A walk-in clinic at a large university campus receives an average of 17 patients per hour. The patient arrival pattern follows a Poisson distribution, and the average time to serve a patient is 10 minutes, which follows an exponential distribution. The clinic has 3 full-time doctors available to see patients. 

1. a) Calculate the utilization of doctors. 
2. b) Calculate the average number of patients waiting (in the queue) to see the doctor. 
3. c) Calculate the average time a patient spends waiting (in the queue) before seeing a doctor. 
4. d) Calculate the average time a patient spends in the system (waiting plus time with the doctor). 
5. e) What is the probability that there are no patients in the system? 
6. f) What is the probability that a new patient has to wait (in the queue)? 
7. g) If the target service level is 85% for a threshold time of 6 minutes, what is the minimum number of doctors required to achieve this target? 

 

Summary of Data: 

• • Arrival rate (λ) = 17 patients per hour 
• • Service rate (μ) = 6 patients per hour (since average service time = 10 minutes) 
• • Number of doctors (s) = 3 

Answer rating: 100% (QA)

To solve the given queuing system problem we can use the MMs queueing model where M denotes the exponential distribution for both arrival and service times s represents the number of servers doctors a... View the full answer