Networks: A
AbstractSocial networks connect people and enable them to exchange information. News and rumors spread through these networks. We explore models of such propagations. The technology behind social networks is the internet where packets travel from queue to queue. We explain some key results about queueing networks.Section 5.1 explores a model of how rumors spread in a social network. Epidemiologists use similar models to study the spread of viruses. Section 5.2 explains the cascade of choices in a social network where one person’s choice is influenced by those of people she knows. Section 5.3 shows how seeding the market with advertising or free products affects adoptions. Section 5.4 studies a model of how media can influence the eventual consensus in a social network. Section 5.5 explores the randomness of the consensus in a group. Sections 5.6 and 5.7 present a different class of network models where customers queue for service. Section 5.6 studies a single queue and Sect. 5.7 analyzes a network of queues. Section 5.8 explains a classical optimization problem in a communication network: how to choose the capacities of different links. Section 5.9 discusses the suitability of queueing networks as models of the internet. Section 5.10 presents a classical result about a class of queueing networks known as product-form networks.