The phrase 'on that route' is correct and usable in written English.
You can use it when referring to a particular course of action or direction. For example, "I decided to take the bus on that route to get to work faster."
The plane was flying towards a large storm system, a common obstacle on that route.
Starting March 15, MAXjet will operate four round trips a week on that route.
Amtrak commands twice as large a market share on that route as it does on the longer run to Boston.
Swiss International Airlines said it had added a stop in Hong Kong on that route as of Monday and modified its timetable.
Singapore Airlines has already doubled its economy-class fares between Singapore and Manila to exploit the exit of its only competitor on that route.
Service on that route is expected to start next spring and will be financed by a grant from the Lower Manhattan Development Corporation.
FirstGroup is bidding to run competing trains on the east coast mainline, barely a week after its rival Virgin Trains started operating the franchise on that route.
As BMI had given up its Glasgow-Heathrow route, regulators did not insist on competition on that route.
Travel time has an additive structure; i.e., route travel time is the sum of link travel time on that route.
Travel cost has a multiplicative cost structure; i.e., route travel cost is a multiplication of link travel cost on that route.
The introduction of a second service provider leads to competition on that route, the effect of a third competitor is small.
