Optimal processor allocation to differentiated job flows

In this paper, we study the problem of dynamic allocation of the resources of a general parallel processing system, comprised of M heterogeneous processors and M heterogeneous traffic flows. Each traffic flow is modeled as a Bernoulli sequence of binary random variables, with the arrival rate depending on the job class. The service times of the jobs are independent random variables with distributions that depend on both the job class and the processor class. We characterize the stability region for this system and introduce a processor allocation policy that stabilizes the system under the maximum possible traffic loadings. We also investigate some special cases of this model and finally characterize its performance in the presence of finite buffers.