I may be underestimating your knowledge of how exchanges work; if so, I apologize. If not, then I believe the answer is relatively straightforward.
Lets say price of a stock at time t1 is 15$ .
There are many types of price that an exchange reports to the public (as discussed below); let's say that you're referring to the most recent trade price. That is, the last time a trade executed between a willing buyer and a willing seller was at $15.00.
Lets say a significant buy order of 1M shares came in to the market.
Here I believe might be a misunderstanding on your part. I think you're assuming that the buy order must necessarily be requesting a price of $15.00 because that was the last published price at time t1. In fact, orders can request any price they want. It's totally okay for someone to request to buy at $10.00. Presumably nobody will want to sell to him, but it's still a perfectly valid buy order.
But let's continue under the assumptions that at t1:
- there already are people who've told NYSE they're willing to sell at $15.00
- there's nobody who's told NYSE they're willing to sell below $15.00
- there already are people who've told NYSE they're willing to buy at $14.99
- there's nobody who's told NYSE they're willing to buy above $14.99
This makes the bid $14.99 and the ask $15.00. (NYSE also publishes these prices.)
There aren't enough people selling that stock.
It's quite rare (in major US equities) for anyone to place a buy order that exceeds the total available shares listed for sale at all prices. What I think you mean is that 1M is larger than the amount of currently-listed sell requests at the ask of $15.00.
So say of the 1M only 100,000 had a matching sell order and others are waiting.
So this means that there were exactly 100,000 shares waiting to be sold at the ask of $15.00, and that all other sellers currently in the market told NYSE they were only willing to sell for a price of $15.01 or higher. If there had been more shares available at $15.00, then NYSE would have matched them.
This would be a trigger to the automated system to start increasing the price.
Here is another point of misunderstanding, I think. NYSE's automated system does not invent a new, higher price to publish at this point. Instead it simply reports the last trade price (still $15.00), and now that all of the willing sellers at $15.00 have been matched, NYSE also publishes the new ask price of $15.01. It's not that NYSE has decided $15.01 is the new price for the stock; it's that $15.01 is now the lowest price at which anyone (known to NYSE) is willing to sell. If nobody happened to be interested in selling at $15.01 at t1, but there were people interested in selling at $15.02, then the new published ask would be $15.02 instead of $15.01 -- not because NYSE decided it, but just because those happened to be the facts at the time.
Similarly, the new bid is most likely now $15.00, assuming the person who placed the order for 1M shares did not cancel the remaining unmatched 900,000 shares of his/her order. That is, $15.00 is now the highest price at which anyone (known to NYSE) is willing to buy.
How much time does the automated system wait to increment the price, the frequency of the price change and by what percentage to increment etc.
So I think the answer to all these questions is that the automated system does none of these things. It merely publishes information about (a) the last trade price, (b) the price that is currently the lowest price at which anyone has expressed a willingness to sell, and (c) the price that is currently the highest price at which anyone has expressed a willingness to buy.
::edit:: Oh, I forgot to answer your primary question.
Can we estimate the impact of a large buy order on the share price?
Not only can we estimate the impact, but we can know it explicitly. Because the exchange publishes information on all the orders it knows about, anyone tracking that information can deduce that (in this example) there were exactly 100,000 shares waiting to be purchased at $15.00. So if a "large buy order" of 1M shares comes in at $15.00, then we know that all of the people waiting to sell at $15.00 will be matched, and the new lowest ask price will be $15.01 (or whatever was the next lowest sell price that the exchange had previously published).