Its about Queuing theory 5. Consider a system like the one shown in the picture. 111 Q2 ili) T (51 QI 1-9 U11 Q3 Customers arrive at rate a to a three-server queuing system (as shown above). Upon being served by station 1, denoted by [Q1, S1), a customer is sent over station 2, denoted as (Q2, 52), with probability q, or sent over to station 3, (Q3, S3), with probability 1-9. Furthermore, customers done with service at (Q2,52] leave the system with probability 1-r, which means that a customer leaving such station can be sent back to start the process all over again at [01, S1) with probability r. a. [8 points) What is the rate at which customers leave station 1, (Q1, S1]? (Hint: call such rate , and use question 1 above to find it) b. (6 points) What is the rate at which customers leave the system via station 3, (Q3, S3]? C. 16 points) If it has been known that queue Q1 holds La customers on average (time average), what is the average time Wa a customer spends in queue Q1? Show transcribed image text Its about Queuing theory 5. Consider a system like the one shown in the picture. 111 Q2 ili) T (51 QI 1-9 U11 Q3 Customers arrive at rate a to a three-server queuing system (as shown above). Upon being served by station 1, denoted by [Q1, S1), a customer is sent over station 2, denoted as (Q2, 52), with probability q, or sent over to station 3, (Q3, S3), with probability 1-9. Furthermore, customers done with service at (Q2,52] leave the system with probability 1-r, which means that a customer leaving such station can be sent back to start the process all over again at [01, S1) with probability r. a. [8 points) What is the rate at which customers leave station 1, (Q1, S1]? (Hint: call such rate , and use question 1 above to find it) b. (6 points) What is the rate at which customers leave the system via station 3, (Q3, S3]? C. 16 points) If it has been known that queue Q1 holds La customers on average (time average), what is the average time Wa a customer spends in queue Q1? Show transcribed image text