Question: Q4. Consider a Jackson network with three service facilities having the parameter values shown below. ev Facility i Hi gi i=1 i=2 #1 30 10

Q4. Consider a Jackson network with three service

Q4. Consider a Jackson network with three service facilities having the parameter values shown below. ev Facility i Hi gi i=1 i=2 #1 30 10 0 0.2 0.6 =2 30 20 0.4 0 0 45 10 0.2 0.5 0 a. Show the data on state diagram and find the total arrival rate at each of the facilities. (16 pts) b. Find the minimum number of facilities for each service provider. (8 pts) Find expected total number of customers and total waiting time in the system. (8 pts) d. What is the probability of at least 1 customer at 1st and 3rd server. (8 pts) c. Q4. Consider a Jackson network with three service facilities having the parameter values shown below. ev Facility i Hi gi i=1 i=2 #1 30 10 0 0.2 0.6 =2 30 20 0.4 0 0 45 10 0.2 0.5 0 a. Show the data on state diagram and find the total arrival rate at each of the facilities. (16 pts) b. Find the minimum number of facilities for each service provider. (8 pts) Find expected total number of customers and total waiting time in the system. (8 pts) d. What is the probability of at least 1 customer at 1st and 3rd server. (8 pts) c

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