On the M(n)/G/∞M(n)/G/∞ steady-state distribution

We present and verify the steady-state distribution of the state of the M(n)/G/∞M(n)/G/∞ system, i.e., an infinite-server system with a general service time distribution that receives customers through a state-dependent Poisson arrival process. Our verification of the steady-state distribution is based on the global balance equation for the system, which takes the form of a partial differential equation. The M(n)/G/∞M(n)/G/∞ model is important for studying admission-controlled, multi-server systems, e.g., communication networks with call/flow admission policies.