Due: $16\mathrm{.}11\mathrm{.}2024$ @$12$:$00$

Do this homework in groups of $7-8!$

You are supposed to upload your Arena files $(.$doe and $.$out$)$ and a document in which you write the group members and answers to the questions to Moodle.

You are the owner of a ballet school and you will select your ballet teachers on the weekend. You want to make a study to explore whether your current system is adequate or not. The description of the selections system is as follows:

The selection will be all day long. Selection will be for two different categories, adult ballet teacher $($Category $1)$ and child ballet teacher $($Category $2).$ Arrival of candidates is expected to be exponentially distributed with mean $5$ minutes for Category $1$ and with mean $10$ minutes for Category $2.$

There are $2$ registration desks with one worker for each to register the candidates. Registration duration for Category $1$ is TRIA $\backslash ((1,3,4)\backslash )$ and TRIA $\backslash ((3,5,10)\backslash )$ for Category $2.$ After registration, they are all directed to a preparation area. Their preparation time is $\backslash (\backslash$operatorname$\{$TRIA$\}(1,3,4)\backslash )$ and $\backslash (\backslash$operatorname$\{$WEIB$\}(2\mathrm{.}5,5\mathrm{.}3)\backslash )$ respectively for Category $1$ and Category $2.$ The maximum amount of ballet teachers that can get into the preparation area is limited with $5.$

After getting prepared ballet teachers are directed to the stage to display their performances. The stage can only be used by one ballet at a time. The duration for their performance is $\backslash (\backslash$operatorname$\{$NORM$\}(2,0\mathrm{.}3)\backslash )$ minutes.

At the end $15\backslash \%$ of all the candidates $($regardless of their category$)$ are selected as ballet teacher, $20\backslash \%$ is given a second chance and $65\backslash \%$ is rejected. After the decision all candidates leave the dance club.

Simulate the system for $8$ hours. Collect statistics on:

$-$ resource utilizations

$-$ avg. queue lengths

$-$ avg. queue waiting times

$-$ time in system for ballets $($regardless of their category$)$

$-$ number of selected ballet teachers, number of ballet teachers who are given a second chance and number of rejected ballet teachers.

You must submit $.$doe and $.$out files to Moodle!

Before you write the answers to the above statistics, be sure that you first define entities, resources, queues, counters and tallies.

Remark:

All time units are in minutes!