# THE FOLLOWING ARE THE ARRIVAL TIMES WE CALCULATED Hospital 1 527 patients per year Hospital 2 1091 patients per year Hospital 3 617 patients per year Hospital 4 689 patients per year Hospital 5

THE FOLLOWING ARE THE ARRIVAL TIMES WE CALCULATED

Hospital 1

527 patients per year

Hospital 2

1091 patients per year

Hospital 3

617 patients per year

Hospital 4

689 patients per year

Hospital 5

492 patients per year

Hospital 6

527 patients per year

1.  Assume that currently, 54 beds have been allocated to each hospital, and that the averageservice time of stroke patients in ICU beds, i.e., 1/μ, is four weeks. Please assume there are52 weeks per year throughout the analysis. What is the throughput and capacity rate for each hospital given the arrival times in the above table?

2. (10 points) What is the utilization, i.e., (λ/54μ), of each stroke hospital?Assume the coefficient of variation (CV) of both the arrival and service processes for allhospitals is equal to one.

3a. (15 points) What is the average waiting time in the queue (in minutes) and the average flowtime of the system (in minutes) for each stroke hospital with utilization strictly less than one?

3b. (5 points) What can you say about the average waiting time of the hospitals that have autilization strictly greater than one?

4. (10 points) What is the minimum number of ICU beds that each unstable hospital shouldhave to serve all of its stroke patients?

5a. (15 points) How many ICU beds do we need in each stroke hospital to ensure that all hospitalshave a utilization less than or equal to 90%? How does the total number of ICU beds under the proposed bed allocation policy compare with the total number of beds under the policy that allocates 54 ICU beds to each stroke hospital?

5b. (5 points) What would be the average waiting time (in minutes) in each hospital under thebed allocation policy proposed in Question 5a?

6. (15 points) What is the minimum number of beds you should allocate to each stroke hospitalto ensure that the average waiting time of each stroke hospital is less than or equal to 10minutes?

Can you please calculate the specific numbers for all questions? for example for question 1: throughput is min(arrival, capacity). the capacity for all the hospitals is 702 patients a year because each hospital has 54 beds and 1 patient takes 4 weeks and there is 52 weeks in a year so (52/4= 13 ) and then (13x 54= 702 patients a year). so would the throughput rate for hospital 2 be 702?