Optimal Resource Allocation Problems (ORAP) G(V ^∗) in TND

Overview

Chapter 7 begins the last of three chapters on optimization problems in topological network design (TND). While all the optimization problems are closely intertwined, we separate them due to the complexity and detail involved. We will build upon the open and closed algorithms which regulate the performance of the network and add optimization algorithms to define the best resources within the network.

• Resource Allocation Problems (ORAP)

These are the foremost problems one considers in improving stochastic flow processes as they are the most obvious ones and also some of the most significant.

• Optimal Routing Problems (ORTE)

Routing problems while related to the resource allocation ones in Chapter 7 are normally distinguishable because of certain application requirements. Accessibility and egress are good examples where routing is critical, but in telecommunications and computer network, routing problems are very significant. We will address these in Chapter 8

• Optimal Topology Problems (OTOP)

Optimal topology problems are perhaps the most challenging and complex network design problems because of their frequent integer requirements. Since they often comprise the resource allocation and routing problems, they are also quite significant to applications. We will close this volume in Chapter 9 by examining the OTOP.

Since the fabric of the universe is most perfect and the work of a most wise Creator, nothing at all takes place in the universe in which some rule of maximum or minimum does not appear

—Leonard Euler

With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.

—John von Neumann

But I think it is a fact that no self-respecting company can get along without having some form of optimization in its planning structure or some kind of optimization in its day-to-day operations. Otherwise they’ll go out of business. They won’t be in competition with the others any more.

—Harold Kuhn