This problem is about the comparison of a queueing model with one fast server ve

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This problem is about the comparison of a queueing model with one fast server versus a queueing mode! with two slow servers. The comparison is between M/M/1 with arrival rate ? and service rate theta, and M/M/2 with arrival rate ? and service rate (at each of the two servers) theta/2. Denote L, Lq, W, Wq, and P0 in the single-server model with the superscript [1] and in the two-server model with the superscript [2]. Your homework problem follows some background information. Background Information You already know that The formula in the textbook for P0 in M/M/s can lie used to show that p 0 [2] is the following expression: The formulas for Lq in M/M/s and p 0 [2] can be used to show that Parts (i) and (ii) imply so (iv) because Parts (iii) and (vi) imply Homework Question 1 Why does the single-server model yield better system attributes (L and W) but worse queue attributes (Lq, and Wq)? The remainder of this question asks you to compare one fast server in M/M/1/5 versus two slow servers in M/M/2/5 with ? = 6 and ? = 8. In this part (b). write and solve the balance equations for M/M/1/5 with ? = 6 and ? = 8. That is. the service rate of the single server is 8 customers per unit time. You may solve the equations analytically (by hand) or with Excel. Write and solve the balance equations for M/M/2/5 with ? = 6 and ? = 8. That is, the service rate of each of the two servers is ?/2 = 4 customers per unit time. You may solve the equations analytically (by hand) or with Excel, (d) Use your results in (b) to calculate P0, W, Wq, L, and Lq for M/M/1/5 with ? = G and ? = 8. That is. the service rate of the single server is 8 customers per unit time. Use your results in (b) to calculate P0, W, Wq, L, and L Q for ?/?/2/5 with ? = 6 and ? = 8. That is, the service rate of each of the two servers is ?/2 = 4 customers per unit time. Use your results in (d) and (e) to find out whether (or not) equations (1), (2), (3), and (4) remain valid when the system capacity is bounded at 5, ? = 6, and ? = 8. In M/M/1/5 with ? = 6 and ? = 8 suppose that the cost of the single server is $20 per hour and there is a cost of $40 per hour per customer in the queueing system. What Is the steady-state average total cost per hour? InM/M/1/5 with ? = 6 and ? = 8 suppose that there is a cost of $40 per hour per customer in the queueing system, the cost of the single server is $20 per hour when the server is busy until a customer, and the cost of the single server is $10 per hour when the server is idle. What is the steady-state average total cost per hour? Suppose in M/M/2/5 with ? = 6 and ? = 8 (that is, the service rate of each of the two servers is ?/2 = 4 customers per unit time) that the cost of each of the two servers is $10 per hour and there is a cost of $40 per hour per customer in the queueing system. What is the steady-state average total per customer in the queueing system. What is the steady-state average total cost per hour? Suppose in M/M/2/5 with ? = 6 and ? = 8 (that is. the service rate of each of the two servers is ?/2 = 4 customers per unit time) tliat the cost of each server is $11 per hour when it is busy, $6 per hour when it is idle, and tliere is a cost of $40 per hour per customer in the queueing system. What is the steady-state average total cost per hour? What is the steady-state average total cost per hour?

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which answer do you want, because it requires hour of work. please be specific where you have stuck so that we can help you properly and prcisely. regards

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