Adding a transaction ID to ruby-on-rails logs

We have a RoR app (rails version 3.2.15 right now). As it has been getting busier, the log-files it's producing are becoming less and less useful for troubleshooting. When they come in like this, it's not a problem:

Started GET "/accounts/28088166/kittens/22894/rendered_png?file_id=5d3eaec77954a489b5ddd75143091767&kitten_store_id=9970569bbacf7b6dbeb4eb9295960d69&size=large" for 172.16.202.30 at 2013-11-12 13:45:00 +0000
Processing by KittenController#rendered_png as HTML
  Parameters: {"file_id"=>"5d3eaec77954a489b5ddd75143091767", "kitten_store_id"=>"9970569bbacf7b6dbeb4eb9295960d69",  "size"=>"large", "kitten_cam_id"=>"280941", "id"=>"kjlak357aw479607t"}
  Rendered text template (0.0ms)
Sent data   (1.8ms)
Completed 200 OK in 1037.4ms (Views: 1.4ms | ActiveRecord: 98.4ms)

Short request, quickly assembled, all the relevant log-lines are in one block.

However, not all of our code renders in 1037ms. There are a few calls that can exceed several seconds, and during that time several of these quicker ones can come in (we are running multiple Passenger instances). When that happens, its very, very hard to identify which log-lines belong to which GET. It's not uncommon to get log-lines like this:

Sent data   (4.1ms)
Completed 200 OK in 947.1ms (Views: 230.9ms | ActiveRecord: 56.8ms)
Completed 200 OK in 767.4ms (Views: 3.2ms | ActiveRecord: 72.2ms)
Completed 200 OK in 2338.0ms (Views: 0.2ms | ActiveRecord: 0.0ms)

Ooookaaaay… which GET goes to what "Processing by" lines?

Is it possible to add something like a transaction-ID to these log-lines? The log-spam would be interspersed, but at least grep-magic would give me the unified entries that I need.