I know several cabbies and there is a lot of urban mythery surrounding cabs. Traffic lights make no difference, wait time is charged but only when initiated by the driver, eg waiting at a chip shop. Distance is what is charged, there is an initial longer distance that is given as part of the initial charge then after that a shorter distance is charged per multiple, a driver should take the shortest route but if requested will take any route you say. There are unscrupulous drivers that will go round the houses if they think they can get away with it but they propbably won;t do that if they have other fares waiting.