Are you referring to an Uber or Lyft clone that only dispatches from your local cab company?
If so, what would the benefits of someone using the app over Uber, for example?
It’s not always the case that “if you build it, they will come.” Sometimes, it makes more sense to just go where the people already are.
Wouldn’t it be more profitable for your cab company to simply operate under Uber?
If I sell homemade jam, for example, it’s more effective for me to get my jam onto the shelves of the most popular supermarkets, where people are already shopping, than to build my own market to sell my jam, convince people to start shopping in it, and only sell my own food in it. It’s an uphill battle to convince people to now go to two stores: one for just my jam, and another for everything else they need.
People use Uber because it works anywhere, in any city, and at any time. What would be the advantage to downloading and installing your app just to use when they happen to need a ride in your city?