Combinatory methods and stochastic Kolmogorov equations in the theory ofqueues with one server
HTML articles powered by AMS MathViewer
- by V. E. Beneš
- Trans. Amer. Math. Soc. 94 (1960), 282-294
- DOI: https://doi.org/10.1090/S0002-9947-1960-0112182-9
- PDF | Request permission
References
- Norman T. J. Bailey, A continuous time treatment of a simple queue using generating functions, J. Roy. Statist. Soc. Ser. B 16 (1954), 288–291. MR 69421, DOI 10.1111/j.2517-6161.1954.tb00172.x
- V. E. Beneš, On queues with Poisson arrivals, Ann. Math. Statist. 28 (1957), 670–677. MR 91571, DOI 10.1214/aoms/1177706878
- J. L. Doob, Stochastic processes, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1953. MR 0058896
- David G. Kendall, Some problems in the theory of queues, J. Roy. Statist. Soc. Ser. B 13 (1951), 151–173; discussion: 173–185. MR 47944, DOI 10.1111/j.2517-6161.1951.tb00080.x A. Khintchine, Matematicheskaya Teoriya Statsionarnoi Ocheredi, Mat. Sb. vol. 39 (1932) pp. 73-84.
- D. V. Lindley, The theory of queues with a single server, Proc. Cambridge Philos. Soc. 48 (1952), 277–289. MR 46597, DOI 10.1017/s0305004100027638
- Edgar Reich, On the integrodifferential equation of Takács. I, Ann. Math. Statist. 29 (1958), 563–570. MR 93834, DOI 10.1214/aoms/1177706632 —, On the mixed-type Markov process of Takács, Abstracts of the International Congress of Mathematicians, Edinburgh, 1958.
- Walter L. Smith, On the distribution of queueing times, Proc. Cambridge Philos. Soc. 49 (1953), 449–461. MR 54870, DOI 10.1017/s0305004100028620
- Lajos Takács, Investigation of waiting time problems by reduction to Markov processes, Acta Math. Acad. Sci. Hungar. 6 (1955), 101–129 (English, with Russian summary). MR 70888, DOI 10.1007/BF02021270
- David Vernon Widder, The Laplace Transform, Princeton Mathematical Series, vol. 6, Princeton University Press, Princeton, N. J., 1941. MR 0005923
Bibliographic Information
- © Copyright 1960 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 94 (1960), 282-294
- MSC: Primary 60.00
- DOI: https://doi.org/10.1090/S0002-9947-1960-0112182-9
- MathSciNet review: 0112182