All access to the broker is by way of connections. Any limit on the number of concurrent connections can affect the number of producing or consuming clients that can concurrently use the broker.
The number of connections to a broker is generally limited by the number of threads available. Message Queue can be configured to support either a dedicated thread model or a shared thread model (see Thread Pool Management).
The dedicated thread model is very fast because each connection has dedicated threads, however the number of connections is limited by the number of threads available (one input thread and one output thread for each connection). The shared thread model places no limit on the number of connections, however there is significant overhead and throughput delays in sharing threads among a number of connections, especially when those connections are busy.