Question regarding period, time and so on

Question

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?

Answer 1

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,

1. it becomes self-evident that for each aircraft, $t/P$ is indeed the fraction of total time devoted to each task.
2. $$\frac NP=\frac{\text{the number of aircraft}}{\text{mean task-recurrence period of each aircraft}}\\=\frac{\text{the number of aircraft $\times$ number of tasks of each aircraft}}{\text{total task-recurrence period of each aircraft}}\\=\frac{\text{total number of tasks}}{\text{total task-recurrence period of each aircraft}}$$ is the task-occurrence rate of each aircraft.