Improved estimation of instantaneous arrival rates via Empirical Bayes

We consider the problem of estimating instantaneous rates for a set of independent arrival flows from (possibly incomplete) passive observations. We introduce a hierarchical Bayesian model with an unknown hyperparameter, whose estimation yields in turn the minimum mean square error (MMSE) estimate of arrival rates for each flow. Such an approach is able to leverage the information from the ensemble of flows in order to improve the local estimate. Since hyperparameter estimation is not available in closed-form, we propose a much simpler estimator based on the best linear unbiased predictor (BLUP) that is computationally comparable to the conventional approach. Simulation results show that our scheme improves the estimation accuracy compared to conventional estimation based on the raw cumulative sum of the arrivals at each flow, especially for small sample sizes, and performs extremely close to the (much more complex) optimal MMSE estimator.