But Mr. Mousa focused on one number: 3,892. That was his position on a New York City food vendor waiting list.

Like thousands of the city’s mobile food vendors, Mr. Mousa cannot get a permit for his cart, the Halal Plates. A longstanding cap limited the number of permits to 5,100, before a 2021 law began allowing for 445 new permits a year for a decade. So far, the city has issued 71 new permits.

Almost 9,500 people were on waiting lists in January, according to the city’s health department. A spokesman said it had released 1,074 applications — a permit prerequisite — since the law was enacted, but most applicants had yet to complete the process.

While he waits, Mr. Mousa said he and his business partner pay $18,000 in cash every two years to rent their permit from a Bronx cabdriver who Mr. Mousa said obtained it decades ago for a few hundred dollars. Mr. Mousa said such arrangements were the only ways many vendors, who otherwise follow regulations, can avoid fines and confiscation of their carts.

Mr. Mousa hopes to negotiate the same price this summer, but anticipates the permit holder will try to raise it.

“What can I do?” Mr. Mousa said, adding, “He has the thing I need.”

Such is the math of chicken and rice — a heavily spiced mound of boneless chicken with yellow rice and a side salad — which swept the city in the 1980s, after a wave of Egyptian immigrants arrived.