Fifteen police officers began surrendering to the authorities in the Bronx at about midnight on Thursday to face criminal charges after a long-running grand jury investigation into the widespread practice of fixing traffic tickets for colleagues, family members and friends, people with knowledge of the matter said. A 16th officer was arrested earlier Thursday night.

Ten of the officers are officials in the union that represents police officers, the Patrolmen’s Benevolent Association, the city’s largest police union, and they served essentially as liaisons for fixing tickets, several of the people said. Also among those facing charges are two sergeants and a lieutenant.

The accusations against the men, one of the people said, were contained in more than a dozen indictments that total roughly 1,000 pages, with about 1,600 criminal counts. Ten of the officers were expected to be charged with multiple counts of ticket-fixing, while six were expected to be charged with unrelated corruption counts, the people said.

The Bronx district attorney’s office, which oversaw the inquiry, said the indictments would be unsealed Friday.