##### University of South Carolina, Arnold School of Public Health, Dept. of Health Services Policy and Management, HSPM J716

Which represents the average number of patients in the system?

Which represents the average length of time spent in the system?

Which represents the average length of time spent waiting?

Now to the problems themselves.

1. Patients arrive at a doc-in-the-box at the average rate of 2 per hour. The doc spends an average of 15 minutes with each patient.

2. Patients arrive at Doc-and-Nurse-in-a-Box at the average rate of 2 per hour. A nurse spends an average of 7.5 minutes with each patient, then the doc spends an average of 7.5 minutes with the patient while the nurse starts with the next patient. (This is not Erlang. This is two systems in series, one after the other. You can again start with your spreadsheet from Assignment 7A.)

Compare the speed of clinic 2 with clinic 1.

Extra credit: Suppose that splitting the process means extra paperwork for the nurse, so that the nurse's average time with the patient is 10 minutes. Is clinic 2 still faster than clinic 1?

3. Patients arrive at Compute-O-Doc at an average rate of 2 per hour. Compute-O-Doc deals with each patient in exactly 15 minutes.
(One old version of the cookbook had the wrong formula for W. The right formula is L/Lambda.)

How does this clinic compare with clinic 1?

4. Patients arrive at Doc-in-a-Matchbox at the rate of 2 per hour. The doc spends an average of 15 minutes with each patient. If an arriving patient finds that there are 2 patients in the waiting room, the patient leaves and doesn't come back.

How does this clinic compare with clinic 1, for those who get in?

5. Patients arrive at Tender-Loving-Care-Docs-in-a-Box at the rate of 2 per hour. There are 2 docs working. Patients don't care which doc they see. Patients spend an average of 30 minutes with the doc.

How does Tender-Loving-Care-Docs-in-a-Box compare with clinic 1?

6. Patients arrive at Urgie-Care-in-a-Box at the rate of 2 per hour. There is one doc who spends an average of 15 minutes with each patient. On arrival, patients are judged to be either urgent or non-urgent. If the doc is serving a non-urgent patient and an urgent patient comes in, the doc interrupts the non-urgent visit and takes care of the urgent patient, returning to the non-urgent patient only when no urgent patients are waiting. Assume that, on the average, one patient per hour is urgent and one is not urgent. Calculate answers for both urgent and non-urgent patients.
For urgent patients:

For non-urgent patients:

How does this clinic compare with clinic 1?.

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