First by "patrol travel length" I mean count of star systems that a patrol fleet would go trough on it's patrol mission,
and "Suppression strength" is patrol fleet piracy suppression strength.
Here is an example of a 7 stars long trade route where the numbers represent "max piracy":
279
239
227
218
191
160
142
Our job here is to assign a patrol fleet to the route above, and the problem is whether to assign 1 or 2 or more patrol fleets and what would be optimal suppression strength of these (or single) fleet(s)?
The ultimate goal is to collect trade value and avoiding pirates popping out on that route.
Before you jump in consider there are 2 major problems that contribute to this issue as follows:
1. More fleets means faster max piracy cool downs because patrol fleet would return sooner to each of the systems due to shorter travel length.
2. The higher the suppression strength (than max piracy) faster will cool down be per system.
Precondition to solve this, results in 2 sub questions:
1. What is the optimal suppression strength relative to max piracy? (ex. I think if max piracy is 240, then optimal suppression strength is 280 or more or less?)
2. What is the optimal patrol travel length? (ex. I think 3-4 systems would be optimal, higher than this is counterproductive while lower is more expensive in terms of naval cap. and ship maintenance)
Therefore suppression strength is relative to travel length in addition to max piracy, but what is the optimal and how to develop some formula to let us calculate optimal?
Please consider sample route above to present your solution to the problem.
Btw. gateways are not a solution I'm looking for because that's late game tech.
EDIT:
Short version solution:
+8% patrol suppression strength increase is required per system.
For example above, a patrol route that covers 7 systems where max piracy of most affected systems is 279 "max piracy", would require 7 x 8 = 56% increase in suppression strength, which means this patrol fleet would need to be of 279 x 1,56 = 435,25 suppression strength or
44 corvettes.
Long version solution