Put together by Kingstone resident Liam Hardcastle, the document garnered 655 signatures.
Cabinet members discussed what will be done in response to its receipt at Wednesday’s meeting, and said the petition’s request will be analysed before the end of April.
Leader of the council Sir Steve Houghton said: “I fully understand the petitioners’ concerns and we will give it a proper analysis.
“It will take a bit of time, but we need to do it properly.
“Any outcomes will be fed back to petitioners and local councillors.”