A controlling process is a Wolfram kernel or front end that handles input, output and scheduling for the computing processes. You can evaluate $MaxLicenseProcesses to check the maximum number of controlling processes available for your license. A computing process (also known as a “subkernel”) is a Wolfram kernel that executes computations while accepting input from and returning output to a controlling process kernel only. Mathematica launches an automatically determined number of subkernels with each controlling process.

Each standalone Mathematica session consumes one controlling process and, on a typical machine, four computing processes. Running two sessions simultaneously therefore consumes all available processes of a standard “2,2,8,8” single-user license. Starting a third session leads to a request for an additional activation key or a kernel license failure message.

Using MathLM, the controlling process is the number of network users that can use Mathematica simultaneously, also known as available client seats. The MathLM computing process is the total number of subkernels the clients can use.