# How to compute the time required to transport one unit of flow on a given path?

My question is related to freight transportation, but I am stuck on the logic. So, I am considering a path between two points $$(a, b)$$ where I am sending $$n$$ trucks where the capacity/truck is $$k$$. The distance is $$d$$ and the truck speed is $$v$$. Let's say that I am trying to get the time required to transport one unit of freight, do I use the standard $$t_{a,b}=\frac{d_{a,b}}{v}$$ or do I consider road capacity (i.e., $$path \ cpty_{a,b} =\frac{60}{headway}$$)? If I consider $$t_{a,b}=\frac{d_{a,b}}{v}$$, and assuming that $$n$$ vehicles are not simultaneously dispatched, then which is it ? The time to transport one unit of freight, $$k$$ units of freight ? Finally, do I need to use queuing theory to compute the total time to transport $$k \times n$$ units of freight ?

An example would be a minimum flow time model where the objective function is to minimize the total amount of transit time or $$Min \ Z= \sum_{a \in O}\sum_{b \in D}t_{a,b}x_{a,b}$$, where $$t_{a,b}$$ is the average time to transport 1 unit of flow over any $$(a,b) \in A$$ and $$x_{a,b}$$, the total flow transiting through any $$(a,b) \in A$$. If I have to solve it, I would need to be able to accurately define a function to compute $$t_{a,b}$$.

• Welcome to ORSE. I think more context would be needed to answer the question. If you could dispatch all $n$ trucks more or less simultaneously, I would say $d_{a,b}/v$ would be the time to transport up to $k\times n$ units of freight.
– prubin
Apr 14, 2022 at 15:27
• Hi, thanks for your response. In fact, I am trying to create a model where I am minimizing the average travel time in a flow network. Therefore, I needed to know whether the time per unit of flow is $t=\frac{d}{v}$. The assumption is that $n$ trucks aren't dispatched simultaneously, therefore the mentioned formula would not be applicable.
– Bree
Apr 14, 2022 at 15:57
• We might need to see the full model to give a useful answer. Based on your edit, I would suggest just tracking the transit time $d/v$ for each truck and sum those up if the total amount of flow (across all routes/trucks) is fixed.
– prubin
Apr 14, 2022 at 16:26
• Thank you, I will try that and see how it works out.
– Bree
Apr 14, 2022 at 16:29
• @Bree, Out of curiosity, Why you don't try to use real-time by asking a driver that drives many times this specific road? Apr 14, 2022 at 18:23