All excavation in the streets, thoroughfares, parks and public places, and all work therein and the restoration thereof, shall be carried on and completed without delay after work has begun. The permittee shall notify the Director of Public Service when work is to be carried on and may require that during hours when work is not in progress, or in hours when traffic requirements justify it, every such excavation, or any part thereof designated by him, shall be securely covered over with such materials and in such manner as to permit the passage of vehicular and pedestrian traffic with the least interference or delay.