Commutes made easier with maths

Silicon Valley start-up Urban Engines hopes to make daily commutes faster - by using advanced maths.

For urban transit operators, its algorithms aim to reveal how crowded commuter buses and trains are on their network, and how long are customers waiting on station platforms - information which until now has not been readily accessible.

It plans to license its so-called "space/time" model to operators in cities around the globe.

It also has just launched a consumer app that uses offline maps and data to let users figure out the best way to navigate around 11 cities - those in which transit operators employ Urban Engines' system.

As well as bringing up a "tabbed" view of expected transit times on favourite routes, it also uses the smartphone's built-in sensors to show an augmented reality view of how to navigate effectively, even when the user is offline.

But how does it rank against mapping giants like Google - the former employer of Urban Engine founder Shiva Shivakumar?

He explained how the system works to the BBC's North America technology correspondent Richard Taylor.

You can follow Richard on Twitter @RichTaylorBBC