Burstiness bounds for some burst reducing servers

A framework for studying a stream of traffic or a message as it is transferred over an asynchronous transfer mode (ATM) connection was previously proposed by the authors (1991). A message is modeled as a deterministic fluid flow, and an ATM node is modeled as a server that allocates bandwidth among concurrent messages. The key concept is that of the burstiness curve of an incoming message, which gives the buffer size needed if the message is served at rate μ. It is shown there that the fixed rate, the leaky bucket, and the affine server are burst reducing. The burstiness bound for each of these servers is presented. A sequence of identical affine servers is related to a fixed rate server, and it is suggested how quality-of-service parameters can usefully be based on the burstiness curve