Case Study: Emergency Room

$($DES$)$

Patients arrive at the Emergency Room following an unknown probability distribution

$($stream $1).$ They will be treated by either of two doctors.

A proportion of the patients are classified as NIA $($need immediate attention$)$ and the

rest as CW $($can wait$).$ NIA patients are given the highest priority, $3,$ see a doctor as soon

as possible for $40\backslash$pm $30$ minutes $($stream $2),$ then have their priority reduced to $2$ and wait

until a doctor is free again, when they receive further treatment for $30\backslash$pm $20$ minutes $($stream

$3)$ and are discharged.

CW patients initially receive a priority of $1$ and are treated $($when their turn comes$)$ for

$15\backslash$pm $10$ minutes $($stream $4)$; their priority is then increased to $2,$ they wait again until a

doctor is free, receive $10\backslash$pm $5$ minutes $($stream $5)$ of final treatment and are discharged.

An important aspect of this system is that patients who have already seen the doctor

once compete with newly arriving patients who need a doctor. As indicated, patients who

have already seen the doctor once have a priority level of $2($either increased from $1$ to $2$ or

decreased from $3$ to $2).$ Thus, there is one shared queue for the first treatment activity and

the final treatment activity. In addition, we assume that the doctors are interchangeable.

That is$,$ it does not matter which of the two doctors performs the first or final treatment.

Simulate for $20$ days of continuous operation, $24$ hours per day. Note, the inter$-$arrival

time and type of $100$ patients are collected $($based on a randomly selected weekday data$).$

The data is attached.

$1.$ Analyze your results and explain your suggestions for reducing the waiting time of the

patients.

$2.$ What is the average flow$-$time for NIA and CW patients before or after applying

suggestions. different suggestions.