In this paper, we propose a generalised minimum queuing delay (GMQD) service discipline for high speed networks, mainly asynchronous transfer mode (ATM) networks. This proposed scheme is similar to service disciplines based on fair queuing, but instead of using only a single service rate for each session for its entire connection lifetime, multiple service rates are used. The service rate of any session at any point in time is computed efficiently based on the number of bits backlogged in the queues of the session and another imaginary reference session at that point in time. The main advantage of this scheme is that the queuing delays suffered by all the sessions connected to a single output node are minimised, leading to a smaller delay variation. In addition, this smaller delay variation also implies a smaller variance in the maximum queue length, thereby, reducing the possibility of buffer overflow.