For a street guitarist who can sing and play a few Beatles tunes, one of the most lucrative public stages in New York City is a park bench just inside the West 72nd Street entrance to Central Park in an area known as Strawberry Fields.

Since the area opened in 1985, a parade of musicians eager to coax tips from the unending flow of tourists has played songs of peace and love in tribute to John Lennon, who in 1980 was killed not far away, outside the Dakota apartment building where he lived.

The Beatles songsters play next to the “Imagine” mosaic memorial and greet tourists with a repeating loop of classics such as “In My Life,” “Strawberry Fields Forever” and, especially, “Imagine,” which Mr. Lennon wrote to invoke world peace and the musicians play to evoke monetary appreciation for their efforts.

But for the past few years peace itself was elusive among the musicians. The idyllic mood had been marred by altercations, vitriolic screaming and performers dueling to sing over one another. The unruliness became worse after the death in 2013 of a man known as the mayor of Strawberry Fields, who had helped maintain order. Signs designating the area a quiet zone proved futile, and numerous visits by the police provided only short-term solutions.