Problem
Medical Zone (MZ) is a small health clinic. Patients arrive to MZ according to a Poisson process with rate λ = 5 patients per hour. Upon arrival, all patients must check in at the reception desk, where the only receptionist can admit 15 patients per hour. 60% of the patients are ?rst sent to a nurse practitioner (NP) - there are two of them - and the other 40% directly to an attending physician (MD). An NP on average takes 12 minutes to examine a patient, and needs an additional 5 minutes per patient to do follow up paperwork, on average. Half of the NP patients do not need any further examination and leave the clinic after seeing the NP. However, the rest of the NP patients need to go to the MD, who can see 4 patients per hour. After their visit with the NP and/or the MD, the patients stop by at the receptionist for collecting paperwork, which takes 3 minutes on average. Assume exponential service times for all servers (i.e., receptionist, NP and MD).
1. What is the effective arrival rate and utilization at each server (receptionist, NP, MD)?
2. What is the average number of patients waiting or being served at each server?
3. What is the average total number of patients in the entire clinic?
4. How long, on average, does a patient spend in MZ?