A wierd rule of thumb I follow is that the bigger the publisher + the bigger the payrate = Longer wait.
Looking at my stats for Pro Rates (i.e. 15 cents per word or better)
I average about 120 days for rejection and about 1/3 no response.
My acceptances (5) have been within 60 days or less for whatever that is worth.
The New Yorker is a very tough nut to crack.
The best way to approach the big boys is to fire and forget. Polish a story as best you can, send off, work on the next piece. Eventually, you will get to the point where you have a bunch of stuff in the pipeline and you will be getting a weekly rejection and bi-weekly acceptance
I track everything via a spreadsheet. If you like, give me your email address and I'll mail you a template you can use.
p.s. I should also mention that the bigger the publisher, the more important it is to familiarize yourself with the types of stories they published. Its a big mistake to think that just becuase you have a good story that they will publish it.
Mel...