A scheduling mechanism that fairly allocates a resource to a number of schedulable elements, of which some are latency-sensitive, is disclosed. Each element's use of the resource is tracked by determining the element's virtual time. An active element is selected from the elements that are ready to use the resource by determining the element that has the smallest effective virtual time. The effective virtual time is the element's actual virtual time modified by a borrowed virtual time value. When an element has a short-term need for the resource, it can borrow the privilege to run by borrowing virtual time. As the element uses the resource, it consumes virtual time according to its weight. When the elements are scheduled for the resource, the ready element having the smallest virtual time is selected. The invention enforces long-term fairness to each element while allowing latency-sensitive elements to be preferably selected.