Patients come to the service where they are treated and then leave. The service schedule is from

$8$ am to $8pm.$ The arrivals are exponentially distributed with a mean time between arrivals of

$0\mathrm{.}3$ hours. After arrival, each patient is assigned a degree of $1$ to $5,$ depending on the severity of

their illnesses. Patients in category $1$ are the most severe, and are sent immediately to a bed to

await medical attention. The remaining patients should first wait in the reception room for

registration before moving to the bed.

The service has three beds, an administration nurse at the reception, and two doctors. In all

cases, the priority for allocating these resources is based on the severity of the condition. The

reception time for patients in categories $2-5$ is uniform between $0\mathrm{.}1$ and $0\mathrm{.}2$ hours. The

treatment time for all patients follows a triangular distribution. The distribution of patients by

category and the corresponding minimum, most likely, and maximum times of treatment are

summarized below.

Questions:

Use queue theory to compute the utilization of nurse, doctors and beds. Compute the mean

treatment time for all patients combined and the mean treatment time for each type of

patient. The mean treatment time is the time from the entrance to the exit.

Model the process using Attributed Timed Petri Nets.

Build a simulation model and perform the following experiment

Determine the utilization of doctors, nurse and beds. Determine the mean treatment time

for all patients combined and the mean treatment time for each type of patient. The mean

treatment time is the time from the entrance to the exit. Compare the results against the

theoretical results obtained using queue theory.

Do a manual simulation of the $6$ first patients until the leave the process. Obtain the random

values for each distribution using the inverse transform.