how many logistic/construction robots needed?

[Ormy]

As soon as you add another journey or other roboports to the same network, bots will dynamically switch between journeys/tasks as they are needed and also pause at different roboports to recharge along the way. It will be impossible to use a formula as there are a multitude of journeys and no way to predict when a specific robot will take a given journey and when it might swap to another journey or task, and no way to predict which roboport it will stop to charge at.

The only way to keep things deterministic and predictable is to have only one journey per logistic network. But that kind of defeats the whole point of a logistic network.

You're not thinking hard enough. If you impose some constraints, you actually get a simple algorithm that can tell you how many robots you need to keep the throughput of a logistics system maxed out.

I was working under the assumption that this thread was asking about a simple formula that could be used to calculate (approximately) number of bots needed for an arbitrarily large logistic network, possibly with dozens (or more) of requester/provider chests. The kind of formula that would allow you to perform a literal 'back of the envelope' calculation by hand by reducing the number of variables. That was my assumption, I may have been wrong.

Everything you say makes perfect sense* except what you suggest is an algorithm (I would call it a 'model') to compute the number of bots needed given all the necessary variables (likely numbering dozens or hundreds). Yes the algorithm would be relatively trivial to write but it would be something you would write in code for a computer to iterate through all the math for all the journeys, not something you could calculate by hand in any practical time-frame. What you describe is really just a simplification of what Factorio actually computes when we build a logisitic network. Your solution is similar to saying "to find out how many bots you need, build it in Factorio and find out".

I'm not saying your solution is useless. A small standalone executable that would accept as inputs a few numeric variables e.g. throughput goals/research levels, and a blueprint string (for number and relative positions of various chests and roboports) and tell you instantly the number of logistic bots required would be incredibly useful to some of us.

*Especially the bit about "Request amounts are set high enough that there's no "ringing" going on in the network". I only discovered this issue myself a few weeks ago causing apparent-bottlenecks in my base with no corresponding shortage of bots or materials, most confusing at first.