Problem $1$:

For the hand simulation of the simple processing system covered in class and presented in Section $2\mathrm{.}4$ in the book, define a new time$-$persistent statistic: At time t $($for $),$ the total number of parts in the system at time is denoted by N$($t$),$ which includes the parts in queue and in service. Augment Table $2-2$ to track this as a new global variable. Add statistical accumulators to update its time$-$weighted value and maximum at the time t of each arrival or departure, and compute these values at the end of the simulation.

You will need to modify the Homework$3\_$Template.xlsx $$ Problem $1$ tab. You will need to add $3$ columns $($in the appropriate places$)$ to the hand simulation table, fill it in$,$ and complete the entire table with the new columns you have added. You also need to fill in the two new performance measures you were asked for in the table $($Revised Table $2-3)$ provided for you below the hand simulation table. The inter$-$arrival times and service times are also in the template for your convenience.

$($Hint for all hand$-$simulation problems in this homework that require revisions to the hand simulation in Table $2-2$ of the book: You may be able to copy and paste some information from Table $2-2$ in the book. In addition, if you are clever with formula writing, you will be able to get Excel to keep track of the integrals and some of the other values in the hand simulation automatically, which makes your life easier.$)$