This book is about stochastic networks and their applications. Large-scale systems of interacting components have long been of interest to physicists. For example, the behaviour of the air in a room can be described at the microscopic level in terms of the position and velocity of each molecule. At this level of detail a molecule's velocity appears as a random process. Consistent with this detailed microscopic description of the system is macroscopic behaviour best described by quantities such as temperature and pressure. Thus the pressure on the wall of the room is an average over an area and over time of many small momentum transfers as molecules bounce off the wall, and the relationship between temperature and pressure for a gas in a confined volume can be deduced from the microscopic behaviour of molecules.

Economists, as well as physicists, are interested in large-scale systems, driven by the interactions of agents with preferences rather than inanimate particles. For example, from a market with many heterogeneous buyers and sellers there may emerge the notion of a price at which the market clears.

Over the last 100 years, some of the most striking examples of largescale systems have been technological in nature and constructed by us, from the telephony network through to the Internet. Can we relate the microscopic description of these systems in terms of calls or packets to macroscopic consequences such as blocking probabilities or throughput rates? And can we design the microscopic rules governing calls or packets to produce more desirable macroscopic behaviour? These are some of the questions we address in this book.