deletions | additions       diff --git a/Arrival rate.tex b/Arrival rate.tex  index 6736e39..7bbe283 100644  --- a/Arrival rate.tex  +++ b/Arrival rate.tex 
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\subsection{Arrival rate}  We can assume our job arrivals to be governed by a Poisson process with parameter $\lambda$. However, our arrival times differ depending on the time of day (e.g. less jobs at night). The arrivals can then be modelled as an inhomogeneous Poisson process $\lambda = f(t)$, where we need to determine $f(t)$ from the data given.  Some days are busier than others, so we normalize the given data (dividing the number of arrivals at each time step  by the number of arrivals in 24 hours)to determine $f(t)$  and write $\lambda = R_i f(t)$ where $R_i$ is the relative business of the day. The easiest approach is to assume $f(t)$ is piecewise linear. For a given segment we can then simply use the fact that the maximum likelihood estimator (MLE) for a homogeneous Poisson population of $n$ samples is its average