Optimal trajectory to overflow in a queue fed by a large number of sources

We analyse the deviant behavior of a queue fed by a large number of traffic streams. In particular, we explicitly give the most likely trajectory (or 'optimal path') to buffer overflow, by applying large deviations techniques . This is done for a broad class of sources, consisting of Markov fluid sou rces and periodic sources. Apart from a number of ramifications of this res ult, we present guidelines for the numerical evaluation of the optimal path .