Are high density buildings larger on avenues than for streets

Does the capacity of the road influence how many agents can travel down it simultaneously?

No. Number of lanes and whether there are stop signs or traffic lights only affect traffic agents. They do not affect non-traffic agents.

• Traffic agents include police, fire, ambulance, garbage trucks, delivery trucks, moving trucks and of course sims driving their cars.
• Non-traffic agents include power, water, sewage and of course pedestrian sims.

Power and water agents are absorbed as they pass buildings with available capacity. While the agents aren't affected by road capacity, they can be depleted by passing many buildings. If you layout your city with a powerplant at position 1, it is unlikely that agents will reach buildings at position 2.

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Update: There was a sewage issue fixed in patch 1.8.

Fixed a clog in the pipes where sewage would sometimes get backed up and act jittery.

The service area is always the entire city. Travel time determined whether you'll reach the destination before a building burns down, patient dies, or criminal gets away.

Early on, with little traffic, one single service placement can usually cover the entire city. Adding more vehicles lets you dispatch to more places at once. Once traffic increases, the effective service area is reduced, no matter how many vehicles you add (except for helicopters). You can wind up in a situation where a vehicle can't reach the building next door because it can't even exit the vehicle bay. Good placement, road layout, and public transportation will keep your services most effective.

You'll notice that the game lets you plop the vehicle bays apart from the building. Don't lay them all next to each other so they exit on the same road in the same direction. Place them on opposite sides of the road and across intersections. That way, traffic in one direction will only clog up some of your vehicles instead of all of them.