Temporal Multiplexing Gains

Effective Bandwidth is a powerful tool in modeling bandwidth and buffer requirements for multiplexed data sources. It is often approximated that an additional service capacity equal to the effective bandwidth of the source is required for every additional data source added to the multiplexed stream given a fixed buffer size and maximum blocking probability. This implies that a multiplexing gain can be achieved since additional buffer is not required with additional data sources. In this work, we consider other choices of bandwidth and buffer for a multiplexed case. By setting a price for bandwidth and buffer, we determine an optimal choice for the two resources. We consider the savings between simpler resource allocation schemes with that of the more complex optimal allocation scheme. We are interested to characterize the multiplexing gain so that we may determine if the savings in multiplexing outweighs the additional complexity of choosing optimal buffer and bandwidth at the multiplexor. In this regard, we find that the cost savings of optimal allocation over certain other allocation schemes is increasing and convex. By considering the case of On/Off Markov Fluids, we are able to obtain expressions for the optimal resource allocation path and resulting cost savings.