Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Transient behavior of single-server queueing processes with Erlang input

Author: Lajos Takács
Journal: Trans. Amer. Math. Soc. 100 (1961), 1-28
MSC: Primary 60.80
MathSciNet review: 0181024
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] David Blackwell, A renewal theorem, Duke Math. J. 15 (1948), 145–150. MR 0024093 (9,452a)
  • [2] B. W. Conolly, The busy period in relation to the queueing process $ {E_K}/G/1$, to be published.
  • [3] A. J. Fabens, The solution of queueing and inventory models, Technical Report No. 20, December 7, 1959. Department of Statistics, Stanford University.
  • [4] 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 0083220 (18,681d)
  • [5] D. V. Lindley, The theory of queues with a single server, Proc. Cambridge Philos Soc. 48 (1952), 277–289. MR 0046597 (13,759h)
  • [6] F. Pollaczek, Über eine Aufgabe der Wahrscheinlichkeitstheorie, Math. Z. vol. 32 (1930) pp. 64-100; 729-750.
  • [7] -, 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.
  • [8] Félix Pollaczek, Sur la répartition des périodes d’occupation ininterrompue d’un guichet, C. R. Acad. Sci. Paris 234 (1952), 2042–2044 (French). MR 0049512 (14,188c)
  • [9] 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 (97k:01072)
  • [10] A. Zygmund, A remark on characteristic functions, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950, University of California Press, Berkeley, and Los Angeles, 1951, pp. 369–372. MR 0044056 (13,362i)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 60.80

Retrieve articles in all journals with MSC: 60.80

Additional Information

PII: S 0002-9947(1961)0181024-9
Article copyright: © Copyright 1961 American Mathematical Society