The Roads Must Roll.

Wiki:

"The Roads Must Roll" is a 1940 science fiction short story by Robert A. Heinlein.

The story is about wide, rapidly moving passenger platforms (similar to moving sidewalks, but reaching speeds of 100 mph). These roads combine the features of highways, railways and highway towns, and all goes smoothly until there is union trouble.

Heinlein's themes are technological change and social cohesion. The (fictional) social movement he calls functionalism (which is unrelated to the real-life sociological theory of the same name) believes that one's status and level of material reward in a society must and should depend on the functions one performs for that society.

In "The Roads Must Roll", the technicians who maintain a section of the San Diego to Reno roadway are persuaded that their role in maintaining the nation's transport infrastructure is more important than that of any other workers and that they should therefore be rewarded more highly than any others. To demonstrate their importance and press their claims, they stop the 100 mph strip, causing transportation chaos and many casualties.

The men who maintain the roads get around beneath them via "tumblebugs": unicycles which are motorized and gyroscopically stabilized much like the later real-life Segway.
Larry Gaines, Chief Engineer of the roadtown, is instrumental in restoring order and bringing the villains to justice, through a combination of clear thinking, swift para-military action at the head of his uniformed cadets, and appeals to patriotism."

Thanks to Otto nero