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40319.2 Modeling and controlling AMoD systems 2. We outline two recent, yet promising approaches for the analysis and control of AMoD systems, which leverage the aforementioned spatial queueing-theoretical model. The first approach, referred to as “lumped” approach, exploits the theory of Jackson networks and allows the computation of key performance metrics and the design of system-wide coordination algorithms. The second approach, referred to as “distributed” approach, transforms the problem of controlling a set of spatially- localized queues into one of controlling a single “spatially-averaged” queue and allows the determination of analytical scaling laws that can be used to select system parameters (e.g., fleet sizing). 3. We discuss two case studies for the deployment of AMoD systems in New York City and Singapore. These case studies suggest that it is much more affordable (and convenient) to access mobility in an AMoD system compared to traditional mobility systems based on private vehicle ownership. The chapter concludes with a discussion about future directions for research, with a pre- liminary discussion about the potential of AMoD systems to decrease congestion. The re- sults presented in this chapter build upon a number of previous works by the author and his collaborators, namely [13] for the lumped approach, [14, 15, 16, 17] for the spatial queue- ing-theoretical framework and the distributed approach, and [13, 18] for the case studies. The rest of this chapter is structured as follows. Section 19.2 presents a spatial queueing model for AMoD systems and gives an overview of two complementary approaches to control AMoD systems, namely, the lumped approach and the distributed approach. Section 19.3 leverages analysis and control synthesis tools from Section 19.2 to provide an initial evaluation of AMoD systems for two case studies of New York City and Singa- pore. Section 19.4 outlines directions for future research, with a particular emphasis on (and some preliminary results for) congestion effects. Finally, Section 19.5 concludes the chapter. 19.2 Modeling and controlling AMoD systems 19.2.1 Spatial queueing model of AMoD systems At a high level, an AMoD system can be mathematically modeled as follows. Consider a given environment, where a fleet of self-driving vehicles fulfills transportation requests. Transportation requests arrive according to an exogenous dynamical process with associated origin and destination locations within the environment. The transportation request arrival process and the spatial distribution of the origin-destination pairs are modeled as stochastic processes, leading to a probabilistic analysis. Transportation requests queue up within the environment, which gives rise to a network of spatially-localized queues dynamically served by the self-driving vehicles. Such network is referred to as “spatial queueing system.” Performance criteria include the availability of vehicles upon the request’s arrival