Infinitesimal Perturbation Analysis in Networks of Stochastic Flow Models: General Framework and Case Study of Tandem Networks with Flow Control

This paper presents a general algorithmic framework for computing the IPA derivatives of sample performance functions defined on networks of fluid queues. The underlying network-model consists of bi-layered hybrid dynamical systems with continuous-time dynamics at the lower layer and discrete-event dynamics at the upper layer. The linearized system, computed from the sample path via a discrete-event process, yields fairly simple algorithms for the IPA derivatives. As an application-example, the paper discusses loss and workload performance functions in a tandem network with congestion control, subjected to signal delays.