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 fill out a name slip, which is then placed in an open slot that passes into another room staffed by up to three nurses. The specific 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 4 minutes. It takes the nurse an average of 3.00 minutes to prepare the patients' serum and administer the injection. (Use the Excel spreadsheet Queue Models.) a. What is the average number of patients you would expect to see in Dr. Martin's facilities? Note: Do not round intermediate calculations. Round your answer to 2 decimal places. Average number of patients b. How long would it take for a patient to arrive, get an injection, and leave? Note: Round your answer to 2 decimal places. Average total time c. What is the probability that there will be three or more patients on the premises? Note: Do not round intermediate calculations. Round your answer to 1 decimal place. Probability minutes % Utilization of the nurse d. What is the utilization of the nurse? Note: Do not round intermediate calculations. Round your answer to 1 decimal place. 66.7 %

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Related questions

Question

Q15 please help me!! Both pics are from the same initial question

3
ences
b. How long would it take for a patient to arrive, get an injection, and leave?
Note: Round your answer to 2 decimal places.
Average total time
c. What is the probability that there will be three or more patients on the premises?
Note: Do not round intermediate calculations. Round your answer to 1 decimal place.
Probability
Utilization of the nurse
minutes
%
d. What is the utilization of the nurse?
Note: Do not round intermediate calculations. Round your answer to 1 decimal place.
Average total time
66.7 %
e. Assume three nurses are available. Each takes an average of 3.00 minutes to prepare the patients' serum and administer the
injection. What is the average total time of a patient in the system?
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
minutes

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 fill out a name slip, which is then placed in an open slot that passes into another room staffed by up to three
nurses. The specific 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 4 minutes. It takes the nurse an average of 3.00 minutes to prepare the patients' serum and administer the injection.
(Use the Excel spreadsheet Queue Models.)
a. What is the average number of patients you would expect to see in Dr. Martin's facilities?
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
Average number of patients
b. How long would it take for a patient to arrive, get an injection, and leave?
Note: Round your answer to 2 decimal places.
Average total time
c. What is the probability that there will be three or more patients on the premises?
Note: Do not round intermediate calculations. Round your answer to 1 decimal place.
Probability
minutes
%
Utilization of the nurse
d. What is the utilization of the nurse?
Note: Do not round intermediate calculations. Round your answer to 1 decimal place.
66.7 %

Expert Solution

Part a

a. We can use the M/M/1 queuing model to find the expected number of patients in the system. The arrival rate λ is 1/4 patients per minute (since patients arrive with an interarrival time of 4 minutes), and the service rate μ is 1/3 patients per minute (since the nurse takes an average of 3 minutes to prepare and administer an injection). Therefore, the traffic intensity ρ is λ/μ = (1/4)/(1/3) = 0.75.

Using the formula for the expected number of customers in the system for an M/M/1 queue with ρ < 1: Ls = ρ / (1 - ρ) = 0.75 / (1 - 0.75) = 3

Therefore, the average number of patients expected to be in Dr. Martin's facilities is 3.