The way I see it is that you have a non-homogeneous poisson process to
describe the way the students arrive and that you're missing the service
time of your tutors.

The way you are modeling the arrival of students is *really *bad. At most,
only a single student can arrive each hour so to "solve" the model you've
created you need to have one tutor available each hour. Check out the
wikipedia articles on poisson process and non-homogeneous poisson process
(the first is simpler to model but the second is the situation you are
modeling).

As for service time, presumably you'll have tutors of different levels
(algebra 1 vs analysis 1) and it is not necessarily the case that your
analysis tutors can do algebra faster but that they command a higher hourly
rate for their expertise. In modeling you'll want to look at minimizing cost
(both direct for paying tutors and indirect for excessive wait time of your
customers)

Hope this helps.

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