Gaussian traffic modelling for Differentiated Services

In the Differentiated Services concept of Internet, packets are handled in the network's interior router nodes according to their belonging to certain classes called Per-Hop Behaviors (PHB). Thus, traffic management works on traffic aggregates, not on individual flows. This calls for robust methods in dimensioning the resources assigned to each class. One such robust technique is to model traffic aggregates as Gaussian processes, assuming traffic in each PHB (or each PHB class) independent. This can be justified by the Central Limit Theorem, which tells that such large aggregates have approximately Gaussian joint distribution when the number of individual flows is big. Queueing theory with general Gaussian traffic has no exact results, but reasonably good approximations are easy to obtain. In the context of Differentiated Services, however, FIFO queues play a minor role. Instead, it is important to understand how priority queues behave when the inputs are Gaussian. For example, how much worse are the delay characteristics in the second priority class than in the first class? This paper focuses at developing practically usable estimates for distributions of Gaussian priority queues. The central idea is to identify the {\em most probable paths} along which a big queue arises. Some of the approximations are compared with simulations, and the results are promising.