Periodic long response from the server while downloading, why?

The website sometimes long replies for some reason - long time to first byte, the rest is working fine, the speed of response does not exceed 500ms . Website is on shared hosting sprinthost one of the maximum tariffs. Caching is used w3total cache, but periodic freezes are not associated with the formation of a new cache of pages (tested with the lack of cache, and with the created cache), as well for site enabled Zend OPCache.
May be associated periodic hang?
March 19th 20 at 08:27
1 answer
March 19th 20 at 08:29
May handle what's coming. Try to create a file aaa.php with the content <?php phpinfo(); ?> and his check on time.

What treatment can be, for example:
check the updates to WP
the rating calculation
updating the cache

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