Consider an assembly line where some parts are produced in a station following a Poisson process with a rate of $\lambda$.
These parts are put directly in a bin (transfer time to the bin is negligible). We have $r$ robot arms that take these parts from the bin and place them in the next station.
Each robot arm is programmed to detect the number of parts in the bin, and it only collects and transfers them when there are precisely $b$ units available.
It takes $t$ time units for an arm to go from the bin to the next station, and it takes $t$ time units for it to return to the bin. The time for grabbing and dropping products is negligible.
If we model the robot arms as $M/D^{(b,b)}/r$, is the service time $t$ or $2t$?
I thought since it takes $t$ for a batch to be "served" which is it being taken from the bin and placed in the next station, the service time is $t$, and the service rate is $1/t$.
Does this make sense?