PLEASE SHOW HOW TO DO IT STEP BY STEP IN SIMIO$(40$ points$)$ Assume you are doing an intern at Delta and is required to simulate the queuing system. Let us assume the inter$-$arrival time of customers is stationary and follows exponential distribution with mean to be $15$ seconds. After customers arrive into the Atlanta airport, they will first greeted by a receptionist who checks the membership status of each customer, whose service time follows an exponential distribution with mean service time to be $25$ seconds. Next, as many customers may confuse the regular membership lounge with the premium location, $74\mathrm{.}9\%$ customers will go to the destination and $25\mathrm{.}1\%$ customers will go to the lounge. Once their premium membership status is confirmed, they are directed to the lounge area if the lounge is not full yet. Note that the lounge has a capacity limit to avoid overcrowding. In case the lounge is full already, the customers can sit and wait near the receptionist desk until someone else departs the lounge. As soon as there is availability, waiting customers enter the lounge on a first$-$come$-$first$-$served basis. The time spent by each customer in the lounge follows an exponential distribution with mean to be $100$ minutes.

For modeling simplicity, you assume the premium members waiting to enter the lounge do not leave before entering the lounge, and the waiting space has no capacity limit$.$ Besides, the connector between Source and Receptionst, Receptionist and Lounge, or Lounge and Destination takes zero travel time. The running time is initially set to be $24$ hours.

$($i$)$ Build the Simio model in the Facility window to simulate the described system. Take a screenshot of your simio model and put it in your pdf document.

$(5$ points$)$

$($ii$)$ Before you simulate this model, you need to decide $($a$)$ the capacity level at Receptionist, and $($b$)$ the capacity level at the Lounge. Notice that for the latter, you can only choose as an increment of $10,$ e$.$g$.,10,20,$cdots. For each server you built in Part $($i$),$ compute the arrival and service rates $($the baseline unit must be in minutes$)$ and report the minimum required capacity to have a stable system.

Please also specify the capacity level for each server in Simio by modifying the Initial Capacity at Properties section. In subsequent questions, we will use the capacity levels specified in this part.

$(10$ points$)$

$($iii$)$ Create a new experiment with $200$ replications. For each server, report its $98\%$ confidence interval on the average waiting time of customers. Provide the expressions for each response variable you defined. Which one spends the longest waiting time $($we call such a server the bottleneck station$)?$

$(10$ points$)$

$($iv$)$ Create a new experiment with $200$ replications. Estimate the probability that the waiting time at the bottleneck station is longer than $1$ minute.

$(5$ points$)$

$($v$)$ Create a new experiment with $400$ replications. Then, set the warm$-$up period in the Experiment's property window to $10$ hours, and set the total run length to $10$ times as long as the warm$-$up period.

Provide a $90\%$ confidence interval on the average time in system of customers. $(5$ points$)$

$($vi$)$ Now, let's compare the expected time in system your Simio model estimated with the exact steady$-$state expected time in system using QueueingTools.xlsm$.$ First, finish the Table below and then utilize Little's law to compute the long$-$run expected time in the