical physicsQuantum physics & quantum informationarXiv
  4. Improved bounds for the two-point logarithmic Chowla conjecture
    Cédric Pilatte
    Journal of the American Mathematical SocietyPeer-reviewedLicence not statedFull text22 citedAlgebra & number theoryOpenAlex
  5. An Adaptive Symplectic Proximal Point Algorithm: Faster Convergence and Improved Numerical Performance
    Yi Zhang
    arXivPreprintCC BY 4.0Full textOptimisation & controlarXiv

Cite

BibTeXRIS
BibTeX
@article{zeifman2026improved,
  title = {{Improved Bounds on the Rate of Convergence to Stationarity of the M/M/N Queue as Both the Number of Servers and the Arrival Rate Grow Large}},
  author = {Alexander Zeifman and Yacov Satin and Rostislav Razumchik},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14213932},
  url = {https://www.mdpi.com/2227-7390/14/21/3932},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Improved Bounds on the Rate of Convergence to Stationarity of the M/M/N Queue as Both the Number of Servers and the Arrival Rate Grow Large
AU  - Alexander Zeifman
AU  - Yacov Satin
AU  - Rostislav Razumchik
PY  - 2026
DA  - 2026/10/28
JO  - Mathematics
DO  - 10.3390/math14213932
UR  - https://www.mdpi.com/2227-7390/14/21/3932
AB  - Consideration is given to the stable M/M/N/∞ queueing system as both the arrival rate and the number of servers tend to infinity, including the Halflin–Whitt regime. One is interested in the asymptotic behavior of the rate of convergence to stationarity of the total number of customers in the system. Bounds for the rate of convergence are provided, which improve upon those available in the literature. The derivations, simpler than those available in the literature, are based on the well-known logarithmic norm method. It is also shown that the obtained results can be adopted to M/M/N/N+R queues as well.
SN  - 2227-7390
ER  -