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A logistics company is planning for a new central terminal. When a trucks with ingoing load arrive at the terminal, if an unloading dock (platform)

A logistics company is planning for a new central terminal. When a trucks with ingoing load arrive at the terminal, if an unloading dock (platform) is free, the cargo of the truck will be unloaded. Otherwise, if all of the docks are taken, the truck has to wait in a queue. The terminal has enough space for all the trucks which have to wait. We expect, when the terminal is open, on average 20 trucks arrive per hour. The time between arrivals of two trucks has exponential distribution. The expected time to unload a truck is 30 minutes and the unloading time has exponential distribution as well. A truck that will not find an empty dock on arrival will have to wait until one is available. The cost for waiting is estimated to be 50 EURO per hour. The terminal is open 16 hours per day. The company has planned two alternative designs for the new terminal. One design (Alternative A) has 12 docks, and the other one (Alternative B) has 15 docks. What would be the expected waiting time for a truck in alternative A and B before the unloading starts, in minutes, and the waiting costs per day for each alternative?

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