The issue with using average waiting times (as opposed to picking a particular time and computing actual waiting times) is stations with multiple trains — the N, R and Q might each stop at Union Square once every 10 minutes, but if you're happy boarding any of those, then your average wait time isn't 5 minutes — it's much less.
What I might try is sampling a couple random start times (e.g. 8:00 AM, 8:03 AM, 8:22 AM) and averaging the predictions of all those.
What I might try is sampling a couple random start times (e.g. 8:00 AM, 8:03 AM, 8:22 AM) and averaging the predictions of all those.