Effective bandwidths with priorities

The notion of effective bandwidths has provided a useful practical framework for connection admission control and capacity planning in high-speed communication networks. The associated admissible set with a single linear boundary makes it possible to apply stochastic-loss-network (generalized-Erlang) models for capacity planning. We consider the case of network nodes that use a priority-service discipline to support multiple classes of service, and we wish to determine an appropriate notion of effective bandwidths. Just as was done previously for the first-in first-out (FIFO) discipline, we use large-buffer asymptotics (large deviations principles) for workload tail probabilities as a theoretical basis. We let each priority class have its own buffer and its own constraint on the probability of buffer overflow. Unfortunately, however, this leads to a constraint for each priority class. Moreover, the large-buffer asymptotic theory with priority classes does not produce an admissible set with linear boundaries, but we show that it nearly does and that a natural bound on the admissible set does have this property. We propose it as an approximation for priority classes; then there is one linear constraint for each priority class. This linear-admissible-set structure implies a new notion of effective bandwidths, where a given connection is associated with multiple effective bandwidths: one for the priority level of the given connection and one for each lower priority level. This structure can be used regardless of whether the individual effective bandwidths are determined by large-buffer asymptotics or by some other method.