1. Solutions Hwk Que
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 = for 4 berths.

2. 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. 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 =

4. 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?

5. Solutions Hwk Que
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

6. Solutions Hwk Que
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: