You can use the exact equations for the M/M/s queue or the non-normalized probability method to solve this problem. If you use the non-normalized probability method, let the state number go from 0 to 100. The non-normalized probability method is easier to use for computing the probability that the number of patients in the clinic is 4 or more.

Dr. Crawford is concerned about the increase in time in the system that patients are experiencing as a result of the increased arrival rate due to the flu. Furthermore, she also believes that the waiting time was excessive prior to the flu season as the number of patients she sees has grown over the years. She is therefore thinking about hiring another physician to work with her. a) Find the values of the following quantities if the arrival rate is 0.9 (the pre-flu season value) a. The probability that there are no patients in the clinic b. The probability that the number of patients in the clinic is 4 or more C. The average number of patients in the clinic d. The average time a patient spends in the clinic e. The average time a patient spends waiting to see the doctor f. The average number of patients waiting to see the doctor b) Now figure out the same 6 values but with the increased arrival rate of 1.2 which she was experiencing during the flu season. Summarize your answers in a table like the following: Metric Arrival Rate 1.2 (this part) 0.9 (first part) Rho P(4 or more) L W Wq Lq c) Accurate to two significant digits beyond the decimal point, find the maximum arrival rate that the system can tolerate without having the total time in the system exceed the value you found in problem 1, part (a). Show the values of the 6 performance metrics listed above along with the arrival rate; i.e., a. The probability that there are no patients in the clinic b. The probability that the number of patients in the clinic is 4 or more c. The average number of patients in the clinic d. The average time a patient spends in the clinic e. The average time a patient spends waiting to see the doctor f. The average number of patients waiting to see the doctor