There are no published timetables for AirTrain service. Service is frequent, and at the time of day that you are traveling, you should not have to wait more than 5 to 10 minutes for an AirTrain from Terminal 1 to Jamaica Station. (Do not board an AirTrain bound for a different destination.)
From Jamaica, service to Ronkonkoma is provided by the Long Island Rail Road. Fare and schedule information can be found at www.mta.info. If you are able to make a train that departs Jamaica before 4:20 PM, you can use an off-peak-fare ticket; after then (until about 8:15 PM) you would need a peak-fare ticket. When you arrive at Jamaica Station, if you use one of the Long Island Rail Road ticket vending machine, you can purchase your railroad ticket and your $5.00 AirTrain fare in a single transaction.
There are no published