Network internal traffic characterization and end-to-end delay bound calculus for generalized processor sharing scheduling discipline

This paper addresses the end-to-end performance bound provisioning problem for one of the most significant traffic scheduling algorithms, generalized processor sharing (GPS). In particular, solutions are given to the network internal traffic characterization and end-to-end delay bound calculation problems in arbitrary topology GPS networks, where sessions are allowed to be arbitrary weighted. In the first part of the paper methods are given for determining internal (at inputs of network nodes) traffic descriptors of sessions, which are originally leaky bucket constrained at the network edge. The output burstiness behaviour of the arbitrary weighted GPS server is analyzed, and based on these results two algorithms are proposed that not only calculate internal traffic descriptors, but can also be used to manage network stability questions in non-feedforward networks. In the second part the end-to-end service curve is introduced to capture end-to-end worst-case traffic conditions of sessions, which forms the basis of the proposed method for end-to-end delay bound calculation. Extensive numerical analysis is shown to illustrate the tightness of this delay bound and various examples for internal traffic characterization are also conducted.