Wasn't sure how to title it.
How about this type of call? You get a call where you have to send your patrol units across the map to chase down either a speeding drunk driver, robbery suspects etc.
What I mean is this. On your map it shows a car moving in a random pattern and you have to send your patrol units out to chase and catch him. Kinda like a high speed chase with moving units and suspect vehicle.
You'd have a time limit to catch the suspect/suspects. Like 5-10 mins or so and if the time was up then you let the suspect get away. It would be up to the player as to how they could strategically catch the suspects vehicle.