Figure $5\mathrm{.}17$ shows that the utilization estimates of the Assembler resource at the Assembly module and the Painter resource at the Painting module are $0\mathrm{.}94$ and $0\mathrm{.}59,$ respectively. These estimates in Figure $5\mathrm{.}17$ correspond to a heavy traffic regime in the former and a medium traffic regime in the latter. These result in long average buffer delays and large average buffer occupancy in the assembly process, and in short average buffer delays and low average buffer occupancy in the painting process as shown in Figure $5\mathrm{.}18.$ Finally, the Tally section of the User Specified output in Figure $5\mathrm{.}19$ displays not only averages, but also the corresponding $95\%$ confidence interval half$-$ widths, as well as the minimal and maximal observations for the number of reworks and flow time per job. Note that some jobs underwent as many as four reworks, while the average number of reworks is just $0\mathrm{.}18,$ indicating a low level of reworks. The average flow time $(49\mathrm{.}5252$ hours$)$ is moderately longer than the sum of the average delays in the Assembly and Painting queues $(35\mathrm{.}42$ hours$)$ and the sum of average processing times there $(7$ hours$),$ due to additional rework performed at module Assembly.

$5\mathrm{.}7$ EXAMPLE: A HOSPITAL EMERGENCY ROOM

This section presents a more detailed model$$in this case, of an emergency room in a small hospital$$to further illustrate the power of simulation modeling.

$5\mathrm{.}7\mathrm{.}1$ PROBLEM STATEMENT

The emergency room of a small hospital operates around the clock. It is staffed by three receptionists at the reception office, and two doctors on the premises, assisted by two nurses. However, one additional doctor is on call at all times; this doctor is summoned when the patient workload up$-$crosses some threshold, and is dismissed when the number of patients to be examined goes down to zero, possibly to be summoned again later. Figure $5\mathrm{.}20$ depicts a diagram of patient sojourn in the emergency room system, from arrival to discharge.

Check In

Figure $5\mathrm{.}20$

Triage

Treatment By Doctor

Check Out

Arriving Patients

Critical

Non Critical

Treatment By Nurse

Discharged Patients

Patient sojourn in a hospital emergency room system.

Patients arrive at the emergency room according to a Poisson process with mean interarrival time of $10$ minutes. An incoming patient is first checked into the emergency room by a receptionist at the reception office. Check$-$in time is uniform between $6$ and

Arena Basics $85$

$12$ minutes. Since critically ill patients get treatment priority over noncritical ones, each patient first undergoes triage in the sense that a doctor determines the criticality level of the incoming patient in FIFO order. The triage time distribution is triangular with a minimum of $3$ minutes, a maximum of $15$ minutes, and a most likely value of $5$ minutes. It has been observed that $40\%$ of incoming patients arrive in critical condition, and such patients proceed directly to an adjacent treatment room, where they wait FIFO to be treated by a doctor. The treatment time of critical patients is uniform between $20$ and $30$ minutes. In contrast, patients deemed noncritical first wait to be called by a nurse who walks them to a treatment room some distance away. The time spent to reach the treatment room is uniform between $1$ and $3$ minutes and the treatment time by a nurse is uniform between $3$ and $10$ minutes. Once treated by a nurse, a noncritical patient waits FIFO for a doctor to approve the treatment, which takes a uniform time between $5$ to $10$ minutes. Recall that the queueing discipline of all patients awaiting doctor treatment is FIFO within their priority classes, that is$,$ all patients wait FIFO for an available doctor, but critical patients are given priority over noncritical ones. Following treatment by a doctor, all patients are checked out FIFO at the reception office, which takes a uniform time between $10$ and $20$ minutes, following which the patients leave the emergency room.

The performance metrics of interest in this problem are as follows:

Utilization of the emergency room staff by type $($doctors$,$ nurses, and receptionists$)$

Distribution of the number of doctors present in the emergency room

Average waiting time of incoming patients for triage

Average patient sojourn time in the emergency room

Average daily throughput $($patients treated per day$)$ of the emergency room

To estimate the requisite statistics, the hospital emergency room was simulated for a

period of $1$ year.