A NEW APPROACH FOR THE PERFORMANCE ANALYSIS OF A SINGLE-BUS MULTIPROCESSOR SYSTEM WITH GENERAL SERVICE TIMES

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