WASHINGTON — Leaders of the Secret Service and Capitol Police apologized Wednesday to thousands of ticket-holders who were shut out of Barack Obama’s swearing-in.

In an incident dubbed the “Purple Tunnel of Doom,” thousands of people with prized tickets to the Jan. 20 ceremonies were left waiting in a tunnel below the National Mall. At a hearing Wednesday on Capitol Hill, Secret Service Director Mark Sullivan and Capitol Police Chief Phillip Morse pledged that such problems would not happen again. The National Park Service has said about 1.8 million people attended the inauguration, making it the largest gathering ever held in Washington.