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A New Approach for the Performance Analysis of a Single-Bus Multiprocessor System with General Service Times
March 1993 (vol. 42 no. 3)
pp. 358-362

The linear algebraic approach to queuing theory is applied to analyze the performance of a typical single-bus multiprocessor system. This system can be modeled as an M/G/1/N queuing system with load-dependent arrivals. The method presented requires only that the nonexponential service time distribution for the system be a matrix-exponential, that is, one with a rational Laplace transform. Using linear algebraic techniques, expressions are obtained for the performance characteristics of interest, such as the processing power for the multiprocessor system. The algorithm does not rely on root finding and can be implemented using symbolic programming techniques. The explicit closed-form expression for the processing power is presented for some special cases.

[1] M. Ajmone Marsan, G. Balbo, and G. Conte, "Comparative performance analysis of single bus multiprocessor architectures,"IEEE Trans. Comput., vol. C-31, no. 12, pp. 1179-1191, Dec. 1982.
[2] I. H.Önyüksel and K. B. Irani, "Markovian queueing network models for performance analysis of a single-bus multiprocessor system,"IEEE Trans. Comput., vol. 39, no. 7, pp. 975-980, July 1990.
[3] J. L. Carroll, A. van de Liefvoort, and L. Lipsky, "Solutions of M/G/1//N-type loops with extensions to M/G/1 and GI/M/1 queues,"Oper. Res., vol. 30, no. 3, pp. 490-514, May-June 1982.
[4] M. Ajmone Marsan and M. Gerla, "Markov models for multiple bus multiprocessor systems,"IEEE Trans. Comput., vol. C-31, no. 3, pp. 239-248, Mar. 1982.
[5] L. Kleinrock,Queueing Systems, Vol. 2. New York: Wiley, 1976.
[6] L. Lipsky,Queueing Theory: A Linear Algebraic Approach. New York: Macmillan, 1991.
[7] L. Lipsky and A. van de Liefvoort, "A linear algebraic approach to queueing theory," inProc. SAC'91, IEEE/ACM Symp. Appl. Comput., Kansas City, Apr. 1991.
[8] L. Takács,Introduction to the Theory of Queues. New York: Oxford University Press, 1962.

Index Terms:
performance analysis; single-bus multiprocessor system; general service times; linear algebraic approach; queuing theory; M/G/1/N queuing system; load-dependent arrivals; rational Laplace transform; symbolic programming techniques; explicit closed-form expression; multiprocessing systems; performance evaluation; queueing theory.
Citation:
A. van de Liefvoort, N. Subramanian, "A New Approach for the Performance Analysis of a Single-Bus Multiprocessor System with General Service Times," IEEE Transactions on Computers, vol. 42, no. 3, pp. 358-362, March 1993, doi:10.1109/12.210178
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