Chapter 3Performance Metrics in Networks
In this chapter we introduce the main performance metrics in network design that will be part of the optimization models along the book. Link and end-to-end delay estimations are provided for packet switching networks, and several models are presented for evaluating blocking probability in circuit switching networks. Average number of hops and network congestion metrics are defined. Then, cost models are introduced that capture the economies of scale discounts appearing in network equipment acquisitions. Network availability is used for evaluating network resilience, under failure risks modeled using the Shared Risk Group (SRG) concept, and we present a method to estimate network availability in general protection or restoration schemes. Finally, we provide a rigorous definition of fairness in the allocation of resources (e.g., bandwidth in the links) among competing entities, and its connection with utility functions.
We pursue, when possible, simplified estimations of the performance metrics to ease its utilization in network models. In such case, their convexity properties are analyzed, since this is a property that can beexploited when designing optimization algorithms.
In packet-switching networks, randomness in the sources reflect in randomness in the packet flows observed in the links. This is the origin of buffering delays in the nodes and even packet drops when these buffers become full. Keeping such ...