lambda cold start & synchronous execution

Hi,

If there is a lambda that is being called frequently enough so that there is always at least one container warm, is there ever a scenario where I could invoke the lambda enough times synchronously, that one (or more) of my invocations could be hit with a warm-up delay while additional containers are spun to handle the load?

Also how many synchronous executions of a lambda will execute on a single container?

For example, if I had a lambda that took 30 seconds to execute and required 256mb – when the first container is created for this lambda to run, how many concurrent threads (each consuming 256mb) would I expect the first container to be able to handle? If I simultaneously call the lambda 100 times, will they all execute on the warm container? Or will more containers be created, and will those subsequent containers cause a warm-up delay in some of the invocations? Alternatively, if I started cold, and then started invoking the lambda consistently every 100ms, will some of these invocations other than the first exhibit a warm-up delay?