Traffic equivalence and substitution in a multiplexer

For a multiplexer fed with a large number of sources, we derive conditions under which a single source can be substituted for a given subset of the sources while preserving the buffer overflow probability and the dominant time scales of buffer overflows. This equivalence is stronger than simple effective bandwidth equality and takes into account the context in which multiplexing takes place. This allows a substitution to be made for arbitrarily large proportions of the traffic without changing the operating point of the multiplexer as experienced by the rest of the traffic. It corresponds to defining a single source which is equivalent in a sense “local” to a given context, rather than equivalent in a sense which is “universal” to all contexts. The proposed methodology does not rely on traffic models and obtains the necessary information from the actual traffic traces. We study the case of fractional Brownian motion as a single source substitute and provide theoretical and experimental results that validate our approach