How long does it take for the newly created pages to start showing up in search results?

We selected about two thousand websites from the Russian Internet. All of these websites inform the search engines about the updates using a special sitemap file (sitemap.xml). All of these websites are generally indexed by the search engines: this is confirmed by the fact that the random pages from these websites are almost always found among the first 10 hits in response to the queries identical to the titles of the relevant pages (the text within <title>). So how long does it take for the newly created pages to start appearing among top 10 results for corresponding queries?

We scan the sitemap files for new pages every day (each website may contribute up to 3 pages per day). Search engines are of course able to do the same - after all this is the purpose of the sitemap files.

For every new page, we record the title and the URL. Within a month from the date when the new page was detected, we check if this page is found in top 10 in response to two types of queries:
a) a query which mentions the text of the title restricts the search to the relevant website.
b) a regular text query using the title
The first type of query assesses the time it takes for the new pages to appear in search results. The second type of query assesses the speed of indexation.

The score in this analyzer is calculated as the mean visibility of the new pages within the last month. We also report the data for smaller periods.
Interestingly, there seem to be pages which appear in the search results in the first couple of days after they were detected but disappear by the end of the first week.