Decomposition of general tandem queueing networks with MMPP input

Performance Evaluation

Volumn 44, Issue 1-4, 2001, Pages 5-23

  Heindl, Armin ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; MARKOV PROCESSES; MATHEMATICAL MODELS; POISSON DISTRIBUTION;

MARKOV MODULATED POISSON PROCESSES (MMPP); TANDEM QUEUEING NETWORKS;

QUEUEING THEORY;

EID: 0035311840     PISSN: 01665316     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-5316(00)00058-4     Document Type: Article

References (32)

1. Baiocchi A. Analysis of the loss probability of the MAP/G/1/. K queue, Part I: asymptotic theory Commun. Statist. Stochastic Models. 10(4):1994;867-893.
2. Bitran G.R., Dasu S. Approximating nonrenewal processes by Markov chains: use of super-Erlang (SE) chains. Oper. Res. 41:1993;903-923.
3. i/Ph/1 queue Oper. Res. 42:1994;158-174.
4. D.R. Cox, V. Isham, Point Processes, Chapman & Hall, New York, 1980.
5. Daley D.J. The correlation structure of the output process of some single server queueing systems. Ann. Math. Statist. 39:1968;1007-1019.
6. Daley D.J. Queueing output processes. Adv. Appl. Prob. 8:1976;395-415.
7. R.L. Disney, P.C. Kiessler, Traffic Processes in Queueing Networks: A Markov Renewal Approach, John Hopkins University Press, Baltimore, MD, 1987.
8. Fischer W., Meier-Hellstern K. The Markov-modulated Poisson process (MMPP) cookbook. Perform. Eval. 18:1992;149-171.
9. P. Franken, D. König, U. Arndt, V. Schmidt, Queues and Point Processes, Wiley, New York, 1982.
10. R. German, SPNL: processes as language oriented building blocks of stochastic Petri nets, in: Proceedings of the Ninth TOOLS'97, Lecture Notes in Computer Science, Vol. 1469, Springer, Berlin, 1997, pp. 123-134.
11. Gouweleeuw F.N. Calculating the loss probability in a BMAP/G/1/. N +1 queue Commun. Statist. Stochastic Models. 12(3):1996;473-492.
12. D. Green, Lag correlations of approximating departure processes of MAP/PH/1 queues, in: Proceedings of the Third International Conference on Matrix-analytic Methods in Stochastic Models, Leuven, Belgium, 2000, pp. 135-151.
13. Gross D., Miller D. The randomization technique as a modeling tool and solution procedure for transient Markov processes. Oper. Res. 32:1984;345-361.
14. Hasslinger G. Waiting time, busy periods and output models of a server analyzed via Wiener-Hopf factorization. Perform. Eval. 40:2000;3-26.
15. Heffes H., Lucantoni D.M. A Markov modulated characterization of packetized voice and data traffic and related statistical multiplexer performance. IEEE J. Select. Areas Commun. 4(6):1986;856-868.
16. A. Heindl, Approximate analysis of queueing networks with finite buffers and losses by decomposition, Technical Report 1998-8, Department of Computer Science, Technische Universität Berlin, 1998.
17. Jagerman D.L. An inversion technique for the Laplace transform. Bell Syst. Tech. J. 61(8):1982;1995-2002.
18. Kouvatsos D.D. Entropy maximisation and queueing network models. Ann. Oper. Res. 48:1994;63-126.
19. Kühn P.J. Approximate analysis of general queueing networks by decomposition. IEEE Trans. Commun. COM-27:1979;113-126.
20. Lucantoni D.M. New results on the single server queue with a batch Markovian arrival process. Commun. Statist. Stochastic Models. 7(1):1991;1-46.
21. Manfield D.R., Downs T. Decomposition of traffic in loss systems with renewal input. IEEE Trans. Commun. COM-27:1979;44-58.
22. K. Mitchell, A. van de Liefvoort, Approximation models of feed-forward G/G/1/ N queueing networks with correlated arrivals, in: Proceedings of the Fourth International Workshop on Queueing Networks with Finite Capacity, Ilkley, UK, 2000, pp. 32, 1-12.
23. M. Neuts, Matrix-geometric Solutions in Stochastic Models, John Hopkins University Press, Baltimore, MD, 1981.
24. M. Neuts, Algorithmic Probability: A Collection of Problems, Chapman & Hall, London, 1995.
25. R. Sadre, B. Haverkort, A. Ost, An efficient and accurate decomposition method for open finite and infinite buffer queueing networks, in: Proceedings of the Third International Workshop on Numerical Solution of Markov Chains, Zaragoza, Spain, 1999, pp. 1-20.
26. Saito H. The departure process of an. N /G/1 queue Perform. Eval. 11:1990;241-251.
27. Shi L. Approximate analysis for queueing networks with finite-capacity and customer loss. Eur. J. Oper. Res. 85:1995;178-191.
28. Simonova S.N. Output flow of single-line queueing systems. Ukr. Matematecheskii Z. 21:1969;501-510.
29. Wang S.S., Silvester J.A. An approximate model for performance evaluation of real-time multimedia communication systems. Perform. Eval. 22:1995;239-325.
30. Whitt W. Performance of the queueing network analyzer. Bell Syst. Tech. J. 62:1983;2817-2843.
31. Whitt W. The queueing network analyzer. Bell Syst. Tech. J. 62:1983;2779-2815.
32. A. Zimmermann, J. Freiheit, R. German, G. Hommel, Petri net modelling and performability evaluation with TimeNET 3.0, in: Proceedings of the 11th TOOLS'2000, Lecture Notes in Computer Science, Vol. 1786, Springer, Berlin, 2000, pp. 188-202.