Most probable paths in Gaussian priority queues

This paper shows how one can apply the methodology developed in [AMN99] for ordinary queues with Gaussian input to priority queueing systems. It turns out to be easy to compute so called most probable paths leading to a large queue or, alternatively, a long waiting time for non-privileged tra c. The norm of such a (multivariate) path in the reproducing kernel Hilbert space gives immediately an estimate of the probability of the corresponding event. In the present paper, which has a preliminary character, we don't consider the accuracy of such estimates but leave it to forthcoming simulation studies. It can be expected that these estimates would be as usable as those for ordinary queues studied in [AMN99], i.e. give the right orders of magnitude and right qualitative tail behavior.