Assuming that the arrivals occur according to a Poisson process and that the time to process each arrival is fixed, how can the optimal number of servers 'c' be calculated such that the waiting time of each arrival and the numbers of 'c' can be kept as low as possible?
Should I approach this problem by taking different numbers of 'c', calculating the average waiting time for each number of 'c' and compare which combination of 'c' and the waiting time would be optimal?
I mean, to ensure a short waiting time, we could simply take a very high value for 'c' which is obviously not what we want.
Context: it concerns an assignment concerning a model describing a tunnel containing tollgates represented by 'c'. The arrivals are cars, and we want to keep the waiting time for the cars as low as possible, and use as less tollgates as possible as those are apparently fairly expensive.
Edit: I'm not so sure whether I've described the problem using the M/D/c queue correctly as I came to that conclusion just after a while of doing research on the internet.