New Yorkers will be able to sleep soundly once the new fleet of livery cabs that can pick up hails hits the road, the city’s taxi czar promised yesterday.

Thanks to a rule change, customers will more easily recognize available liveries — they will have roof lights — which will reduce the honking that drivers do to get their attention, said Yassky

“Yellow taxis don’t go around honking for customers,” Taxi & Limousine chief David Yassky said.

The new cabs will be on the road by summer.

jennifer.fermino@nypost.com