It is the New York City driver’s public shame — a sentence of solitary front-seat confinement levied against those for whom subways, buses and taxis are insufficient.

For at least 90 minutes each week, residents move their vehicles from their curbside berths, slide into formation behind a row of double-parked neighbors and moor together in a singular urban traffic jam, beholden to a hulking contraption whose distinguishing feature appears to be this: It swirls plastic bags and cigarette stubs briefly before returning them to the earth.

But the ignominy of alternate-side-of-the-street parking, which allows city workers to clean roadways without the obstruction of parked cars, could soon be eased. A bill that will have a hearing before the City Council on Monday would allow drivers to return to parking spaces once the street sweepers pass, causing a potentially significant reduction in wait times for those doomed to mornings in their cars.

Councilman Ydanis Rodriguez, a Democrat from Manhattan and the bill’s sponsor, said the legislation would prevent accidents by reducing the duration of double-parking; help the environment, with fewer cars idling or driving in search of spaces; and save New Yorkers “millions of dollars” in lost time.