SummaryThe number of vehicles on the road (worldwide) is constantly increasing, causing traffic jams and congestion especially in city traffic. Anticipatory vehicle routing techniques have thus far been applied to fairly small networked traffic scenarios and uniform traffic. We note here a number of limitations of these techniques and present a routing strategy on the assumption of a city map that has a large number of nodes and connectivity and where the vehicles possess highly varying speed capabilities. A scenario of operation with such characteristics has not previously been sufficiently studied in the literature. Frequent short‐term planning is preferred as compared with infrequent planning of the complete map. Experimental results show an efficiency boost when single‐lane overtaking is allowed, traffic signals are accounted for and every vehicle prefers to avoid high traffic density on a road by taking an alternative route. Comparisons with optimistic routing, pessimistic routing and time message channel routing are given. Copyright © 2014 John Wiley & Sons, Ltd.