The multiplexing of variable bit rate traffic streams in a packet network g
ives rise to two types of queueing. On a small time-scale, the rates at whi
ch the sources send is more or less constant, but there is queueing due to
simultaneous packet arrivals (packet-level effect). On a somewhat larger ti
me-scale, queueing is the result of a relatively high number of sources sen
ding at a rate that is higher than their average rate (burst-level effect).
This paper explores these effects. In particular, we give asymptotics of t
he overflow probability in the combined packet/burst scale model. It is sho
wn that there is a specific size of the buffer(i.e. the 'critical buffer si
ze') below which packet-scale effects are dominant, and above which burst-s
cale effects essentially determine the performance-strikingly, there is a s
harp demarcation: the so-called 'phase transition'. The results are asympto
tic in the number of sources n. We scale buffer space B and link rate C by
n, to nb and nc, respectively; then we let n grow large. Applying large dev
iations theory we show that in this regime the overflow probability decays
exponentially in the number of sources n. For small buffers the correspondi
ng decay rate can be calculated explicitly, for large buffers we derive an
asymptote (linear in b). The results for small and large buffers give rise
to an approximation for the decay rate (with general b), as well as for the
critical buffer size. A numerical example (multiplexing of voice streams)
confirms the accuracy of these approximations.