Question 2 - A Walk-In Clinic Model Patients arrive at a walk-in clinic according to a Poisson process of rate 4 patients/hour. The patients are seen by a single physician on a first-come, first-served basis. The physician sees patients more quickly when there are other patients waiting. A time study conducted by a business simulation analytics student suggests that the mean patient consult time when there are 0, 1, 2, and 3 patients waiting to see the physician is 22, 18, 17, and 15 respectively. Assume exponentially distributed consult times, only one exam room, and waiting space for at most 3 patients. minutes, a) Let N(t) be the number of patients in the walk-in clinic at time t (waiting and being seen by the physician). Model the evolution of N(t) over time as a continuous time Markov chain by providing the corresponding graphical representation. Feel free to use any of the alterative characterizations discussed in class. b) Simulate the evolution of the number of patients in the walk-in clinic for a minimum of 5 2-day replications. Assume that the system is empty at the beginning of the simulation and that the walk-in clinic operates 24/7. c) Based on your simulation results, determine: The average number of patients waiting to see the physician over time. The average physician utilization. Please do not forget to provide the corresponding confidence intervals. d) Determine the stationary (i.e., steady state) probabilities for this process and answer the questions in part c) based on your results. Explain any differences.