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Marine Transportation

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  • Marine Transportation

    The Port Authority of St. Thomas (Virgin Islands) wants to improve their cruise ship port facility. Figure 1 shows the current situation with three berth positions to accommodate large cruise ships of up to 70,000 metric tons. During the peak season, cruise ships arrive to the port randomly at a rate of 1.7 per day. The average ship docks at port for one full day allowing visitors to enjoy the weather and visit the local attractions. Assume the service times for a ship to be negative exponentially distributed. If all berths are busy, cruise ships wait outside the port at great inconvenience to passengers and the cruise line.
    Under the current conditions, estimate the expected number of cruise ships unable to dock at port during the peak season
    How often is the port facility empty?
    I do not understand the formulas that are used to arrive at the answers. Please help