Fuel efficient driving patterns are well investigated for highway driving, but less so for applications with varying speed requirements, such as urban driving. In this paper, the driving mission of a heavy-duty vehicle in urban driving is formulated as an optimal control problem. The velocity of the vehicle is restricted to be within upper and lower constraints referred to as the driving corridor. The driving corridor is constructed from a test cycle with large variations in the speed profile, together with statistics from vehicles in real operation. The optimal control problem is first solved off-line using Pontryagin's maximum principle. A sensitivity analysis is performed in order to investigate how variations in the driving corridor influence the energy consumption of the optimal solution. The same problem is also solved using a model predictive controller with a receding horizon approach. Simulations are performed in order to investigate how the length of the control horizon influences the potential energy savings. Simulations on a test cycle with varying speed profile show that 7% energy can be saved without increasing the trip time or deviating from a normal driving pattern. A horizon length of 1000 m is sufficient to realize these savings by the model predictive controller. The vehicle model used in these simulations is extended to include regenerative braking in order to investigate its influence on the optimal control policy and the results.