Consider a Jackson network with three service facilities having the parameter values shown below. Facility j...

 

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Consider a Jackson network with three service facilities having the parameter values shown below. Facility j i = 1 i = 2 i = 3 25 0.2 0.4 j = 2 j= 3 30 8. 0.5 0.3 1 20 4 0.4 0.3 (a) Find the total arrival rate at each of the facilities. (b) Find the steady-state distribution of the number of customers at facility 1, facility 2, and facility 3. Then show the product form solution for the joint distribution of the number at the respective facilities. (c) What is the probability that all the facilities have empty queues (no customers waiting to begin service)? (d) Find the expected total number of customers in the system. (e) Find the expected total waiting time (including service times) for a customer. Consider a Jackson network with three service facilities having the parameter values shown below. Facility j i = 1 i = 2 i = 3 25 0.2 0.4 j = 2 j= 3 30 8. 0.5 0.3 1 20 4 0.4 0.3 (a) Find the total arrival rate at each of the facilities. (b) Find the steady-state distribution of the number of customers at facility 1, facility 2, and facility 3. Then show the product form solution for the joint distribution of the number at the respective facilities. (c) What is the probability that all the facilities have empty queues (no customers waiting to begin service)? (d) Find the expected total number of customers in the system. (e) Find the expected total waiting time (including service times) for a customer.

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