Consider looking into queueing theory. Check, for example: http://en.wikipedia.org/wiki/M/M/c_queue. Observe that a waiting time or a length of stay is never normally distributed because you cannot stay for less time than not at all.

Queueing theory is a good place to start. You can also try using a Poisson Regression. You can create a response variable, say patients per hour/12hrs. On top of that, you can use Doctor and Day of the week as predictor variables, among others. 

Many thanks Marc and Andrew, I wasn't familiar with queueing theory but it will definitely be useful. Good point regarding the distribution not being normal, it worked fairly well here (with censoring indeed) as my data didn't seem to be skewed, but I can see how that is inaccurate. For the context of my question though, I guess the answer is that there is no simple solution.

I have used Markov models so far, since the number of cycles allowed me to handle scheduled events. However I now have to use a simple decision tree (limited data) and it comes down to basic inputs such as: mean LoS is 13.3 hours, visits are scheduled every 4 hours – what's the mean number of visits?

Marc. You are using the function Y= 12hs/Npatients. If you have a sample with N=10 doctors, you may make a series with the data you have. I see no reasons to round them, data may be for example of X3= 2.4 if doctor visited 5 during the 12 hours fix time, including any lost time. Does this help? emilio