A method includes receiving in a network element a packet, which includes a delay field that indicates an overall time delay accumulated by the packet until arriving at the network element. Upon receiving the packet, an interim value is substituted in the delay field. The interim value is indicative of a difference between the overall time delay and an arrival time of the packet at the network element. Before sending the packet from the network element, the overall time delay is updated in the delay field based on the interim value and on a departure time at which the packet is to exit the network element. The packet, including the updated overall time delay, is transmitted from the network element.