Modelling of heterogeneous multiprocessor systems with randomly changing parameters

  J. Sztrik

Abstract:

  A queueing theoretic approach is developed to analyse the performance of heterogeneous multiprocessor computer systems evolving in random environments. The time intervals from the completion of theprevious bus usage to the generation of a new request as well as the holding times of the common bus are assumed to be exponentially distributed random variables with parameter depending on the state of the corresponding random environment. Each processor is characterised by its own acces and service rate. The bus arbiter selects the processor to usethe common bus according to a First-Come, First-Served (FCFS) disciplone. Supposing that the acces rates of the processors are much greater than the corresponding service rates ("fast" arrival), it is shown that the busy period length of the bus converges weakly, under appropriate norming, to an exponenetially distributed random variable. As a consequence the main steady-state performance measures, such as utilizations, throughput, mean delay time, expected waiting time, the average number of requests served during a busy period, and mean number of active processors can be calculated. Moreover, exact and approximate validation results are presented to illustrate the credibility of the proposed method.

  Keywords: queueing, multiprocessor system, performance measures, weak convergence, random environments, utilization

 Gyenizse Pal 1996. Szeptember 4. Szerda 14:20:32 MET DST