Here's a paper on an aspect of cloud computing by two Microsoft economists. (Microsoft's cloud service is called Microsoft Azure.) In addition to the capacity question the paper models, it presents a brief, clear overview of the market for cloud computing.
Efficient Capacity Provisioning for Firms with Multiple Locations: The Case of the Public Cloud by Patrick Hummel∗ and Michael Schwarz* March 26, 2021
Abstract: This paper presents a model in which a firm with multiple locations strategically chooses capacity and prices in each location to maximize efficiency. We find that the firm provisions capacity in such a way that the probability an individual customer will be unable to purchase the goods the customer desires is lower in locations with greater expected demand. The firm also sets lower prices in larger locations. Finally, we illustrate that if a customer is indifferent between multiple locations, then it is more efficient to place this customer in a location with greater expected demand. These theoretical results are consistent with empirical evidence that we present from a major public cloud provider.
"2.1 Industry Overview
"The cloud computing industry is young, large, and rapidly growing. Although some of the concepts behind the public cloud were developed as early as the 1960s, all modern public clouds first emerged in the 21st century (Foote 2017). Today annual world cloud revenues exceed $250 billion and are expected to grow by another 20% in 2021 (Graham et al. 2020a).
"The public cloud consists of a wide range of services including infrastructure as a service (IaaS), platform as a service (PaaS), and software as a service (SaaS). SaaS involves providing applications such as web-based email and productivity software to a consumer that can be accessed via the Internet. PaaS provides a platform for deploying consumer created applications using the provider’s programming languages, libraries, and tools.
"And IaaS provisions fundamental computing resources such as processing, storage, and network to a consumer that can be used to deploy and run arbitrary software (Mell and Grance 2011)."