= Queue population
{title2=$N(t),\quad L;\qquad N_q(t),\quad L_q$}
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,
$$
N_q(t)=\max\{N(t)-1,0\},\qquad L=L_q+\rho,
$$
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.
Back to article page
