CMA Intermediate · Operations Management and Strategic Management · Scheduling and Queuing Models
A single-server M/M/1 clinic has arrival rate 6 patients per hour and service rate 8 patients per hour. What is the average time a patient spends waiting in the queue before consultation begins (Wq)?
Average waiting time in the queue is 22.5 minutes. Wq = 6/(8 x (8-6)) = 0.375 hour. The 30-minute figure is the total time in the system, which also includes the 7.5 minutes of average service, so it overstates the pure waiting time.
- A22.5 minutesCorrect
- B30 minutes
- C7.5 minutes
- D45 minutes
Explanation
Wq = lambda/[mu(mu - lambda)] = 6/(8 x 2) = 0.375 hour = 22.5 minutes. Check: Lq = 36/(8 x 2) = 2.25, and Wq = Lq/lambda = 2.25/6 = 0.375 hour. The 30 minutes is Ws = 1/(mu - lambda) = 0.5 hour, which includes service time.
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