Prepare a $".$docx" or $".$doe" $($ARENA project$)$ file $(3)$ which contains your simulation model and a $".$pdf$"$ file $(4)$ which contains your answers for Question $2.$ Finally, prepare a $".$pdf$",$ or $".$zip" file containing these five files. The submission deadline is January $7$th$,2023,23$:$59.$ Only submissions made through the corresponding submission link provided in LMS page will be graded.

Consider a simple call center that works for seven days a week and $24$ hours a day. The call center works in $2$ shifts. The first shift starts at $08$:$00$ and ends in $20$:$00,$ employing $3$ identical call center agents. The second shift starts at $20$:$00$ and ends in $08$:$00,$ employing $2$ identical call center agents. In the end of the first shift, if the third agent is busy, s$/$he does not end his$/$her shift until that task is complete. However, s$/$he does not compensate this extra work, and tomorrow, $\frac{s}{?}$ he starts his$/$her shift at the regular time at $08$:$00.$

Through out the day, the inter$-$arrival times of the calls arriving to the center $($and the arrival of the first caller$)$ follow exponential distribution with an average of $5$ minutes. The call$$rs are calling according to a Poisson process with a rate $=12$ calls per hour. When a caller calls, $\frac{s}{?}$ he waits until an agent becomes idle, then the service starts. A caller can be any of the three types of callers:

Type I Caller: $20\%$ of the callers are Type I callers. The service duration of type I callers is normally distributed with an average of $12$ minutes and standard deviation of $1\mathrm{.}75$ minutes.

Type II Caller: $42\%$ of the callers are Type $H$ callers. The service duration in minutes of type II callers is Erlang distributed with shape parameter $k=4$ and scale parameter $($exponential mean$)2\mathrm{.}5.$

Type III Caller: $38\%$ of the callers are Type III callers. The service duration of type III callers is deterministic with fixed period of $12\mathrm{.}25$ minutes.

Callers wait in a single queue until an agent becomes idle. This queue adapts a FIFO discipline between type I and type II callers, and a FIFO discipline between type III callers. However, type III callers are given a priority and they always get in front of type I and type II callers in the queue.

$($a$)(12$p$)$ Develop a simulation model $("*.$doe" file$)$ in ARENA that will be run for $100$ replications, where each replication is $20$ days long with a warm$-$up period of $1$ day. In your ARENA model, as animation:

a plot diagram must show the number of callers in the system,

a variable must show the number of busy agents at any moment,

a clock must show the time of the day $($in hours, minutes, and seconds$),$

Type I, II$,$ and III clients should respectively be animated as a green, blue, and red balls before they enter the service queue.

$($b$)(18$p$)$ Prepare a $".$pdf$"$ file that provides answers to the following questions.

What fraction of callers spends more than $40$ minutes in the system? Provide an estimate.

What is the average time spent in the queue by a client? Provide an estimate and a $95\%$ confidence interval.

What is the instantaneous utilization of the agents? Provide an estimate and a $95\%$ confidence interval.

What is the average number of clients in the system? Provide an estimate and a $95\%$ confidence interval.

I know that it requires Arena but it's enough for me just to draw the simulation Thanks:$)$