Digital displays are a ubiquitous feature of public spaces; London recently deployed a whole network of new displays in its Underground stations, and the screens on One Time Square (New York) allow for presentation of over 16, 000 square feet of digital media. However, despite decades of research into pervasive displays, the problem of scheduling content is under-served and there is little forward momentum in addressing the challenges brought with large-scale and open display networks. This paper presents the first comprehensive architectural model for scheduling in current and anticipated pervasive display systems. In contrast to prior work, our three-stage model separates out the process of high level goal setting from content filtering and selection. Our architecture is motivated by an extensive review of the literature and a detailed consideration of requirements. The architecture is realised with an implementation designed to serve the world's largest and longest-running research testbed of pervasive displays. A mixed-methods evaluation confirms the viability of the architecture from three angles: demonstrating capability to meet the articulated requirements, performance that comfortably fits within the demands of typical display deployments, and evidence of its ability to serve as the day-to-day scheduling platform for the previously described research testbed. Based on our evaluation and a reflection on paper as a whole, we identify ten implications that will shape future research and development in pervasive display scheduling.