PROVIDENCE — Mark ­Simmons began dialing Rhode Island’s unemployment call center at 8 a.m. on a recent Monday. He got a busy signal. He tried 67 more times before the automated system picked up and told him that because of heavy call volume, he should try back another time.

People applying for unemployment benefits in the state with the nation’s highest jobless rate must wait on hold an average of 51 minutes. Not only that, but some of those interviewed say that their benefits are often weeks late and that when they try to speak to a human about the problem, they are ­referred to a computer.