Consider a parking lot simulation. There are $2$ barrier exit points in the existing system. One of

them is reserved to serve the subscribers. The other serves the vehicles of non$-$subscribers. The

present system is schematized in Figure $1.$ According to the previous data, $20\%$ of the vehicles

arriving at the parking lot belong to subscriber customers.

Figure $1.$ Current System

According to the results of the analysis of the previous period data, in the current system, the inter$-$

arrival time of the vehicles to the "non$-$subscribers" exit fits to the exponential distribution with a

mean duration of $75$ seconds. However, the payment time at the payment counter corresponds to

the normal distribution with an average of $120$ seconds and a standard deviation of $20$ seconds

$($License plate reading and barrier opening time is accepted within the payment period$).$ The inter$-$

arrival time of "subscriber" vehicles fits to the exponential distribution with an average of $300$

seconds, and there is a uniformly distributed time delay between $10$ and $15$ seconds when crossing

the barrier $($due to the time of license plate reading and barrier opening$).$

As an alternative system, the parking lot owner is considering adding another payment counter to

the "subscribers" exit as a solution especially for reducing the waiting times of non$-$subscribers. In

this way, there will be two payment points serving non$-$subscribers, and the non$-$subscribers

customers can enter the shortest queue.

Considering this information and the fact that there are no vehicles in the system at the beginning.

a$)$ Build a simulation model for each option $/$ system, calculate the average waiting times

in the system by running both models for the first $10$ vehicles.

b$)$ Find the confidence interval for the average waiting time per customer by doing $3$

replications for each option $/$ system.

c$)$ Show which of these two options $/$ systems is better

d$)$ Calculate the number of additional replications required for the current system $(=0\mathrm{.}4$ minute$)$

hello

please solve this question by making a simulation data table writing down all the calculations and formulas $,$ and please dont use char gpt it will nor work as well $,$ solve it by hand without software $.$

thats all thank you