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2020 | 30 | 4 | 57-64

Article title

On the law of the iterated logarithm in hybrid multiphase queueing systems

Content

Title variants

Languages of publication

EN

Abstracts

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.

Year

Volume

30

Issue

4

Pages

57-64

Physical description

Contributors

  • Institute of Data Science and Digital Technologies, Akademijos St. 4, Vilnius, LT-04812, Lithuania

References

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  • BOROVKOV A.A., Asymptotic Methods of the Queueing Theory, Nauka, Moscow 1980, 420 (in Russian).
  • IGLEHART D.L., Limiting diffusion approximations for many queues and the repairman problem, J. Appl. Prob., 1965, 2, 429–441.
  • IGLEHART D.L., Multiple channel queues in heavy traffic. IV. Law of the iterated logarithm, Zeits. Wahrs.Theory, 1971, 17, 168–180.
  • IGLEHART D.L., Functional limit theorems for the GI/G/1 queue in light traffic, Adv. Appl. Prob., 1971, 3, 269–281.
  • IGLEHART D.L., Extreme values in the GI/G/1 queue in light traffic, Ann. Math. Stat., 1972, 43, 627–635.
  • IGLEHART D.L., Weak convergence in queueing theory, Adv. Appl. Prob., 1973, 5, 570–594.
  • IGLEHART D.L., WHITT W., Multiple channel queues in heavy traffic. I, Adv. Appl. Prob., 1970, 2, 150–177.
  • IGLEHART D.L., WHITT W., Multiple channel queues in heavy traffic. II. Sequences, networks and batches, Adv. Appl. Prob., 1970, 2, 355–369.
  • KYPRIANOU E., The virtual waiting time of the GI/G/1 queue in heavy traffic, Adv. Appl. Prob., 1974, 3, 249–269.
  • MINKEVIČIUS S., Transient phenomena in multiphase queues, Liet. Mat. Rin., 1991, 31 (1), 136–145.
  • MINKEVIČIUS S., On the law of the iterated logarithm in multiphase queues, Liet. Mat. Rin., 1995, 35 (1), 360–365.
  • MINKEVIČIUS S., On the law of the iterated logarithm in multiserver open queueing networks, Stochastics, 2014, 86, 46–59.
  • 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.
  • 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
  • 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.
  • REIMAN M., Open queueing networks in heavy traffic, Math. Oper. Res., 1984, 9, 441–459.
  • SAKALAUSKAS L., MINKEVIČIUS S., On the law of the iterated logarithm in open queueing networks, Eur. J. Oper. Res., 2000, 120, 632–640.
  • STRASSEN V., An invariance principle for the law of the iterated logarithm, Zeits. Wahrs. Theory, 1964, 3, 211–226.
  • WHITBY B., Artificial Intellgence. A beginners guide, Oneworld, Oxford 2004.
  • WHITT W., Heavy traffic limit theorems for queues. A survey, Lecture Notes in Economics and Mathematical Systems, 98, Springer-Verlag, Berlin 1974

Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.desklight-08ee5fbf-bcf9-4e68-94ee-85cad137ffe8
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