Abstract
Approximate MVA algorithms for separable queueing networks are based upon an iterative solution of a set of modified MVA formulas. Although each iteration has a computational time requirement of O(MK2) or less, many iterations are typically needed for convergence to a solution. (M denotes the number of queues and K the number of closed chains or customer classes.) We present some faster approximate solution algorithms that are noniterative. They are suitable for the analysis and design of communication networks which may require tens to hundreds, perhaps thousands, of closed chains to model flow-controlled virtual channels. Three PAM algorithms of increasing accuracy are presented. Two of them have time and space requirements of O(MK). The third algorithm has a time requirement of O(MK2) and a space requirement of O(MK).
- 1 Y. Bard, "Some Extensions to Multiclass Queueing Network Analysis," Performance of Computer Systems, M. Arato et al. (ed.), North-Holland, Amsterdam, 1979. Google ScholarDigital Library
- 2 F. Baskett, K. M. Chandy, R. R. Muntz, and F. Palacios, "Open, Closed and Mixed Networks of Queues with Different Class of Customers," JACM, Vol. 22, 1975, pp. 248-260. Google ScholarDigital Library
- 3 W.-M. Chow, "Approximations for Large Scale Closed Queueing Networks," Performance Evaluation, Vol. 3, No. 1, Feb. 1983, pp. 1-12.Google ScholarCross Ref
- 4 K. M. Chandy and D. Neuse, "Linearizer: A Heuristic Algorithm for Queueing Network Models of Computer Systems," Comm. ACM, Vol. 25, No. 2, Feb. 1982, pp. 126-134. Google ScholarDigital Library
- 5 D. L. Eager and K. C. Sevcik, "Bound Hierarchies for Multiple-Class Queueing Networks,'! Journal of ACM, Vol. 33, No. 1, Jan. 1986, pp. 179-206. Google ScholarDigital Library
- 6 K. P. Hoyme, S. C. Bruell, P. V. Afshari, and R. Y. Kain, "A Tree-Structured Mean Value Analysis Algorithm," ACM Trans. on Computer Systems, Vol. 4, No. 2, May 1986, pp. 178-185. Google ScholarDigital Library
- 7 C.-T. Hsieh and S. S. Lain, "Two Classes of Performance Bounds for Closed Queueing Networks," Performance Evaluation, Vol. 7, No. 1, 1987, pp. 3-30. Google ScholarDigital Library
- 8 C.-T. Hsieh, "Models and Algorithms for the Design of Store-and-Forward Communication Networks," Ph.D. Thesis, Department of Computer Sciences, University of Texas at Austin, 1987. Google ScholarDigital Library
- 9 C.-T. Hsieh and S. S. Lain, "A Noniterative Approximate Solution Method for Closed Multichain Queueing Networks," Technical Report TR-87-28, Dept. of Computer Sciences, University of Texas at Austin, July 1987. Google ScholarDigital Library
- 10 S. S. Lain and Y. L. Lien, "A Tree Convolution Algorithm for the Solution of Queueing Networks," Comm. ACM, Vol. 26, No. 3, March 1983, pp. 203-215. Google ScholarDigital Library
- 11 S. S. Lam and Ching-Tarng Hsieh, "Modeling, Analysis, and Optimal Routing of Flow-Controlled Communication Networks," Technical Report TR-87-24, Dept. of Computer Sciences, Univ. of Texas at Austin, June 1987. Google ScholarDigital Library
- 12 S. S. Lam and Y. L. Lien, "Modeling and Analysis of How-Controlled Packet Switching Networks," Proc. 7th Data Communications Symposium, Mexico City, October 1981. Google ScholarDigital Library
- 13 M. Reiser and H. Kobayashi, "Queueing Networks with Multiple Closed Chains: Theory and Computational Algorithms," IBM J. Res. Develop., Vol. 21, 1975, pp. 283-294.Google ScholarDigital Library
- 14 M. Reiser, "A Queueing Network Analysis of Computer Communication Networks with Window Flow Control," IEEE Trans. on Communication, Vol. COM-27, 1979, pp. 1199-1209.Google Scholar
- 15 M. Reiser and S. Lavenberg, "Mean Value Analysis of Closed Multichain Queueing Networks," Journal of ACM, Vol. 27, No. 2, April 1980, pp. 313-322. Google ScholarDigital Library
- 16 P. Schweitzer, "Approximate Analysis of Multiclass Closed Networks of Queues," Proc. Int. Conf. Stochastic Control and Optimization, Amsterdam, 1979.Google Scholar
- 17 E. de Souza e Silva, S. S. Lavenberg, and R. R. Muntz, "A Clustering Approximation Technique for Queueing Network Models with a Large Number of Chains," IEEE Trans. on Computers, Vol. C-35, No. 5, May 1986, pp. 419-430. Google ScholarDigital Library
- 18 E. de Souza e Silva and R. R. Muntz, "A Note on the Computational Cost of the Linearizer Algorithm for Queueing Networks," Technical Report CSD-870025, Dept. of Computer Science, UCLA, June 1987.Google Scholar
- 19 K. Steiglitz, P. Weiner, and D. J. Kleitman, "The Design of Minimum Cost Survivable Networks," IEEE Transactions on Circuit Theory, Vol. CT-16, 1969, pp. 455-460.Google Scholar
- 20 S. Tucci and C. H. Sauer, "The Tree MVA Algorithm," Performance Evaluation, Vol. 5, No. 3, August 1985, pp. 187-196. Google ScholarDigital Library
- 21 J. Zahorjan, K. C. Sevcik, D. L. Eager, and B. GaUer, "Balanced Job Bound Analysis of Queueing Networks," Comm. ACM, Vol. 25, No. 2, 1982, pp. 132-141. Google ScholarDigital Library
- 22 J. Zahorjan, D. L. Eager, and H. Sweillam, "Accuracy, Speed, and Convergence of Approximate Mean Value Analysis," Technical Report, Dept. of Computer Science, Univ. of Washington, August 1986; to appear in Performance Evaluation. Google ScholarDigital Library
Index Terms
- PAM-a noniterative approximate solution method for closed multichain queueing networks
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