Emma is not convinced that this ambulance routing protocol is suitable in the time of the COVID-19 pandemic; she suspects that it may lead to high patient waiting times due to excessive congestion in hospital EDs. If deemed practically inefficient, she intends to explore different op- erationally feasible options, including a revision to the routing protocol and/or the reallocation of resources from one Stroke Hospital to another.

Emma thinks a queueing model could capture the trade-off between ambulance routing protocols and the variability (in the service and arrival processes). She needs to provide policies that can improve the status quo as soon as possible. Since over 98% of stroke patients arrive at a hospital via an ambulance, Emma assumes that all stroke patients arrive at stroke hospitals via ambulances.

THE FOLLOWING ARE THE ARRIVAL TIMES WE CALCULATED

Hospital	Arrival Time
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 average service time of stroke patients in ICU beds, i.e., 1/, is four weeks. Please assume there are 52 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., (/54), of each stroke hospital? Assume the coefficient of variation (CV) of both the arrival and service processes for all hospitals is equal to one.

3a. (15 points) What is the average waiting time in the queue (in minutes) and the average flow time 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 a utilization strictly greater than one?

4. (10 points) What is the minimum number of ICU beds that each unstable hospital should have 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 hospitals have 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 the bed allocation policy proposed in Question 5a?

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

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?