Powiadomienia systemowe
- Sesja wygasła!
- Sesja wygasła!
Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
The target of this research in the queueing theory is to prove the law of the iterated logarithm (LIL) under the conditions of heavy traffic in multiphase queueing systems. In this paper, the LIL for global maxima is proved in the phases of a queueing system studied for an important probability characteristic of the system (total waiting time of a customer and waiting time of a customer).
Czasopismo
Rocznik
Tom
Strony
575--588
Opis fizyczny
Bibliogr. 25 poz.
Twórcy
autor
- Institute of Mathematics and Informatics Akademijos 4, 2600 Vilnius, Lithuania
autor
- Vilnius Gediminas Technical University Sauletekio 11, 2040 Vilnius, Lithuania
Bibliografia
- Billingsley, P. (1977) Convergence of probability measures. Nauka, Moscow.
- Bingham, N. (1986) Variants on the law of the iterated logarithm. Bulletin London Mathematical Society 18, 433–467.
- Borovkov, A. (1972) Probability processes in theory of queues. Nauka, Moscow, (in Russian).
- Borovkov, A. (1980) Asymptotic methods in theory of queues. Nauka, Moscow, (in Russian).
- Kuo-Hwa Chang (1997) Extreme and high-level sojourns of the single serverqueue in heavy traffic. Queueing Systems 27, 17–35.
- Grigelionis, Br. and Mikulevicius, R. (1987) Functional limit theorems for a queueing system in heavy traffic. Lietuvos Matematikos Rinkinys 27, 441–454, 660–673.
- Harrison, J. (1978) The diffusion approximation for tandem queues in heavy traffic. Advances in Applied Probability 10, 886–905.
- Harrison, J. (1985) Brownian Motion and Stochastic Flow Processes. Wiley, New York.
- Harrison, J. and Nguyen, V. (1993) Brownian models of multiclass queueing networks: current status and open problems. Queueing Systems 13, 5–40.
- Iglehart, D. (1971) Multiple channel queues in heavy traffic. IV. Zeitschrift fur Wahrscheinlichkeitstheorie und Verwandte Gebiete 17(1), 168–180.
- Iglehart, D. (1972) Extreme values in the GI/G/1 queue. Annals of Mathematical Statistics 43 (1), 627–635.
- Iglehart, D. (1973) Weak convergence in queueing theory. Advances in Applied Probability 5, 570–594.
- Karpelevich, F. I. and Kreinin, A. I. (1994) Heavy traffic limits for multiphase queues. American Mathematical Society, Providence, Rhode Island.
- Kendall, D. (1961) Some problems in the theory of queues. J. R. Statist. Soc., Ser. B. 13, 151–185.
- Kingman, J. (1962a) On queues in heavy traffic. J. R. Statist. Soc. 24, 383–392.
- Kingman, J. (1962b) The single server queue in heavy traffic. Proc. Camb. Phil. Soc. 57, 902–904.
- Kobyashi, H. (1974) Application of the diffusion approximation to queueing networks. Journal of ACM, 21, 316–328.
- Minkevicius, S. (1986) Weak convergence in multiphase queues. Lietuvos Matematikos Rinkinys 26, 717–722.
- Minkevicius, S. (1991) Transient phenomena in multiphase queues. Lietuvos Matematikos Rinkinys 31, 136–145.
- Minkevicius, S. (1997) On the law of the iterated logarithm in multiphase queueing systems. II. Informatica 8, 367–376.
- Prohorov, Y. (1963) Transient phenomena in queues. Lietuvos Matematikos Rinkinys 3, 199–206.
- Reiman, M. (1984) Open queueing networks in heavy traffic. Mathematics of operations research, 9, 441–459.
- Sakalauskas, L. and Minkevicius, S. (2000) On the law of the iterated logarithm in open queueing networks. European Journal of Operational Research 120, 632–640.
- Strassen, V. (1964) An invariance principle for the law of the iterated logarithm. Zeitschrift fur Wahrscheinlichkeitstheorie und Verwandte Gebiete 3, 211–226.
- Whitt, W. (1974) Heavy Traffic Limit Theorems for Queues: A Survey. Lecture Notes in Economic and Mathematical Systems 98, Springer-Verlag, Berlin-Heidelberg-New York, 307–350.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0007-0104