WASHINGTON — After years of criticism of the wireless service on its trains, Amtrak announced on Thursday that it had upgraded its cellular-based Wi-Fi using broadband technologies that will improve the speed and reliability of the Internet in its passenger cars.

Amtrak’s Wi-Fi has been the target of technology jokes since the railroad introduced the service, with some passengers comparing it to dial-up services like America Online or Prodigy. But others have praised the service, saying it allows them to be productive while traveling between cities, unlike airline travel. Because of the technical difficulties of maintaining a strong Internet connection on a moving train, the increase in speed would still be less than most people experience at home.

The railroad said the broadband upgrade was complete on the high-speed Acela trains that travel the more than 400 miles between Washington and Boston. Several state-supported routes in California, including the Capitol Corridor, Pacific Surfliner and San Joaquin routes, have also been upgraded.

Amtrak said it would roll out the upgrades to all remaining Amtrak trains equipped with Wi-Fi, including the Northeast Regional, by late summer.