Asymptotic analysis of a heterogeneous multiprocessor system in a randomly changing environment

An asymptotic queuing theoretic approach is proposed to analyze the performance of an FCFS (first-come, first-served) heterogeneous multiprocessor computer system with a single bus operating in a randomly changing environment. All stochastic times in the system are considered to be exponentially distributed and independent of the random environment, while the access and service rates of the processors are subject to random fluctuations. It is shown under the assumption of `fast´ arrivals that the busy period length of the bus converges weakly, under appropriate normalization, to an exponentially distributed random variable. As a consequence, main steady-state performance measures such as system throughput, mean delay time, expected waiting time, and mean number of active processors can be approximately determined. The reliability of the proposed method is validated by comparing the new approximations with known exact results