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\subsection{Modelling approach}  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). We The arrivals  can then describe our arrivals be modelled  as an inhomogeneous Poisson process $\lambda = f(t)$, where we need to determine $f(x)$ from the data given. Some days are busier than others, so we normalize the given data (dividing 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  \[  \widehat{\lambda} = \frac{1}{n}\sum_{i=1}^n k_i.