L. Winston Martin (an allergist) has an excellent system for handling his regular patientswho come in just for allergy injections. Patients arrive for an injection and i llout a name slip, which is then placed in an open slot that passes into another roomstaffed by one or two nurses. The specii c injections for a patient are prepared, andthe patient is called through a speaker system into the room to receive the injection.At certain times during the day, patient load drops and only one nurse is needed toadminister the injections.Let’s focus on the simpler case of the two—namely, when there is one nurse. Also,assume that patients arrive in a Poisson fashion and the service rate of the nurse is exponentiallydistributed. During this slower period, patients arrive with an interarrival time ofapproximately three minutes. It takes the nurse an average of two minutes to prepare thepatients’ serum and administer the injection.a. What is the average number you would expect to see in Dr. Martin’s facilities?b. How long would it take for a patient to arrive, get an injection, and leave?c. What is the probability that there will be three or more patients on the premises?d. What is the utilization of the nurse?e. Assume three nurses are available. Each takes an average of two minutes to preparethe patients’ serum and administer the injection. What is the average total time of apatient in the system?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

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L. Winston Martin (an allergist) has an excellent system for handling his regular patients
who come in just for allergy injections. Patients arrive for an injection and i ll
out a name slip, which is then placed in an open slot that passes into another room
staffed by one or two nurses. The specii c injections for a patient are prepared, and
the patient is called through a speaker system into the room to receive the injection.
At certain times during the day, patient load drops and only one nurse is needed to
administer the injections.
Let’s focus on the simpler case of the two—namely, when there is one nurse. Also,
assume that patients arrive in a Poisson fashion and the service rate of the nurse is exponentially
distributed. During this slower period, patients arrive with an interarrival time of
approximately three minutes. It takes the nurse an average of two minutes to prepare the
patients’ serum and administer the injection.
a. What is the average number you would expect to see in Dr. Martin’s facilities?
b. How long would it take for a patient to arrive, get an injection, and leave?
c. What is the probability that there will be three or more patients on the premises?
d. What is the utilization of the nurse?
e. Assume three nurses are available. Each takes an average of two minutes to prepare
the patients’ serum and administer the injection. What is the average total time of a
patient in the system?

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