Multiplexing gains in bit stream multiplexors

We are concerned with characterizing the variation of multiplexing gains with source type and burstiness in integrated service systems such as ATM. We model a fixed capacity high speed bit pipe that multiplexes a moderate number of bit streams with minimal buffer under a low loss constraint. Each service type is defined by its instantaneous bitrate distribution, but the bitrate distribution of multiplexed streams is approximated as Gaussian. The Gaussian approximation is not as accurate as Chernoff bounds, but it allows for stronger characterization of multiplexing gains. We consider three schemes for allocating bandwidth to services: by individual user, by path and service type, and by path only. We find explicit formulae for sensitivities of required capacity to source rate mean and variance and to loss rate. We characterize multiplexing gains and costs to identify the benefits of each allocation policy. We find that the capacity savings resulting from sharing resources is proportional to the square root of the ratio of source rate variance to source rate mean. This suggests that although bursty sources require more bandwidth, multiplexing gains are increasing with burstiness. We also find that the extra capacity required to multiplex dissimilar source types is increasing with the difference between their burstinesses. This suggests that when bit streams are partially grouped, it is most important first, to group similar source types.