Well, if you make it a point to attend every meeting and make sure you study consistantly (prove it by you underlining your watchtower or bookstudy publication which shows them you are taking it seriously), they will meet with you sooner than later. If they have another matter they are attending to, you will automatically get put on the back burner. But the standard operating procedure is roughly 2 weeks before you get a phone call to schedule a meeting with you.
Also, if your looking to get reinstated, make sure you point out in your letter how much you hurt Jehovah and your relationship with him; that is what they are looking for. Don't say stuff like I miss my friends and family, those are the wrong reasons. Sometimes it can depend on the elders in the hall as blondie pointed out (the good ol boy network. eg. elders wife or son/daughter), I see it all the time.
But the biggest factor I would say on how quick you get reinstated is this: If you engaged in gross sin and you are not repentant, you will probably be disfellowshipped. If you engaged in gross sin and are repentant, yet your sin is well known among those in the hall, you will probably get disfellowshipped in order to make an example out of you. If you engaged in gross sin and are repentant, yet your sin is known among only a few in the congregation, you may only get public reproof. If you engaged in gross sin and are repentant, yet your sin is not known at all among others in the congregation, you will probably only get privately reproved.
Most elders in congregations will keep telling you no on your reinstatement no matter how repentant you are for a minimum of six months to a year.
I like spilling the beans...
iamwhoiam