48
Views
7
CrossRef citations to date
0
Altmetric
Original Articles

A simple approach to the map/d/s queue

Pages 543-556 | Received 27 Mar 2000, Accepted 26 Aug 2000, Published online: 21 Mar 2007

References

  • Crommelin , C. D. 1932 . Delay probability formulae when the holding times are constant . Post Office Electrical Engineer's Journal , 25 : 41 – 50 .
  • Iversen , V. B. 1983 . Decomposition of an M/D/r. k queue with FIFO into rEk/D/r queues with FIFO . Opns. Res. Lett , 2 : 20 – 21 .
  • Lucantoni , D. M. and Ramaswami , V. 1985 . Efficient algorithms for solving the non-linear matrix equations arising in phase type queues . Stoch. Mod , 1 : 29 – 51 .
  • Lucantoni , D. M. , Meier-Hellstern , K. S. and Neuts , M. F. 1990 . A single-server queue with server vacations and a class of non-renewal arrival processes . Adv. Appl. Prob , 22 : 676 – 705 .
  • Neuts , M. F. 1982 . “ The c-server queue with constant service times and a versatile Markovian arrival process ” . In Applied Probability - Computer Science: The Interface, Vol.1 , Edited by: Disney , R. L. and Ott , T. J. 31 – 67 . Boston : Birkhäuser .
  • Neuts , M. F. 1989 . “ Structured Stochastic Matrices of the M/G/l Type and Their Applications ” . New York : Marcel Dekker .
  • Nishimura , S. A spectral analysis of a MAP/D/N queue . Proceedings of The Third International Conference on Matrix-Analytic Methods in Stochastic Models . to appear
  • Ramaswami , V. 1988 . Stable recursion for the steady state vector for Markov chains of M/G/l type . Stoch. Mod , 4 : 183 – 188 .
  • Takine , T. and Hasegawa , T. 1994 . The workload in the MAP/G/1 queue with state-dependent services: Its application to a queue with preemptive resume priority . Stoch. Mod , 10 : 183 – 204 .
  • Takine , T. , Matsumoto , Y. , Suda , T. and Hasegawa , T. 1994 . Mean waiting times in nonpreemptive priority queues with Markovian arrival and i.i.d. service processes . Perfor. Eval , 20 : 131 – 149 .
  • Takine , T. and Takahashi , Y. 1998 . On the relationship between queue lengths at a random instant and at a departure in the stationary queue with BMAP arrivals . Stoch. Mod , 14 : 601 – 610 .
  • Takine , T. 1998 . “ Queue length distribution in a FIFO single-sever queue with multiple arrival streams having different service time distributions ” . submitted for publication
  • Takine , T. 2000 . “ Distributional form of Little's law for FIFO queues with multiple Markovian arrival streams and its application to queues with vacations ” . to appear in Queueing Systems
  • Tijms , H. C. 1994 . “ Stochastic Models ” . In An Algorithmic Approach , Chichester : Wiley .

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.