A new measure would give residents the chance to reduce the number of times a week cars need to be moved for street cleaning. Alternate-side parking rules exist in 54 of the city’s 59 districts and are seen by many as nothing more than an inconvenient revenue stream for the city because of the dismally poor performance of the city’s street-sweeping trucks. The bill, which was recently passed by New York City’s Council,  would allow community boards that keep their streets clean for two years in a row, with a 90 percent clean grade, to reduce the local street cleaning to once a week. The move would ease residents’ stress over moving their cars, finding parking spots and getting tickets.