In order for networks to support the delay and loss requirements of interac
tive multimedia applications, resource management algorithms are needed tha
t efficiently allocate network resources. In this paper, we introduce a new
resource allocation scheme based on rate variance envelopes. Such envelope
s capture a flow's burstiness properties and autocorrelation structure by c
haracterizing the variance of its rate distribution over intervals of diffe
rent length. From this traffic characterization, we develop a simple and ef
ficient resource allocation algorithm for static priority schedulers by emp
loying a Gaussian approximation over intervals and considering a maximal bu
sy period. Our approach supports heterogeneous quality-of-service requireme
nts via our consideration of prioritized service disciplines, and supports
heterogeneous and bursty traffic flows via our general framework of traffic
envelopes. To evaluate the scheme, we perform trace-driven simulation expe
riments with long traces of compressed video and show that our approach is
accurate enough to capture most of the available statistical multiplexing g
ain, achieving average network utilizations of up to 90% for these traces a
nd substantially outperforming alternate schemes.