PORTSMOUTH, Va.—The Port of Virginia, one of the nation’s largest, was built to handle high volumes of cargo traffic entering and exiting the U.S.

But on his way recently to pick up a load of bedding, Albert Newcomb was stalled for two hours before his rig could make it through a mile-long line to one of the port’s terminals. Once inside, the 43-year-old independent truck driver hit a traffic jam 13 lanes wide and 10 trucks deep. By the time he left with his load, he had waited for a total of eight hours. “It’s ridiculous,”...