A free cheesecake promotion celebrating Cheesecake Factory's 40th anniversary turned ugly as orders and DoorDash delivery drivers flooded restaurants. A brawl broke out at one location, and one person was arrested.

The nationwide promotion, which kicked off at 11:30 a.m. local time Wednesday, offered 40,000 free slices of cheesecake to customers who ordered through the DoorDash app. The promotion comes at a time when more restaurants are adding delivery and digital ordering capabilities to meet growing consumer demand for fast and convenient access to food.

Within two hours, all free slices had been ordered, leading some disappointed respondents to complain on social media that they were not able to get their hands on a piece of cheesecake, or if they did, it arrived hours after it was ordered.

"Our Day of 40,000 Slices promotion had such a tremendous response from our guests that we extended it and delivered more than 60,000 complimentary slices," a spokeswoman for Cheesecake Factory told CNBC. "We were truly humbled by the popularity of the offer and by how quickly our fans responded as all of the 60,000 complimentary slices were ordered within an hour of the promotion's start time."

Tweet 4

Tweet 1

However, disgruntled customers were the least of Cheesecake Factory's worries. The promotion brought crowds of DoorDash delivery drivers to restaurants, disrupting business. Some locations saw drivers double parking their vehicles so they could enter the restaurant and pick up their orders.

Tweet 2

Tweet 6

In one instance, police were called to a Cheesecake Factory in Arlington County, Virginia, after a fight broke out while drivers were picking up orders. While there was no active fight in progress when officers arrived, one person refused to listen to police commands and was arrested on disorderly conduct charges, according to ARLnow, a local news organization.

"DoorDash was made aware of this incident, and we are cooperating with local law enforcement," DoorDash told CNBC.

Tweet 5

tweet 3

Restaurants like the Cheesecake Factory, which typically have not offered delivery in the past, are doing more promotions and partnerships with delivery services. Free or discounted food is one way for these restaurants to bring awareness to their new delivery and online ordering capabilities and get more customers to download apps and order again in the future. Digital and delivery orders also give restaurants a chance to upsell customers, leading to larger checks.

WATCH: Bobby Flay on his expanding empire