Somewhere in Cupertino, Apple executives are probably breathing sighs of relief — if not celebrating — as demand for the new iPhone 11 appears to be off to a good start.

Apple (AAPL) announced three versions of the new model at its annual media event last week: the more basic iPhone 11, and the premium iPhone 11 Pro and iPhone 11 Pro Max. The iPhone 11 looks largely the same as its predecessors, with functional improvements such as longer battery life and more cameras. But analysts say early demand for the new phone has been stronger than last year since Apple and several retailers began accepting preorders on Friday.

It's a win Apple desperately needs from its single biggest revenue driver. Declining iPhone sales have been a drag on Apple's business as customers hold onto their smartphones longer and Apple works to reverse a slowdown in China, once its most promising market, amid an ongoing trade war with the United States.

Analysts often measure demand for smartphones in expected shipment delivery times — the more preorders that are made, the longer it will take for those orders to arrive on consumers' doorsteps.

Delivery times have been pushed out on a number of iPhone 11 models, with many now expected to arrive two to three weeks after the phone's September 20 release date, Wedbush analyst Dan Ives said in a note to investors Sunday. Ives said there has been particularly strong demand for a larger-storage version of the iPhone 11 Pro, and for Space Gray and Gold colored models. A research note from data analytics firm Nomura Group similarly pegged the shipment time for the iPhone 11 Pro and Pro Max models at 17 days, versus 11 days for last year's iPhone XS and XS Max.

"We are careful about extrapolating first weekend data, though it is fair to say it is ahead of last year's launches," Nomura analysts said in the note.

Among the reasons for the iPhone 11's early success may be that fewer people upgraded to last year's iPhone XR and XS models. The XR and XS were Apple's most expensive iPhones yet (the basic XR version started at $749), with relatively few new innovations to excite customers. But with the way technology is designed, people still typically need to upgrade every few years, and Apple dropped the price of the basic iPhone 11 model back down to $699 and held the price of its flagship models flat.

Roughly 350 million of the total 900 million iPhones out in the market could soon be ready for an upgrade, Ives estimates. However, he points out that orders could be hurt by expectations that next year's iPhone release could feature 5G capability.

Continued tensions in China could also lower iPhone 11 sales, though Nomura analysts said preorders of the new model from China so far appear to be on par with last year.

More iPhone 11 sales would likely mean more subscribers to Apple digital services, an area the company is increasingly leaning on to drive profits and future growth.

At its event last week, Apple announced the prices and some offerings for its Apple Arcade and Apple TV+ services, with Apple TV+ slated to be the cheapest streaming service on the market when it launches November 1 at $4.99 per month. CEO Tim Cook also said all new purchases of iPhones, iPads and Macs would come with one year of free Apple TV+.

That offer could help Apple secure future paying customers for the service. Ives said he now expects Apple could gain 100 million Apple TV+ customers in the next three to four years, so long as Apple delivers on its promise of content good enough to stack up against the fierce competition in the streaming market. That could mean Apple bringing home nearly $6 billion in annual Apple TV revenue by 2024.

However, analysts from Goldman Sachs said in a note to investors Thursday the one-year free offer could harm Apple's earnings in 2020. The company refuted that idea, saying: "We do not expect the introduction of Apple TV+, including the accounting treatment for the service, to have a material impact on our financial results."

Now, with the basic version of the iPhone 11 set to hit shelves in Apple stores this Friday, the company will likely soon see whether that early demand will translate to actual iPhone sales.