What performance parameters of the ticket system are the most informative?

Question

Task Management

Consider a typical ticket system.
Let it be a process management system or bug tracking system, or whatever.
The main thing is that an application appears in the system and it passes through the authorities, acquires documentation, passes through statuses, and at the end is documented and closed.
The system works, administrators administer, managers manage, the number of processed applications is growing.
Applications are different: typical and non-standard, urgent and ordinary, etc. etc.
So, if at some point the company decided to apply this system, then subsequently the management will be very interested in the question of whether all this is not in vain?
And for this, it is necessary to somehow quantify the effectiveness of the system.
As an option, you can use the following absolute and relative characteristics:
absolute: number of tasks, number of critical, number of closed, etc.
relative: the percentage of completed requests, the percentage of closed on time, the percentage of overdue, the percentage of critical closed on time, etc.
There is an opinion that absolute characteristics are not very informative (they say it is not even very clear that from the point of view of the management process they speak about efficiency) and it is worth using only relative ones, showing how effectively the process copes with the task.
So, dear community, I ask you to share your knowledge and experience:
what are the efficiency parameters commonly used in such systems in world practice?
What other performance parameters should you pay attention to?
what resources or articles are worth looking at?
maybe there are just interesting thoughts about the evaluation of effectiveness?

Answer 1

Efficiency is the ratio of results to costs.
If a company decides to apply this system, then it is done for some purpose. In the direction of these goals and look for the result. For example, if the system is implemented to reduce the number of errors, this will be the result (preferably converted into money). If the goal was to reduce the amount of manual work - similarly. Etc.
The acquisition and implementation costs are even easier to calculate. By the way, if we are talking about potential implementation, then there are free systems like Redmine, Trac, etc.