Problem:
Wilshire Clinic has thirty clinicians. Currently, the arrival rate for each clinician is 2 patients per hour and the service rate for each clinician is 5 patients per hour. Both interarrival time and service time are exponentially distributed. Suppose each clinician serves his or her own patients.
Required:
Question 1) What is the utilization rate of a clinician? (Round your answer to 4 decimal places.)
Question 2) What is the average waiting time in line? (Do not round intermediate calculations. Round your answer to the nearest whole number.)
Question 3) To improve patients' experience, Wilshire Clinic decides to divide thirty clinicians into five teams, each of which consists of 6 clinicians. A patient's information is shared within the team, so a clinician can serve a patient who comes to any clinician on the same team.
Question 4) What is the arrival rate for each team?
Question 5) What is the utilization rate of a clinician? (Round your answer to 4 decimal places.)
Question 6) What is the average waiting time in line? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Question 7) What is the average number of patients waiting in line for each team? (Round your answer to 4 decimal places.)
Solve the given numerical problem and illustrate step by step calculation.