TL;DR Most grievance systems promise an acknowledgment (often within 3 days) and resolution within a stated time (e.g. 15–30 days for routine issues). You can expect a reference number and status updates. If there is no response by the due date, you can escalate. This doc explains what to expect.
Common timelines
CPGRAMS (Centre) and many State portals: acknowledgment in a few days, resolution in 15–30 days for many civic issues. Complex issues may take longer. RTI: 30 days (or 45 in some cases) for a reply from the PIO.
What you can expect
A unique reference number, ability to check status online or via helpline, and a response when the issue is closed. If not resolved, you can expect a reason and the next step (e.g. appeal). You can escalate if you get no response by the stated date.
Related: Government Responses and Accountability · How to Raise a Public Issue