One embodiment of the present invention provides a system for routing packets in a network. A router may receive a packet at an input port which originated from a source system and which is destined to a destination system. The packet may include a traffic-management field which enables the source system to influence how the packet is routed through the network without requiring the source system to explicitly specify nodes that the packet should traverse. The router can use the traffic-management field to select an output port from a set of output ports of the router that are associated with different paths to the destination system. Since the traffic-management field's value is set by the source system, it enables the source system to influence how the router selects the output port, thereby enabling the source system to influence how the packet is routed through the network.