Sorry, in France we don't learn much statistitics during high school, some binomial, some Gauss law ..
i will obviously test once I get the datas different laws, including the continous Markov chain that you describe.
But more important, is to find if it exists a trend to increase ou decrease during these 6 years.
Last year, our head department said that we could stop this task, as (that's what he thought, he's retired now) we did such a good job in another place that near zero consultations per day were made in urgencies.
Actually, I see (and our new head department too) that we're rarely under 2-3 consultations per day (last 15 days, that was once only under 5 consultations asked, and twice 7 consultations)
Thus, what is your advice about the more powerful way (meaning the second order risk) to find if a trend exist ? 6x325 observations are something, but on the other hand a mean of 2 consultations per day will probably don't help..