There are a number of items on the various 'roads' that move along with the strips; shops, airbreaks and passenger cars. The road system itself is divided into a series of "circles", either moving around nominated cities or simply travelling from one location to another and back;
The faces of two men flicked into view on the visor screen. The
younger answered him with the same air of acting under supervision.
They were at once replaced by two more. "Angeles Sector--rolling!"
Then: "Bakersfield Sector--rolling!"
And: "Stockton Sector--rolling!''
Finally, when Reno Circle had reported, the cadet turned to Davidson
and reported: "Rolling, sir."
The roads themselves are not conveyor belts (the Engineer describes the earliest strip as "hardly more than a conveyor belt" but rather they are made up from a series of
which presumably allow the belts to feed in a continuous circle without stopping, much like an airport carousel. The stationary items therefore remain in constant motion, making a lap of their designated circle every few hours.
It's particularly notable that when the engineer makes plans to visit a specific restaurant, his first instinct is to check his watch. Although it's not stated in canon, this presumably would be to ensure that when they arrive at the appropriate strip, the restaurant will have orbited back to their location.