Is there an upper limit on how many concurrent connections that MarkLogic can process? For example, ASP.NET is restricted to processing 10 requests concurrently, regardless of infrastructure and hardware. Is there a similar restriction in MarkLogic server? If not, are there any benchmarks that give some indication as to how many connections a typical instance can handle?
Given a large enough budget there is no practical limit on the number of concurrent connections.
The basic limit is the application server thread count, although excess requests will also pile up in the backlog queue. According to groups.xsd each application server is limited to at most 256 threads. The backlog seems to have no maximum, but most operating systems will silently limit it to something between 256-4096. So depending on whether or not you count the backlog, a single app server on a single host could have 256-4352 concurrent connections.
After that you can use multiple app servers, and add hosts to the cluster. Use a load balancer if necessary. Most operating systems will impose a limit of around 32,000 - 64,000 open sockets per host, but there is no hard limit on the number of hosts or app servers. Eventually request ids might be a problem, but those are 64-bit numbers so there is a lot of headroom.
Of course none of this guarantees that your CPU, memory, disk, and network can keep up with the demand. That is a separate problem, and highly application-specific.