NEW YORK — Despite having already waited years for the freedom to switch mobile phone companies without losing their numbers, cell users might want to wait a bit longer before lining up for "wireless emancipation" when it takes effect on Monday.

Critics say wireless companies spent so much time and effort fighting to delay the new rules that their preparations may prove inadequate for the expected torrent of customers wanting to bring their cell numbers to a different carrier.

Wireless companies assert they are ready, having added the systems and staffing needed to make the process of switching carriers run smoothly.

But for an event experts see as a monumental undertaking, most of the carriers did not sign required interconnection agreements or begin extensive testing until the past month.

To switch service for just one phone number, there are "minimally" 11 transactions or handoffs of information between the two carriers, and that's just to "port" a single phone number, explained Helen Harris, spokeswoman for TSI Telecommunication Services Inc.

TSI, based in Tampa, Fla., was hired by five of the six national cell companies to serve as intermediary for the process. The company has brought on 200 additional workers to handle the expected workload for verifying information and troubleshooting problems between carriers.

Similarly, carriers such as Verizon Wireless and T-Mobile have opened new facilities with hundreds of new hires to deal specifically with the new process.

At least one cellular carrier, Sprint, encountered major technological problems during multi-carrier tests last week, two industry sources told The Associated Press.

Sprint characterized the problem as no more significant than any other carriers have encountered during testing, and said it has since been fixed.

Earlier this month, AT&T Wireless was temporarily unable to activate tens of thousands of new customers because of a glitch in software that was designed to help sales and customer service representatives handle inquiries related to the new phone number rules.

Regardless of preparations and testing, the biggest wild card simply may be how many people seek out the switch on Monday.

"Industry estimates have varied widely. We've heard estimates as high as 9 million on day one. We believe it will be more in line with 1 million, and we have engineered our systems to handle more than the anticipated volumes," Harris said.

But if the number of requests approaches millions, she said, "It's reasonable to expect some hiccups on day one with an implementation of this magnitude."

Although the Federal Communications Commission has set a target of 2.5 hours for carriers to complete the transfer of a number to a rival, experts and most of the companies say the process is likely to take at least a day at first.