As part of a specific disease prevention program, a clinic is considering setting up a
screening service in a town. They are considering the following design: After waiting in a
single line, each walk-in patient is served by one of three available nurses. Each nurse has
their own booth, where the patient is first asked some medical health questions, then the
patient’s vitals are taken, and finally, a glucose test is performed to check for the disease.
In this design, each nurse performs the tasks in sequence for the patient. If the glucose
test indicates a chance of the disease, the patient is sent to a separate clerk to schedule an
appointment for a follow-up at the clinic. If the test is not positive, then the patient departs.
Patients’ are eager to get tested but they are reluctant to wait for to screening operations.
To clarify, if the number of people waiting for nurses is larger than 4, they prefer to go to
a park nearby the screening booths, and spend 15 minutes therein. After this 15 minute
period they again return to booths to check if the number of people is acceptable or not.
Noting that, there is no limit on the number of times for park visiting, i.e. people are get
Patients arrive to the system according to an exponential distribution with a mean
of 4 minutes. Assume that there is a 5% chance that the glucose test will be positive.
For the given design, the time that it takes to have the paperwork completed, the vitals
taken, and the glucose tested are all lognormally distributed with means of 6.5, 6.0, and
5.5 minutes, respectively. They all have a standard deviation of approximately 0.5 minutes.
The distribution used to model the time that it takes to schedule a follow-up visit is a
WEIB(2.6, 7.3) distribution (in minutes). Moreover, distance between park and screening
booths requires a travel time of uniformly distributed between 1 and 2 minutes.
In addition, nurses are working based on a schedule (valid for just nurses, not the clerk).
All breaks are given in a staggered manner that is, one nurse goes on break and immediately
upon return the next nurse goes on break until all nurses have had their breaks. Nurses
are kind people, hence they wait until the patient they are testing is done and returns
after completing their scheduled amount of time for the breaks. Assuming the screening
operations start at 8:00, first 10 minute breaks should be given starting at 10:00. Upon
completion of 4 hours of work (i.e. at 12:00), they have a 30 minute lunch break. And
finally, at 15:00, they have one another small break session for 10 minutes. The booths are
closed at 17:00.
Collect statistics for queue length, queue time and utilization of the resources for 30
State the average number of people screened as positive and negative.
What are the average cycle times for positive and negative patients