Control Techniques for Complex Networks (Pre-publication Version)

What’s in here?

The book is divided into three parts. The first part entitled modeling and control contains numerous examples to illustrate some of the basic concepts developed in the book, especially those topics listed in (i) and (ii) concerning the fluid and CRW models. Lyapunov functions and the dynamic programming equations are introduced; Based on these concepts we arrive at the Max Weight policy along with many generalizations.

Workload relaxations arc introduced in Part II. In these three chapters we show how a cost function defined for the network can be ‘projected’ to define the effective cost for the relaxation. Applications to control involve first constructing a policy for the low-dimensional relaxation, and then translating this to the original physical system of interest. This translation step involves the introduction of hedging to guard against variability.

Most of the control techniques are contained in the first two parts of the book. Part III entitled Stability & Performance contains an in-depth treatment of Lyapunov stability theory and optimization. It contains approximation techniques to explain the apparent solidarity between control solutions for stochastic and deterministic network models. Moreover, this part of the book develops several approaches to performance evaluation for stochastic network models.