Perturbation analysis of stochastic fluid models with respect to the fluid arrival process

The deployment of network applications (e.g., multimedia and other real time applications) has put extra pressure on network scarce resources (bandwidth and buffers) thus generating a need for effective resource allocation and management. In this paper we adopt a stochastic fluid model (SFM) framework and derive sensitivity estimators for three performance measures of interest (workload, throughput and loss volume) with respect to the fluid inflow process parameters. The motivation is to use the sensitivity estimators for dynamic control and optimisation of the systems performance. Subsequently these estimators are evaluated based on data observed from a single sample path of the discrete-event system and are used to dynamically control the input process to the system allowing the network to work continuously at an optimal or near optimal point. The proposed analysis naturally leads to a distributed algorithm for evaluating the propagation of perturbations in a network (e.g., due to changes in the buffer size of upstream nodes).