Solutions Hwk Que3 1 The port of Miami has 3 docking berths for loading and unloading ships but is considering adding a 4th berth.

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Solutions Hwk Que3 1 The port of Miami has 3 docking berths for loading and unloading ships but is considering adding a 4th berth. Ships arrive in accordance with a Poisson Process at a rate of 6 ships per day. Docking berths can unload and reload a ship in 10 hours. Calculate performance metrics to decide if the 4th berth should be considered or not. We have an M/M/c infinite queue. From Table 16, we could use the formula To find po, where r = 6/c(2.4 for a 3 shiftt day) and c = 3 or 4. I will assume a 3 shift day so r = 0.83 for 3 berths and r = 0.625 for 4 berths.

Solutions Hwk Que3 2 For s=3 births, L = 5.8-6 Similarly, we can find L from the charts For s=3 births, L = 5.8-6 For s = 4 births, L = 3.8-4.2

Solutions Hwk Que3 3 For s=3 births, L = 5.8-6 Alternatively, we can find these same numbers more precisely from the formulas. Below is the formula with calculations for 3 berths. For s=3 births, L = 5.8-6 For s = 4 births, L = 3.8-4.2

Solutions Hwk Que3 4 Summary metric estimates for 3 vs 4 berth model. 3 Berths 4 Berths po 0.045 0.08 L 6.01 4.0 W 1.0 0.66 Lq 3.51 1.5 Wq 0.59 0.25 Based on this summary data, which model would you choose? 3 or 4 berths?

Solutions Hwk Que 3 5 You are asked to evaluate a queuing system. After some analysis, it appears that inter-arrival times are exponential at a rate of l = 4 per hour. You also determine that a single server can serve customers every 10 minutes on average and that service are close to exponential. If the company uses a waiting time cost function of h(W) = 10W, determine the expected waiting time cost per unit for a single server model. Soln: E[S] = 1/6 hr yields m = 6. Then (m-l) = 2 and

Solutions Hwk Que3 6 Parts arrive at a processing center which can service one part at time with a buffer capacity of 3 units. Management is considering one of two machines to service parts. Machine 1 has daily operating costs of $160. Machine 2 has larger daily costs of $220 but can service parts faster. The g(N) form is used to compute waiting time costs for the parts and is given by g(N) = 80N. You are given the following table showing costs, and steady state probabilities for Machines 1 and 2 respectively. Compute the better alternative between the two machines. Soln: