Approximate Analysis of Load Dependent General Queueing Networks

IEEE Transactions on Software Engineering

Volumn 14, Issue 11, 1988, Pages 1537-1545

  Akyildiz, I F ^a   Sieber, Albrecht ^a,b  

^a LOUISIANA STATE UNIVERSITY   (United States)

^b UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

Conditional throughputs; performance analysis; performance measures; queueing networks

Indexed keywords

COMPUTER SIMULATION; COMPUTER SYSTEMS, DIGITAL--PERFORMANCE; MATHEMATICAL TECHNIQUES--ITERATIVE METHODS; SCHEDULING;

CONDITIONAL THROUGHPUTS; FIRST-COME-FIRST-SERVED SCHEDULING; GENERAL SERVICE-TIME DISTRIBUTIONS; LOAD-DEPENDENT CLOSED QUEUEING NETWORKS;

PROBABILITY;

EID: 0024104391     PISSN: 00985589     EISSN: None     Source Type: Journal    
DOI: 10.1109/32.9042     Document Type: Article

References (39)

1. S. C. Agrawal, J. P. Buzen, and A. W. Shum, “Response time preservation: A general technique for developing approximate algorithms for queueing networks,” in Proc. ACM Sigmetrics Conf., Cambridge, MA, Aug. 21-24, 1984, pp. 63-77.
2. I. F. Akyildiz, “Mean value analysis of closed queueing networks with Erlang service time distributions,” Comput. J., vol. 39, pp. 219-232, Oct. L987.
3. F. Baskett, K. M. Chandy, R. R. Muntz, and F. G. Palacios, “Open, closed, and mixed networks of queues with different classes of customers,” J. ACM, vol. 22, no. 2, pp. 248-260, Apr. 1975.
4. W. Bux and U. Herzog, “The phase concept: Approximation of measured data and performance analysis,” in Computer Performance Proceedings, K. M. Chandy and M. Reiser, Eds. Amsterdam, The Netherlands: North-Holland, 1977.
5. J. P. Buzen, “Computational algorithms for closed queueing networks with exponential servers,” Commun. ACM, vol. 16, no. 9, pp. 527-531, Sept. 1973.
6. K. M. Chandy, U. Herzog, and L. Woo, “Parametric analysis of queueing network models,” IBM J. Res. Develop., pp. 36-42, Jan. 1975.
7. “Approximate analysis of general queueing networks,” IBM J. Res. Develop., vol. 19, no. 1, pp. 43-49, Apr. 1975.
8. K. M. Chandy, J. H. Howard, and D. Towsley, “Product form and local balance in queueing networks,” in Modelling and Performance Evaluation of Computer Systems, Workshop Preprints, 1976, pp. 89-103.
9. K. M. Chandy and J. Martin, “A characterization of product form queueing networks.” J. ACM. vol. 30, no. 2, pp. 286-299, 1983.
10. D. R. Cox, “A use of complex probabilities in the theory of stochastic processes,” J. Proc. Cambr. Phil. Soc, vol. 51, pp. 313-319, 1955.
11. P. J. Courtois, Decomposability: Queueing and Computer System Applications. New York: Academic, 1977.
12. D. Ferrari, G. Serazzi, and A. Zeigner, Measurement and Tuning of Computer Systems. Englewood Cliffs, NJ: Prentice-Hall, 1983.
13. E. Gelenbe, “On approximate computer system models,” J. ACM. vol. 22, no. 2, pp. 261-269, Apr. 1975.
14. E. Gelenbe and I. Mitrani, Analysis and Synthesis of Computer System Models. London: Academic, 1980.
15. W. J. Gordon and G. F. Newell, “Closed queueing systems with exponential servers,” Oper. Res., vol. 15, pp. 254-265, 1967.
16. U. Herzog, L. Woo, and K. Chandy, “Solution of queueing problems by a recursive technique,” IBM J. Res. Develop., pp. 295-300, May 1975.
17. P. Jackson, “Job shop like queueing systems,” Management Sci., vol. 10, no. 1, 1963.
18. H. Kobayashi, “Application of the diffusion approximation to queueing networks. Part I: Equilibrium queue distributions,” J. ACM, vol. 21, no. 2, pp. 316-328, Apr. 1974.
19. “Application of the diffusion approximation to queueing networks, Part II: Nonequilibrium distributions and computer modelling,” J. ACM, vol. 21, no. 3, pp. 459-469, July 1974.
20. D. D. Kouvatsos. “A maximum entropy queue length distribution for a G/G/l finite capacity queue,” ACM Sigmetrics Perform. Eval. Rev., vol. 14, no. 1, pp. 224-237, May 1986.
21. P. J. Kuehn, “Approximate analysis of general queueing networks by decomposition,” IEEE Trans. Commun., vol. 27, no. 1, pp. 113- 126, Jan. 1979.
22. R. Marie, “Methodes iteratives de resolution de modeles mathematiques de systemes informatiques,” R.A.I.R.O. InformatiquelComput. Sri., vol. 12, pp. 107-122, 1978.
23. “An approximate analytical method for general queueing networks,” IEEE Trans. Software Eng., vol. SE-5, no. 5, pp. 530-538, Sept. 1979.
24. “Calculating equilibrium probabilities for λ(n)/C/l - N queues,” Perform. Eval. Rev., (ACM Sigmetrics Conference), vol. 9, no. 2, pp. 117-125, Summer 1980.
25. R. Marie, P. M. Snyder, and W. J. Stewart, “Extensions and computational aspects of an iterative method,” in Proc. ACM Sigmetrics Conf, vol. 11, no. 4, Seattle, WA, Aug. 1982, pp. 186-195.
26. R. R. Muntz, “Poisson departure process and queueing networks,” in Sciences and Systems, Proc. 7th Annu. Princeton Conf. Information, Princeton Univ., Princeton, NJ, Mar. 1973, pp. 435-440.
27. A. S. Noetzel, “A generalized queueing discipline for product form network solutions,” J. ACM, vol. 26, no. 4, pp. 779-793, Oct. 1979.
28. H. G. Perros, “The queue length distribution of the M/Ck /1queue,” ACM Sigmetrics Perform. Eval., pp. 21-24, 1983.
29. M. Reiser, “Mean value analysis of queueing networks: A new look at an old problem,” in Proc. Fourth Int. Symp. Modeling and Performance Evaluation of Computer Systems, vol. I, Feb. 1979.
30. M. Reiser and S. S. Lavenberg, “Mean value analysis of closed multichain queueing networks,” J. ACM, vol. 27, no. 2, pp. 313-322, Apr. 1980.
31. M. Reiser, “Mean value analysis and convolution method for queueing dependent servers in closed queueing networks,” Perform. Eval., vol. I, no. 1, pp. 7-18, Jan. 1981.
32. C. H. Sauer and K. M. Chandy, Computer Systems Performance Modeling. Englewood Cliffs, NJ: Prentice-Hall, 1981.
33. C. H. Sauer, “Computational algorithms for state dependent queueing networks,” ACM Trans. Comput. Syst., vol. 1, no. 1, pp. 67-92, Feb. 1983.
34. A. W. C. Shum, “Queueing models for computer systems with general service time distributions,” Ph.D. dissertation, Div. Eng. Appl. Phys., Univ. Massachusetts, Dec. 1976.
35. J. P. Spirn, “Queueing networks with random selection for service,” IEEE Trans. Software Eng., vol. SE-5, pp. 287-289, 1979.
36. W. J. Stewart, “A comparison of numerical techniques in Markov modeling,” Commun. ACM, vol. 21, no. 2, pp. 144-152, Feb. 1978.
37. W. L. Stewart and R. Marie, “A numerical solution for the λ(n) / Ck/ r/N queue,” European J. Oper. Res., vol. 5, pp. 56-68, 1980.
38. D. Towsley, “Queueing network models with state-dependent routing,” J. ACM, vol. 27, no. 2, pp. 323-337, Apr. 1980.
39. R. H. Walstra, “Non-exponential networks of queues: A maximum entropy analysis,” ACM Sigmetrics Perform. Eval. Rev., vol. 13, no. 2, Aug. 1985.