Transient behavior of single-server queueing processes with Erlang input
HTML articles powered by AMS MathViewer
- by Lajos Takács PDF
- Trans. Amer. Math. Soc. 100 (1961), 1-28 Request permission
References
- David Blackwell, A renewal theorem, Duke Math. J. 15 (1948), 145–150. MR 24093 B. W. Conolly, The busy period in relation to the queueing process ${E_K}/G/1$, to be published. A. J. Fabens, The solution of queueing and inventory models, Technical Report No. 20, December 7, 1959. Department of Statistics, Stanford University.
- R. R. P. Jackson and D. G. Nickols, Some equilibrium results for the queueing process $E_k/M/1$, J. Roy. Statist. Soc. Ser. B 18 (1956), 275–279. MR 83220, DOI 10.1111/j.2517-6161.1956.tb00234.x
- 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 F. Pollaczek, Über eine Aufgabe der Wahrscheinlichkeitstheorie, Math. Z. vol. 32 (1930) pp. 64-100; 729-750. —, Problèmes stochastiques posés par le phénomène de formation d’une queue d’attente à un guichet et par des phénomènes apparentés, Paris, Gauthier-Villars, 1957.
- Félix Pollaczek, Sur la répartition des périodes d’occupation ininterrompue d’un guichet, C. R. Acad. Sci. Paris 234 (1952), 2042–2044 (French). MR 49512
- E. T. Whittaker and G. N. Watson, A course of modern analysis, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1996. An introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions; Reprint of the fourth (1927) edition. MR 1424469, DOI 10.1017/CBO9780511608759
- A. Zygmund, A remark on characteristic functions, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950, University of California Press, Berkeley-Los Angeles, Calif., 1951, pp. 369–372. MR 0044056
Additional Information
- © Copyright 1961 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 100 (1961), 1-28
- MSC: Primary 60.80
- DOI: https://doi.org/10.1090/S0002-9947-1961-0181024-9
- MathSciNet review: 0181024