Queue population ($N(t),L;N_q(t),L_q$)

The population $N(t)$ of a queue counts every admitted customer still inside the selected system at time $t$, including customers receiving service when the server is inside that boundary. Its long-run time average is $L$. The waiting population $N_q(t)$ excludes customers currently receiving service, and its long-run time average is $L_q$. For a single server that serves whenever work is present,where $\rho$ is the server utilization, assuming at most one customer receives service at a time. In a stationary process with ergodicity and finite expected values, these time averages equal $\mathbb{E}N(t)$ and $\mathbb{E}{N}_q(t)$. The workload of a queue instead counts unfinished work, so two queues with the same population can have very different remaining workloads.