12
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

On some relations between stationary time and customer state probabilities for qneueing systems G/GI/s/r

Pages 261-272 | Published online: 27 Jun 2007

References

  • Borovkov A.A. Stochastic processes in queueing theory Springer-Verlag Berlin 1976 Heidelberg/New York ;Translated from the Russian, Izdat. Nauka, Moscow 1972.
  • Brumelle , S.L. 1971 . On the relation between customers and time averages in queues . J. Appl. Probability , 8 : 508 – 520 .
  • Burke , P.J. 1975 . Delays in single-server queues with batch input . Operations Res , 23 : 830 – 833 .
  • Cohen , J.W. 1969 . The single-server queue , Amsterdam : North Holland Publishing Company . London
  • Cohen , J.W. 1976 . On a single-server queue with group arrivals . J. AddL Probability , 13 : 619 – 622 .
  • Cohen , J.W. 1976 . “ On regenerative processes in queueing theory ” . In Lect. Notes in Econ. Math. Syst , Vol. 121 , Berlin : Springer-Verlag . Heidelberg/New York
  • Franken , P. 1976 . Some applications of the theory of stochastic point processes in queueing theory . Math. Nachr , 70 : 309 – 316 . Germ
  • Le Gall , P. 1974 . Stochastic integral equations applied to telecommunications traffic without delay . Stoch. Processes Appl , 2 : 261 – 280 .
  • Kerstan , J. , Matthes , K. and Mecke , J. 1978 . Infinitely divisible point processes , New York : Wiley Interscience .
  • König , D. , Matthes , K. and Nawrotzki , K. 1967 . Generalizations of the Erlang and Engset formulae (a method in queueing theory) , Berlin : Akademie-Verlag . Germ
  • König , D. , Rolski , T. , Schmidt , V. and Stoyan , D. 1978 . Stochastic processes with imbedded marked point processes (PMP) and their application in queueing . Math. Operationsforsch. Statist., Ser. Optimization , 9 : 125 – 141 .
  • König , D. , Schmidt , V. and Stoyan , D. 1976 . On some relations between stationary distributions of queue lengths and imbedded queue lengths in G/G/s queueing systems . Math. Operationsforsch. Statist , 7 : 577 – 586 .
  • Kopocinska , I. and Kopocinski , B. 1977 . Steady-state distributions of queue length in the GI/G/s queue . Zastosow. Matem , 16 : 39 – 46 .
  • Kopocinski , B. and Rolski , T. 1977 . A note on the virtual waiting time in the GI/G/s queue . Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys , 25 : 1279 – 1280 .
  • Marshall , A.W. and Proschan , F. Classes of distributions applicable in replacement with renewal theory implications . Proc. 6th Berkeley Symposium math. Statist. Probab . Vol. 1 , pp. 495 – 514 . Univ. Californ . Berkeley-Los Angeles 1972
  • Miyazawa , M. 1976 . Stochastic order relations among GI/G/1 queues with common traffic intensity . J. Operations Res. Soc. Japan , 19 : 193 – 208 .
  • Schmidt V. A remark on a paper of Le Gall 1976 Preprint
  • Shanbhag , D.N. and Tambouratzis , D.G. 1973 . Erlang's formula and some results on the departure process for a loss system . J. Appl. Probability , 10 : 233 – 240 .
  • Stoyan , D. 1977 . Qualitative orooeriies and bounds of stochastic models , Berlin : Akademie-Verlag . Germ
  • Stoyaint , T. 1977 . Math. Operationsforsch. Statist., Ser. Optimization , 8 ( 4 ) : 541 – 548 .
  • Takacs , L. 1962 . Introduction to the theory of queues , New York : Oxford University Press .
  • Takacs , L. 1969 . “ On Erlang's formula ” . In Ann. Math. Statist Vol. 40 , 71 – 78 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.