Shiny Server launches one R process per application and R itself is single threaded, so requests are serialized. If, for example, it takes 10 seconds to react to a request and 2 people make requests very close to each other; it will likely take ~ 20 seconds for both requests to complete. However, with Shiny Server Pro you can control how many R processes are started for each application and how many connections you want to support per R process.
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