Question: Problem 6: Let's consider an M/M/m/m/M system, which is a birth-death system. We assume that we have a finite population of M customers, each with

Problem 6: Let's consider an M/M/m/m/M system, which is a birth-death

Problem 6: Let's consider an M/M/m/m/M system, which is a birth-death system. We assume that we have a finite population of M customers, each with an "arriving" parameter . In addition, the system has m servers, each with parameter p. The system also has finite storage room such that the total number of customers in the system is no more than m. We assume M 2 m; customers arriving to find m already in the system are "lost." (1) Please draw the state-transition-rate diagram. (2) Please specify the birth-death coefficients (i.e., Xk and k) (3) Please explain why this is an ergodic system. (4) Please find the equilibrium probabilities p (Express your answer in terms of po) Problem 6: Let's consider an M/M/m/m/M system, which is a birth-death system. We assume that we have a finite population of M customers, each with an "arriving" parameter . In addition, the system has m servers, each with parameter p. The system also has finite storage room such that the total number of customers in the system is no more than m. We assume M 2 m; customers arriving to find m already in the system are "lost." (1) Please draw the state-transition-rate diagram. (2) Please specify the birth-death coefficients (i.e., Xk and k) (3) Please explain why this is an ergodic system. (4) Please find the equilibrium probabilities p (Express your answer in terms of po)

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