Computational procedures for a class of GI/D/k systems in discrete time

Journal of Probability and Statistics

Volumn , Issue , 2009, Pages

  Rahman, Md Mostafizur ^a   Alfa, Attahiru Sule ^a  

^a UNIVERSITY OF MANITOBA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77956174913     PISSN: 1687952X     EISSN: 16879538     Source Type: Journal    
DOI: 10.1155/2009/716364     Document Type: Article

References (31)

1. Crommelin C. D., Delay probability formulae when the holding times are constant Post Ofiice Electrical Engineers Journal 1932 25 41 50
2. Alfa A. S., Algorithmic analysis of the BMAP/D/k system in discrete time Advances in Applied Probability 2003 35 4 1131 1152
3. Alfa A. S., Waiting time distribution of the MAP/D/k system in discrete timea more efficient algorithm Operations Research Letters 2003 31 4 263 267
4. Wuyts I., Bruneel H., Analysis of discrete-time multiserver queueing models with constant service times Operations Research Letters 1994 15 5 231 236
5. Chaudhry M. L., Kim N. K., A complete and simple solution for a discrete-time multi-server queue with bulk arrivals and deterministic service times Operations Research Letters 2003 31 2 101 107
6. Chaudhry M. L., Templeton J. G. C., Medhi J., Computational results of multiserver bulk-arrival queues with constant service time MX/D/c Operations Research 1992 40 2 229 238
7. Chaudhry M. L., Yoon B. K., Chae K. C., Waiting-time distribution of a discrete-time multiserver queue with correlated arrivals and deterministic service times: D-MAP/D/k system Operations Research Letters 2002 30 3 174 180 (Pubitemid 34782510)
8. Franx G. J., A simple solution for the M/D/c waiting time distribution Operations Research Letters 2001 29 5 221 229 (Pubitemid 34065063)
9. Franx G. J., The MX/D/c batch arrival queue Probability in the Engineering and Informational Sciences 2005 19 3 345 349
10. Gao P., Wittevrongel S., Bruneel H., Delay analysis for a discrete-time GI-D-c queue with arbitrary-length service times Proceedings of the 1st European Performance Engineering Workshop (EPEW 04) September 2004 Toledo, Spain 184 195
11. Gao P., Wittevrongel S., Bruneel H., Analysis of discrete-time multiserver queues with constant service times and correlated arrivals Proceedings of the 12th International Conference on Analytical and Stochastic Modelling Techniques and Applications (ASMTA 05) May 2005 Riga, Latvia 1 8
12. Gao P., Wittevrongel S., Bruneel H., Delay and partial system contents for a discrete-time G-D-c queue 4OR: A Quarterly Journal of Operations Research 2008 6 3 279 290
13. Gao P., Wittevrongel S., Walraevens J., Bruneel H., Analytic study of multiserver buffers with two-state Markovian arrivals and constant service times of multiple slots Mathematical Methods of Operations Research 2008 67 2 269 284 (Pubitemid 351659993)
14. Gao P., Wittevrongel S., Walraevens J., Moeneclaey M., Bruneel H., Calculation of delay characteristics for multiserver queues with constant service times European Journal of Operational Research 2009 199 1 170 175
15. Iversen V. B., Decomposition of an M/D/rk queue with FIFO into K Ek/D/r queues with FIFO Operations Research Letters 1983 2 1 20 21
16. van Hoorn M. H., Numerical analysis of multiserver queues with deterministic service and special phase-type arrivals Zeitschrift fr Operations Research 1986 30 1 A15 A28
17. Nishimura S., Latouche G., Taylor P., A spectral analysis for MAP/D/N queue Advances in Algorithmic Methods for Stochastic Models 2000 Neshanic Station, NJ, USA Notable 279 294
18. Takine T., A simple approach to the MAP/D/s queue Stochastic Models 2000 16 5 543 556
19. Wittevrongel S., Bruneel H., Discrete-time queues with correlated arrivals and constant service times Computers Operations Research 1999 26 2 93 108 (Pubitemid 29346478)
20. Xerocostas D. A., Demertzes C., Steady state solution of the Ek /D/r queueing model OR Spektrum 1982 4 1 47 51
21. Kim N. K., Chaudhry M. L., The use of the distributional littles law in the computational analysis of discrete-time GI/G/1 and GI/D/c queues Performance Evaluation 2008 65 1 3 9 (Pubitemid 350016410)
22. Neuts M. F., Matrix-Geometric Solutions in Stochastic Models 1981 2 Baltimore, Md, USA Johns Hopkins University Press
23. Chaudhry M. L., Computing stationary queueing-time distributions of GI/D/1 and GI/D/c queues Naval Research Logistics 1992 39 7 975 996
24. Alfa A. S., Combined elapsed time and matrix-analytic method for the discrete time GI/G/1 and GIX/G/1 systems Queueing Systems 2003 35 1 5 25 (Pubitemid 38117963)
25. Alfa A. S., Xue J., Efficient computations for the discrete GI/G/1 system INFORMS Journal on Computing 2007 19 3 480 484
26. Latouche G., Ramaswami V., A logarithmic reduction algorithm for quasi-birth-death processes Journal of Applied Probability 1993 30 3 650 674
27. Bini D. A., Meini B., Stewart W. J., On cyclic reduction applied to a class of toeplitz-like matrices arising in queueing problems Computations with Markov Chains 1995 Dordrecht, The Netherlands Kluwer Academic Publisher 21 38
28. Akar N., Sohraby K., An invariant subspace approach in M/G/1 and G/M/1 type Markov chains Stochastic Models 1997 13 3 381 416 (Pubitemid 127761588)
29. Hadley G., Linear Algebra 1969 Reading, Mass, USA Addison-Wesley
30. Rahman M. M., Alfa A. S., Computational procedures for a class of GI/D/ k systems in discrete timean extended analysis. http://www.ee.umanitoba.ca/ mmrahman/gidkreport.pdf
31. Watters P. A., Solaris 10: The Complete Reference 2005 New York, NY, USA McGraw-Hill