Dovhai B.V., Matsak I.K.
Asymptotic behavior of extreme values of queue length in M/M/m systems

The paper investigates the asymptotic behavior of almost surely maximum length in queueing systems. For a system M / M / m, 1≤ m< ∞, a statement of the type of the law of iterated logarithm is established. We also consider the case m = ∞ for which the asymptotic behavior is much different. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: asymptotic behavior almost surely, extreme values of queue length, M, m, queuing system M, Queueing networks, Queueing theory, Asymptotic behaviors, Extreme value, Law of iterated logarithm, Queue lengths, Queueing system, Queuing systems, Asymptotic analysis

Cite:
Dovhai B.V., Matsak I.K. (2019). Asymptotic behavior of extreme values of queue length in M/M/m systems. Cybernetics and Systems Analysis, 55 (2), 171-179. doi: https://doi.org/10.1007/s10559-019-00137-4 http://jnas.nbuv.gov.ua/article/UJRN-0000968707 [In Ukrainian].