On the tail of the stationary waiting time distribution and limit theorems for the M/G/1 queue

J. W. Cohen

Annales de l'I.H.P. Probabilités et statistiques (1972)

  • Volume: 8, Issue: 3, page 255-263
  • ISSN: 0246-0203

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Cohen, J. W.. "On the tail of the stationary waiting time distribution and limit theorems for the M/G/1 queue." Annales de l'I.H.P. Probabilités et statistiques 8.3 (1972): 255-263. <http://eudml.org/doc/76960>.

@article{Cohen1972,
author = {Cohen, J. W.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
language = {eng},
number = {3},
pages = {255-263},
publisher = {Gauthier-Villars},
title = {On the tail of the stationary waiting time distribution and limit theorems for the M/G/1 queue},
url = {http://eudml.org/doc/76960},
volume = {8},
year = {1972},
}

TY - JOUR
AU - Cohen, J. W.
TI - On the tail of the stationary waiting time distribution and limit theorems for the M/G/1 queue
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1972
PB - Gauthier-Villars
VL - 8
IS - 3
SP - 255
EP - 263
LA - eng
UR - http://eudml.org/doc/76960
ER -

References

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  1. [1] J.W. Cohen, Regular variation of the stationary waiting time distribution for the GI/G/1 queueing system, to appear in J. Appl. Prob.1972. 
  2. [2] J.W. Cohen, The Single Server Queue. North Holland Publ. Co., Amsterdam, 1969, chapter III . 7. Zbl0183.49204MR250389
  3. [3] J.W. Cohen, The suprema of the actual and virtual waiting times during a busy cycle of the Km/Kn/1 queueing system, to appear in Advances Appl. Prob., t. 4, 1972. Zbl0239.60090MR336837
  4. [4] Van Vugt, Limit theorems for the distribution of the supremum of the actual waiting times in a Km/G/1 and a G/Kn/1 queueing system. Report Technological Univ. Delft, 1969, in Dutch. 
  5. [5] D.L. Iglehart, Extreme values in the GI/G/1 queue. Report Stanford Univ., 1971, to appear in Ann. Math. Stat. Zbl0238.60072MR305498
  6. [6] H. Callaert and J.W. Cohen, A lemma on regular variation of a transient renewal function. Report Technological Univ. Delft, 1971, to appear in Zeitschrift für Wahrscheinlichkeitsrechnung. Zbl0237.60036MR341651
  7. [7] W. Feller, An Introduction to Probability Theory and its Applications. Wiley, New York, vol. II, 1966. Zbl0138.10207MR210154
  8. [8] J.F. Teugels, Regular variation of Markov renewal theorems. London Math. Soc., t. 2, 1970, p. 179-190. Zbl0186.50301MR251808
  9. [9] S.M. Berman, Limiting distributions of the maximum term in sequences of dependent variables. Ann. Math. Stat., t. 33, 1962, p. 894-908. Zbl0109.11804MR142142

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