4. Seattle Grace Hospital is short staffed, and has asked their interns, Christina Yang and Meredith Grey, to serve as customer service representatives to direct phone calls to the proper recipients; the hospital receives an average of 80 calls per hour, following a Poisson process. Yang and Grey can each handle an average of 30 calls per hour. The time to handle a call is exponentially distributed. The hospital can put up to 4 people on hold, i.e. if 4 people are already on hold, any incoming callers receive a busy signal. Callers are known to be impatient, and they hang up following an exponential distribution with an expected time of 3 minutes. ooo a Screen Shot 2020-04-17 at 12.46.57 PM | O Q Q Zvo @ Q Search (a) Create a model for this system. Be sure to include how you define your state space, the list of events that can occur, the transition rate diagram, and the transition rate matrix. (b) Numerically solve for the steady state probabilities. (c) Application of Little's Law: i. What is the expected number of callers who are waiting to talk to the interns? ii. What is the effective throughput rate? iii. How long on average do callers wait before either talking with an intern or hanging up? (d) Yang gets stressed when she sees that x callers are in the system (either waiting or being helped). Her stress level can be modeled as S(x) = 26. What is her expected stress level? 4. Seattle Grace Hospital is short staffed, and has asked their interns, Christina Yang and Meredith Grey, to serve as customer service representatives to direct phone calls to the proper recipients; the hospital receives an average of 80 calls per hour, following a Poisson process. Yang and Grey can each handle an average of 30 calls per hour. The time to handle a call is exponentially distributed. The hospital can put up to 4 people on hold, i.e. if 4 people are already on hold, any incoming callers receive a busy signal. Callers are known to be impatient, and they hang up following an exponential distribution with an expected time of 3 minutes. ooo a Screen Shot 2020-04-17 at 12.46.57 PM | O Q Q Zvo @ Q Search (a) Create a model for this system. Be sure to include how you define your state space, the list of events that can occur, the transition rate diagram, and the transition rate matrix. (b) Numerically solve for the steady state probabilities. (c) Application of Little's Law: i. What is the expected number of callers who are waiting to talk to the interns? ii. What is the effective throughput rate? iii. How long on average do callers wait before either talking with an intern or hanging up? (d) Yang gets stressed when she sees that x callers are in the system (either waiting or being helped). Her stress level can be modeled as S(x) = 26. What is her expected stress level