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Amazon Prime Day has begun — and some shoppers are not impressed  logos. (Andrew Harrer/Bloomberg)

Prime Day is underway, and it appears that some customers are disappointed with the massive sale the e-commerce giant is holding to commemorate its 20th anniversary.

Some shoppers took to social media Wednesday morning to criticize the selection of items offered. Some were also frustrated that some deals are apparently being scooped up so fast that would-be buyers are being put on a waitlist.

Here's a sample of some of the venting:

Indeed, it did appear that some deals were running out quickly. As of 8:13 a.m. Eastern time, the short-term "lightning deals" on items such as a video game, a knee brace and a probiotic supplement were fully claimed. And even some of the deals that are supposed to be available to customers all day long appeared to be at risk of running out. About 72 percent of the Fire HD 7 Kids edition, which is marked down $60, are already claimed.

An Amazon spokeswoman promised that shoppers will continue to see fresh deals throughout the day, including on televisions and the Amazon Fire TV Stick and Echo.

"We have years of experience with these types of events and we stagger the deals to make sure the fun will last through tonight," Amazon's Julie Law said in an e-mail.

Despite the gripes on social media, there was evidence that many shoppers indeed found the sales enticing.  Amazon said that, by Wednesday afternoon, peak order rates had already surpassed those it saw during the most recent Black Friday.

Prime Day, which Amazon announced last week, is shaping up to be something of a duel with retail heavyweight Wal-Mart. The big-box chain launched its own blitz of sales to rival Prime Day and issued a statement emphasizing that its sale wouldn't come with "an admission fee" -- a dig at Amazon's decision to make its sale available to members of its $99 per year Prime program.

Amazon fired back: “We’ve heard some retailers are charging higher prices for items in their physical stores than they do for the same items online,” said Greg Greeley, vice president of Amazon Prime in a statement. “The idea of charging your in-store customers more than your online customers doesn’t add up for us, but it’s a good reminder that you’re usually better off shopping online.”

Amazon chief executive Jeffrey P. Bezos owns The Washington Post.