Problem $1$: Estimation

This problem studies the estimation of a banking service using a $\frac{M}{M}\frac{?}{1}$ queue.

The average number of customers coming to the service window is $2$ per a $10-$minute interval. Moreover, the average number of services that can be completed is $2\mathrm{.}3$ per a $10-$minute interval. Please write a simulation program to show the number of people in the queue in w two$-$hour span. For one of the sample runs, please record the time the customers coming to the window $($in the unit of minutes$)$ and leaving the window when their services are complete $($also in the unit of minutes$).$

Now let us start from the sequences of arrival times and leaving times that you generated in the above problem. Please use these two sequences of data to estimate the arrival rate and service rate. Do they match with the rates that you originally used to generate the data? Write down the details how you solved this problem and include the data, Matlab codes and results.