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2020 | 30 | nr 4 | 57-64
Tytuł artykułu

On The Law of the Iterated Logarithm in Hybrid Multiphase Queueing Systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The model of a hybrid multiphase queueing system (HMQS) has been developed to measure the performance of complex computer networks working under conditions of heavy traffic. Two probability limit theorems (laws of the iterated logarithm, LIL) are presented for a queue length of jobs in HMQS. (original abstract)
Rocznik
Tom
30
Numer
Strony
57-64
Opis fizyczny
Twórcy
  • Institute of Data Science and Digital Technologies, Vilnius, Lithuania
Bibliografia
  • [1] BILLINGSLEY P., Convergence of probability measures, Nauka, Moscow 1977, 352 (2), 137-168 (in Russian).
  • [2] BOROVKOV A.A., Probability Processes in the Queueing Theory, Nauka, Moscow 1972, 300 (in Russian).
  • [3] BOROVKOV A.A., Asymptotic Methods of the Queueing Theory, Nauka, Moscow 1980, 420 (in Russian).
  • [4] IGLEHART D.L., Limiting diffusion approximations for many queues and the repairman problem, J. Appl. Prob., 1965, 2, 429-441.
  • [5] IGLEHART D.L., Multiple channel queues in heavy traffic. IV. Law of the iterated logarithm, Zeits. Wahrs. Theory, 1971, 17, 168-180.
  • [6] IGLEHART D.L., Functional limit theorems for the GI/G/1 queue in light traffic, Adv. Appl. Prob., 1971, 3, 269-281.
  • [7] IGLEHART D.L., Extreme values in the GI/G/1 queue in light traffic, Ann. Math. Stat., 1972, 43, 627-635.
  • [8] IGLEHART D.L., Weak convergence in queueing theory, Adv. Appl. Prob., 1973, 5, 570-594.
  • [9] IGLEHART D.L., WHITT W., Multiple channel queues in heavy traffic. I, Adv. Appl. Prob., 1970, 2, 150-177.
  • [10] IGLEHART D.L., WHITT W., Multiple channel queues in heavy traffic. II. Sequences, networks and batches, Adv. Appl. Prob., 1970, 2, 355-369.
  • [11] KYPRIANOU E., The virtual waiting time of the GI/G/1 queue in heavy traffic, Adv. Appl. Prob., 1974, 3, 249-269.
  • [12] MINKEVIČIUS S., Transient phenomena in multiphase queues, Liet. Mat. Rin., 1991, 31 (1), 136-145.
  • [13] MINKEVIČIUS S., On the law of the iterated logarithm in multiphase queues, Liet. Mat. Rin., 1995, 35 (1), 360-365.
  • [14] MINKEVIČIUS S., On the law of the iterated logarithm in multiserver open queueing networks, Stochastics, 2014, 86, 46-59.
  • [15] MINKEVIČIUS S., On the analysis of the law of the iterated logarithm in open queueing networks, Int. J. Comp. Math., Comp. Syst. Theory, 2019, 4 (2), 76-94.
  • [16] MINKEVIČIUS S., Fluid limits for the waiting time of a customer in multiphase queues, 2019, https://elib.bsu.by/bitstream/123456789/233376/1/249-252.pdf
  • [17] MINKEVIČIUS S., GREIČIUS E., Heavy Traffic Limits for the Extreme Waiting Time in Multiphase Queueing Systems, Meth. Comp. Appl. Prob., 2019, 21 (1), 109-124.
  • [18] REIMAN M., Open queueing networks in heavy traffic, Math. Oper. Res., 1984, 9, 441-459.
  • [19] SAKALAUSKAS L., MINKEVIČIUS S., On the law of the iterated logarithm in open queueing networks, Eur. J. Oper. Res., 2000, 120, 632-640.
  • [20] STRASSEN V., An invariance principle for the law of the iterated logarithm, Zeits. Wahrs. Theory, 1964, 3, 211-226.
  • [21] WHITBY B., Artificial Intelligence. A beginners guide, Oneworld, Oxford 2004.
  • [22] WHITT W., Heavy traffic limit theorems for queues. A survey, Lecture Notes in Economics and Mathematical Systems, 98, Springer-Verlag, Berlin 1974, 307-350.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ekon-element-000171614691
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