In my local vaccination center, there are 6 work centers (each work center is staffed by a
Question:
In my local vaccination center, there are 6 work centers (each work center is staffed by a care worker that provides the vaccine) to serve 35 citizens per hour (they aim to serve 280 citizens in 8 hours) It takes on average 10 mins to serve one citizen. This includes preptalk, giving the vaccine shot, and some posttalk to make the citizen feel at ease (all done by the care worker in its work center) After that, citizens go to a separate restroom before going home. This restroom is separated from the waiting room where citizens wait prior to seeing the care worker in their work center. Assume exponential service times and interarrival times, which implies you can use the spreadsheet Queuexlsm.
[3.a] What percentage of the time are the care workers idle? How much time, on average, does a patients spend waiting in line (i.e., prior to getting their vaccine), and how many patients are on average in the waiting room (this is the room prior to their shot, not the ‘rest’-room afterwards)?
The care workers are idle ______ percent of their time.
A citizen spends on average _____ minutes waiting in line.
On average _____ citizens are in the waiting room (waiting for their shot).
Explain:
[3.b] To reduce the time that a patients spends in the center (this includes both the waiting time as well as the “service” time by the care worker), the following two options are considered:
- Hire 2 additional care workers, so that we increase the capacity from 6 work centers to 8.
- Let the pre- and post-talk be done by volunteers and let the care worker only do the vaccination itself. This would effectively reduce the care workers’ time to complete a vaccination by 25 percent (i.e., from 10 minutes down to 7.5 minutes on average). For simplicity, you may assume there is an infinite pool of volunteers willing to help (such that the volunteers never become the bottleneck in the process).
Assuming the cost of both options to be the same, which one is preferred from a patients perspective that would like to minimize the time (s)he spends in the center. Motivate your choice.
- Hire 2 additional care workers b. Reduce the care workers’ time by 25%
Explain:
[1] Disclaimer: Numbers are slightly changed. The real process may slightly deviate from my description.
Introduction to Probability
ISBN: 978-0716771098
1st edition
Authors: Mark Daniel Ward, Ellen Gundlach