Fortunately, the New Haven Railroad published a little booklet titled "Arranged Freight Train Service." Also known as a "symbol book," this document listed all of the freight trains on the railroad and what schedule they generally maintained. As far as I can tell, new books were issued at regular intervals on or around the same date as the employee timetable.
The symbol book I really need for my chosen era is the one issued September 28, 1947, but - alas - I haven't yet found a copy. What I do have though are relevant parts from the book from the previous year (9/29/46) as well as April 25, 1948 and April, 1949. So, based on the information I have on-hand, I just have to make some educated assumptions about operations in the Autumn of 1947. Here's what I discovered (remember, you can always click on images to enlarge):
Symbol Book #76, September 29, 1946
The Valley Local
Turning to the section titled "Hartford Division Local Service" (p. 153), I see that such service generally occurred every day except Sunday & legal holidays, unless otherwise specified. Looking down the list, I see #7 (aka Hartford Division Local #7 or HDX-7) is the Valley Local. It leaves Hartford at 9:30am and goes to East Berlin (via Middletown) on Mondays, Wednesdays and Fridays and to East Haddam on Tuesdays, Thursdays, and Saturdays. It connects at East Haddam with the New London-Cedar Hill Local (aka PDX-2, more on that in a minute) and the Shore Line crew (i.e. PDX-2) does the switching in East Haddam.
The Air Line Local
Continuing in the Hartford Division Local Service section (p. 154), I see that train #12 runs from Cedar Hill to Colchester and back - HDX-12, aka the Air Line Local. It goes on-duty at Cedar Hill yard at 9am and services all the towns to Colchester, including Middletown where it meets and exchanges cars with the Valley Local.
The Shore Line Local(s)
Saying "the" Shore Line Local is a little misleading since there were actually at least three of them listed in the Providence Division Local Service section (p. 157) . But relevant to my layout, I need only concern myself with two: The Cedar Hill-New London local (PDX-1) and the New London-Cedar Hill local (PDX-2). PDX-1 went on-duty at 9am in Cedar Hill and PDX-2 went on-duty at New London at 12:30pm. Interestingly, the eastbound local (PDX-1) didn't service the towns of Pine Orchard, Stony Creek, and Westbrook, but instead brought cars bound for those towns to Old Saybrook to hand them off to the westbound local (PDX-2). For its part, the westbound local skipped the towns of Lyme, Black Hall, Millstone, Madison, and Guilford, leaving cars destined for those towns at Old Saybrook for the eastbound local to handle. There was clearly a lot of interchange of cars at Old Saybrook, but I don't know what time that interchange took place. I suspect - especially given the big difference in on-duty time - that the cars were just left. Unlike the typical interchange between the Valley Local and Air Line Local, the two Shore Line locals were probably not in Saybrook at the same time.
As an aside, while I'm not there yet, I do plan to model Old Saybrook. And when it's operational, my layout will have the distinction of being the home of four separate and distinct local freights.
But which Shore Line Local exchanged cars with the Valley Local in East Haddam? It depends on what year you're talking about, and in 1946 it was PDX-2 - the New London-Cedar Hill local - that went up the Valley line.
Symbol Book #?, September 25, 1948
I only have a very small part of this symbol book, so I don't even know the number. I do, however, see the Valley Local is on page 156 and this edition contains more-detailed schedule information. See below:
The page for the Air Line Local shows similar detail, and an earlier departure as well (7:45a):
PDX-2 still goes up the Valley to East Haddam in 1948, but the coolest thing about the info in this edition of the symbol book is that it shows when the two Shore Line locals were in Old Saybrook: PDX-2 got there at 12:14p and left for East Haddam at 12:35. Just 5 minutes later, PDX-1 arrived and didn't leave Old Saybrook until 1:10pm.
Symbol Book #?, April ?, 1949
As I detailed on my website, diesels had supplanted steam on these locals by the spring of 1949. Freight service changed quite a bit too in the seven months since the prior symbol book was issued.
You can see that the Valley Local (HDX-7) is now a M/W/F only job, departing Hartford at 8:30, and it no longer services East Berlin. The Air Line Local (HDX-12) now has that chore, running (crawling, actually, given the poor track) up to East Berlin on Tuesdays/Thursdays/Saturdays. PDX-1 (the Cedar Hill-New London local) goes up the Valley line now, and the exchange of cars happens in Essex rather than East Haddam. Unfortunately, the information I have doesn't include PDX-2 so I'm not sure what it does in 1949.
As you can see, prototype modeling really is all about the details and prototype operations can vary widely, even within the span of a few short months. Thankfully, railroads tended to be very paperwork-heavy, keeping records of just about everything imaginable. The secret to having prototypically correct operations is to find those records if you can. The thrill of that hunt and the research that's involved is just another fun aspect of our hobby.