The meeting room at Quincy City Hall was standing-room-only Tuesday for a zoning board of appealshearing on Alpha Billings Realty Trust's request to turn what was a dry cleaning shop into an Asian hot pot restaurant at 67 Billings Road.

QUINCY -- Brian McMahon showed up at Quincy City Hall on Tuesday night bearing a parking ticket he had received while at the barber shop during the afternoon.

“Guess who got a ticket for parking on Vane Street because he couldn’t find a space in the parking lot?” he said. “It’s a real problem.”

It was standing-room-only in the city hall meeting room for the zoning board of appeals’ hearing on plans to turn the former dry cleaning shop at 67 Billings Road in North Quincy into an Asian hot pot restaurant.

About a dozen residents and business owners said the 81-seat restaurant would exacerbate parking and traffic problems in the already-congested Norfolk Downs neighborhood, which is home to more than a dozen restaurants.

Jack Milgram, an attorney for Hung Ying Wong of Alpha Billings Realty Trust, withdrew the request without prejudice after five appeals board members said they would reject the restaurant proposal because of the existing parking problems in that area.

At-large City Councilor Joseph Finn and state Rep. Bruce Ayers, D-Quincy, said they had heard from many residents, business owners and patrons of existing businesses who think the parking situation in the area is already bad. Residents said they avoid leaving their homes on Saturdays so they won’t lose their parking pots, and that double-parking has become necessary for people who want to pay quick visits to businesses.

“If anyone is supporting it, I have to be honest, I haven’t heard,” Finn said, talking about the restaurant plan. “I’m asking you to take very seriously the constituents’ concerns.”

The restaurant would have no designated on-site parking; it would rely entirely on public spaces. The city’s zoning rules typically require new restaurants to provide one parking spot for every four seats.

That would mean the proposed restaurant would need 20 spots – seven more than the building’s previous tenant, Fashion Quality Cleaners, had to provide. Milgram said the dry cleaning shop used spots in the public parking lot off Vane Street. He said there is street parking on Hancock Street and Billings Road.

Concerns that the restaurant would worsen parking problems first surfaced in September at a neighborhood meeting hosted by the late Brian McNamee, who represented Ward 6 on the city council.

Prior to that meeting, Milgram said he counted cars in the Vane Street parking lot daily for two weeks during peak times: noon to 2 p.m. and 5 to 7 p.m. He said the lot was one-third empty at lunchtime and half-empty at dinnertime.

“When I said that, they laughed at me and said I was making up my counts, or I must have counted while people were on vacation,” Milgram said Tuesday.

Milgram commissioned a report from traffic engineer Jack Gillon, who presented the findings to the appeals board. He conducted his study in November.

Gillon, who used to work for the city, said there are parking spots on Vane Street and Billings Road that have high turnover rates.

“The bottom line is that even on a Saturday, the whole Vane Street is at capacity during the day, but there are available parking spaces within walking distance from the restaurant,” he said.

Because the area is mostly restaurants rather than retail, resident Alie Shaughnessy said he’d like to see an evening traffic study.

“To do a study that stops at 6 o’clock at night is not the full approach,” he said.

Also Tuesday night, the appeals board postponed its hearing on a proposed six-story hotel off West Squantum Street in North Quincy. The hearing was rescheduled for March 22 because the applicant is modifying the plans.

CPI Management LLC of Boston is proposing a redevelopment project at 1-15 Arlington St. and 22-30 Fayette St. in North Quincy.

The plans call for a 135-room hotel and a 102-space parking lot. The project requires a special permit from the appeals board because the property is in the flood plain district.