Sam is operating a small clinic. There are 2 doctors

Sam is operating a small clinic. There are 2 doctors in the clinic. Each doctor diagnoses the patients independently. Patients arrive to each doctor as two independent Poisson processes. The arrival rate to each doctor is 3 patients per hour. So in total there come 6 patients per hour. The diagnose time of each doctor for each patient has mean of 10 minutes and coefficient of variation (CV) of 4. In summary, the clinic has two M/G/1 queues.

1.What is the average waiting time in queue of a patient before the diagnosis?

2.On average, how many patients are waiting in the clinic?

Sam received some complaints from patients about the long waiting. So he decided to formulate one queue in the waiting room. We assume the arrival pattern is still Poisson with the rate of 6 patients per hour, and the doctors’ service time distribution keeps the same. Now the queue is M/G/2.

3. What is the new average waiting time in queue of a patient before the diagnosis?

4.On average, how many patients are waiting in the clinic?

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