New Jersey Transit trains will begin operating again on Tuesday after the agency reached a deal with striking rail engineers on wage increases, ending a work stoppage that affected about 350,000 passengers. The statewide rail strike, the first to hit NJ Transit in more than 40 years, had begun just after midnight on Thursday, leaving tens of thousands of commuters to New York scrambling to find alternate transportation. The Brotherhood of Locomotive Engineers and Trainmen union, which represents 450 NJ Transit engineers who drive the agency's commuter trains, said it reached an agreement on pay with the agency on Sunday and that its members would return to work on Tuesday.