A method to schedule multiple traffic flows through a multiplexer server to provide fairness while minimizing the sizes of the associated queues, is proposed. The multiplexer server minimizes a quantity called the maximum Normalized Service Lag for each traffic flow. In each time-slot, the normalized service lag of every traffic flow may be updated by adding the normalized lag increment value, whether or not there is a packet in the queue associated with the flow. In each time-slot, a multiplexer server selects a traffic flow to service with an available packet and with the maximum normalized service lag. When the traffic rate requested by each traffic flow is stable, the multiplexer server schedule may repeat periodically. Efficient methods to compute periodic schedules are proposed. The methods can be applied to packet-switched Internet routers to achieve reduced queue sizes and delay.