The River Clinic has two general practitioners who see patients daily. An averag

Question

The River Clinic has two general practitioners who see patients daily. An average of six patients arrive at the clinic per hour. Each doctor spends an average of 15 minutes with a patient. The patients wait in a waiting area until one of the doctors is able to see them. However, because patients typically do not feel well when they come to the clinic, the doctors do not believe it is good idea to have a patient wait longer than an average of 15 minutes. Should this clinic add a third doctor, and, if so, will this alleviate the waiting problem? 

Explanation / Answer

= 6 per hour µ = 4 per hour (15 minutes per patient) s = 2 Average Utilization of the system p = / Sµ = 6/(2*4) = 0.75 Probability that there are 0 patients in the system (P0 = 1 / [1 + / µ + {( / µ)^s / s!} * (1 / 1-p)] = 1 / [ 1 + 6/4 + (6/4^2 / 2!) * (1 / 1 - 0.75) ] = 1 / [ 1 + 1.50 + (1.125 * 4)] = 1 / (2.5 + 4.5) = 1 / 7 = 0.1429 Average number of patients in waiting line = Lq = P0*(/µ)^s*p / s! (1 -p)^2 = (0.1429 * 1.5^2 * 0.75) / (2! * 0.25 ^2) = 0.24107 / 0.125 = 1.9286 customers Average waiting time of patients in line = Lq / = 1.9286/6 = 0.32143 hours or 19.286 minutes Since the waiting time is more than 15 minutes, another doctor should be added = 6 per hour µ = 4 per hour (15 minutes per patient) s = 3 Average Utilization of the system p = / Sµ = 6/(3*4) = 0.50 Probability that there are 0 patients in the system (P0 = 1 / [1 + / µ + {( / µ)^s / s!} * (1 / 1-p)] = 1 / [ 1 + 6/4 + (6/4^3 / 3!) * (1 / 1 - 0.75) ] = 1 / [ 1 + 1.50 + (0.5625 * 4)] = 1 / (2.5 + 2.25) = 1 / 4.75 = 0.2105 Average number of patients in waiting line = Lq = P0*(/µ)^s*p / s! (1 -p)^2 = (0.2105 * 1.5^3 * 0.50) / (3! * 0.50 ^2) = 0.35526 / 1.5 = 0.2368 customers Average waiting time of patients in line = Lq / = 0.2368/6 = 0.0395 hours or 2.368 minutes Yes this will alleviate the waiting problem as the waiting time would reduce by = 19.286 - 2.368 = 16.918 minutes

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.