Question

Nine junior doctors work in a clinic dealing with patients with non-urgent medical problems. A single senior doctor works in an office in the clinic and is available to help the junior doctors with any issues that they feel they aren’t qualified to deal with. The doctor is generally working on paper work and is immediately available to help a junior doctor as needed (as long as they aren’t busy assisting another junior doctor, in which case they will have to wait). On average, a junior doctor needs the help of the senior doctor once every two hours (assume Poisson arrivals); the senior doctor can deal with an issue in an average of five minutes (assume exponential distribution). What percent of the time will the doctor be busy helping junior doctors resolve problems?

Answer 1

The no. of junior doctors = 9.

The time which the senior doctor spends with each junior doctor = 5 minutes

Time spend by the senior doctor = 5 x 9 = 45 minutes

Each junior doctor seeks help from senior once in every 2 hours. 2 hours = 120 minutes.

Total time spend by the senior doctor to help juniors in 2 hours = 45 minutes

Percentage of time = Time spend by the senior/Total time x 100 = 45/120 x 100

= 0.375 x 100 = 37.5

Therefore, the senior doctor will be spending 37.5% of his time in helping to resolve the problems of junior doctors.