I depends on if you followed all of the proper procedures in filing the case.
First, you must have properly served a 5 day notice to the tenant or someone over the age of 13 residing at the apartment. If the tenant has abandoned the apartment this can be done by posting. One particularity if the eviction is for non-payment of rent you must have the correct dollar amount in the 5 day notice that the tenant must pay in order to "cure" their breach of the lease.
Second, after the 5 day notice expires you can file the lawsuit. In Cook County you MUST attempt service with the Sheriff first even if you know the tenant won't answer the door. The Sheriff gets the first try. You can ask for leave of court to do service by posting on the first return date. It depends on the Judge as to whether they will grant service by posting.
Last, once you obtain service by posting the Sheriff then physically posts a summons on the apartment with a return date. On that return date you can get an order for possession only. The return date in Cook County on a Notice by Posting must be at least 10 days from the date of posting. So if you followed all of the correct procedures and properly obtained leave to perform service by posting and then filed the new alias summons giving the Sheriff ample to to post it then the soonest you can get a Judgment is October 31. Many Judges place a stay on enforcement of an order for possession. So you won't be able to physically enforce the order until that time period lapses.
Illinois Legal Aid has a great guide on the eviction process and specifically tailors it to performing an eviction in Chicago. I included a link. Hope this helps. Good Luck!
Your question is what every landlord wants to know. Unfortunately, there is no concrete answer. Depends if the tenant shows up in court. If they don't, which is likely with posting, you can receive a judgment on the inita court date. If they do show up in court, you can get a judgment within a couple of weeks, if there is no jury demand. If there is a jury demand filed, it can take many months to receive a judgment.
You shod hire an attorney to be sure that the process is expedited.
And of course in Cook County, even after you win your judgment, that does not mean your tenant is "out." You cannot change the locks, move their stuff, or put them out on your own or with help from friends or staff. Sheriff has to do it, and they don't necessarily do that when it is cold out.
Posting of what? Landlord's Notice? Or Service of process? Totally different issues. But as far as how long? Well, if the tenant objects to either and is correct (technically posting a landlord's notice is ONLY good when nobody actually lives in the place), you could be back to square 1. If it's posting, it may take as long as personal service for a variety of reasons totally unrelated to your having posted versus having the person served personally. One reason is that the Sheriff's office may be bogged down when you are able to execute on the judgment.
the law requires you to conduct an honest and well directed effort to serve the tenant, either by using a special process server or by serving them at their job. or by alternative service.such as mailing it. Posting is a last resort and the tenant may quash the posting notice if it is not done correctly.