Server utilization ($\rho$)

The long-run fraction of time a work-conserving server is busy. Applying Little's law to the server alone gives utilization equal to admitted queue throughput times mean service time. In a finite-buffer queue, the blocking probability must be included in that throughput.

For a work-conserving single-server queue with independent Poisson arrivals, finite buffer and independent identically distributed admitted service times of mean $\mu$, Poisson arrivals see time averages give admitted rate $\lambda (1-P_n)$. Little law for the server alone then gives the displayed busy fraction. The time parameter is the mean service duration, and need not be exponentially distributed.