Question regarding period, time and so on I'm reading a paper regarding the workload of air traffic controller.
In this paper, P is a mean task recurrence period per aircraft.
In this context, 'task' mean 'recurring task' which is a repeated activities of controllers (e.g. checking route compliance of traffic)
t is a mean required time for controllers to complete this task, and N is a number of aircraft in a sector of airspace.
In this case, what N/P and t/P mean, respectively?
Paper noted that N/P is an occurrence rate of this task, and t/P is the fraction of total time devoted to recurring task for each aircraft. But I still don't get it... can anyone please explain the logic?
 A: Given definitions:

*

*$N :=$ the number of aircraft

*$t :=$ the mean task duration

*$P :=$ the mean task-recurrence period $\color{red}{\text{per aircraft}}$
Claims:

*

*$t/P$ is the fraction of total time devoted to each recurring task
for each aircraft

*$N/P$ is a task occurrence rate

From the above information, it is clear that $P$ is a simple duration (a time quantity), not a rate, and that each aircraft has its own value of $P:$ so, $P$ is actually the mean task-recurrence period of each aircraft (nor per aircraft).
With this correction,

*

*it becomes self-evident that for each aircraft, $t/P$ is indeed the
fraction of total time devoted to each task.

*$$\frac NP=\frac{\text{the number of aircraft}}{\text{mean
task-recurrence period of each aircraft}}\\=\frac{\text{the number
of aircraft $\times$ number of tasks of each aircraft}}{\text{total
task-recurrence period of each aircraft}}\\=\frac{\text{total number
of tasks}}{\text{total task-recurrence period of each aircraft}}$$
is the task-occurrence rate of each aircraft.

