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Markovian Queueing Network Models for Performance Analysis of a Single-Bus Multiprocessor System
July 1990 (vol. 39 no. 7)
pp. 975-980

An exact solution for the performance analysis of a typical single-bus multiprocessor system is presented. The multiprocessor system is modeled by a Markovian queueing network. An r-stage hypoexponential distribution or an r-stage hyperexponential distribution is used to represent the nonexponential service times. Consequently, the equilibrium probabilities of two-dimensional Markov chains are expressed by simple recurrence relations. Processing efficiency is used as the primary measure of performance. To investigate the effects of different service time distributions on system performance, comparative results are obtained for a large set of input parameters. The numerical results illustrate that processing efficiency attains its maximum value for a constant (deterministic) service time; if service time of common memory is hypoexponentially distributed, then approximating the service time by an exponential distribution produces less than 6% error on the system performance.

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Index Terms:
Markovian queueing network models; performance analysis; single-bus multiprocessor system; r-stage hypoexponential distribution; hyperexponential distribution; equilibrium probabilities; recurrence relations; service time distributions; Markov processes; multiprocessing systems; performance evaluation; queueing theory.
I.H. Onyuksel, K.B. Irani, "Markovian Queueing Network Models for Performance Analysis of a Single-Bus Multiprocessor System," IEEE Transactions on Computers, vol. 39, no. 7, pp. 975-980, July 1990, doi:10.1109/12.55702
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