On steady-state queue size distributions of the discrete-time GI/G/1 queue

Advances in Applied Probability

Volumn 28, Issue 4, 1996, Pages 1177-1200

  Yang, Tao ^a   Chaudhry, M L ^b  

^a DALHOUSIE UNIVERSITY   (Canada)

^b ROYAL MILITARY COLLEGE OF CANADA   (Canada)

Author keywords

GI G 1 discrete time queues; Matrix analytic technique

Indexed keywords

EID: 0042408657     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0001867800027609     Document Type: Article

References (28)

1. ATM Forum (1992) ATM User-Network Interface Specification. Version 3.0.
2. ACKROYD, M. H. (1980) Computing the waiting time distribution for the GI/G/1 queue by signal processing methods. IEEE Trans. Commun. 6, 52-58.
3. BRUNEEL, H. AND KIM, B. G. (1993) Discrete-Time Models for Communication Systems Including ATM. Kluwer, Boston.
4. CHAUDHRY, M. L. (1993) Alternative numerical solutions of stationary queueing-time distributions in discrete-time queues: GI/G/1. J. Operat. Res. Soc. 44, 1035-1051.
5. CHAUDHRY, M. L. AND TEMPLETON, J. G. C. (1983) A First Course in Bulk Queues. Wiley, New York.
6. FRYER, M. J. AND WINSTEN, C. B. (1986) An algorithm to compute the equilibrium distribution of a one dimensional bounded random walk. Operat. Res. 34, 449-454.
7. GAIL, H. R. AND HANTLER, S. L. (1996) Solutions of the basic matrix equation for M/G/1 and G/M/1 type Markov chains. Stoch. Models.
8. GAIL, H. R., HANTLER, S. L., KONHEIM, A. G. AND TAYLOR, B. A. (1996) An analysis of a class of telecommunications models. Perf. Eval. (to appear).
9. GRASSMANN, W. K. AND JAIN, J. L. (1989) Numerical solutions of the waiting time distribution and idle time distribution of the arithmetic GI/G/1 queue. Operat. Res. 37, 141-150.
10. GRAVEY, A., LOUVION, J.-R. AND BOYER, P. (1990) On the Geo/D/1 and Geo/D/1/n queues. Perf. Eval. 11, 117-125.
11. GROSS, D. AND HARRIS, C. M. (1974) Fundamentals of Queueing Theory. Wiley, New York.
12. HAYES, J. F. (1984) Modeling and Analysis of Computer Communications Networks. Plenum, New York.
13. HUNTER, J. J. (1983) Mathematical Techniques of Applied Probability. Vol. II: Discrete Time Models: Techniques and Applications. Academic Press, New York.
14. KNOPP, K. (1956) Infinite Sequences and Series. Dover, New York.
15. KONHEIM, A. G. (1975) An elementary solution of the queueing system G/G/1. SIAM J. Comput. 4, 540-545.
16. LEVEQUE, W. J. (1956) Topics in Number Theory. Addison-Wesley, Reading, MA.
17. NEUTS, M. F. (1973) The single server queue in discrete-time -numerical analysis I. Naval Res. Logist. Quart. 20, 297-304.
18. NEUTS, M. F. (1978) Markov chains with applications in queueing theory, which have a matrix-geometric invariant probability vector. Adv. Appl. Prob. 10, 185-212.
19. NEUTS, M. F. (1980) The probabilistic significance of the rate matrix in matrix-geometric invariant vectors. J. Appl. Prob. 17, 291-296.
20. NEUTS. M. F. (1981) Matrix-Geometric Solutions in Stochastic Models. The Johns Hopkins University Press, Baltimore.
21. NEUTS, M. F. (1989) Structured Stochastic Matrices of M/G/1 Type and Their Applications. Marcel Dekker, New York.
22. NEUTS, M. F. AND KLIMKO, E. M. (1973) The single server queue in discrete-time -numerical analysis III. Naval Res. Logist. Quart. 20, 557-567.
23. PONSTEIN, J. (1974) Theory and solution of a discrete queueing problem. Statist. Neerland. 20, 139-152.
24. ROBERTS, J. W. (1992) Performance Evaluation and Design of Multiservice Networks. ECSC-EEC-EAEC, Brussels.
25. SAKASEGAWA, H., MIYAZAWA, M. AND YAMAZAKI, G. (1993) Evaluating the overflow probability using the infinite queue. Management Sci. 39, 1238-1245.
26. TSUCHIYA, T. AND TAKAHASHI. Y. (1993) On discrete-time single-server queues with Markov modulated batch Bernoulli input and finite capacity. J. Operat. Res. Soc. Japan 36, 29-45.
27. VAN OMMEREN, J. C. W. (1991) The discrete-time single-server queue. Queueing Systems: Theory Appl. 8, 279-294.
28. YANG, T. (1993) A note on GI/M/1 type Markov chains. Working Paper 93-08. Technical University of Nova Scotia, Canada.