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<p>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.</p>
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.
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. , pp. 358-362, March 1993, doi:10.1109/12.210178
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