A method and system for controlling access of a resource among several users of a resource. A plurality of service queues are established, each service queue handling requests for a predetermined range of the resource. A plurality of time slots are also established, and each service queue has a number of time slots in proportion to the amount of resource handled by that queue. One or more requestors request access to the resource, indicating a desired amount of the resource. Each request is assigned to one of the service queues based on the requested amount of the resource. A reference to the request is inserted in a number of slots associated with the queue to which the requestor was assigned. The references in the slots establish a service order which controls the order and frequency with which a requestor can access the resource. A quota can be established for each requestor to prevent any requestor from using a disproportionate amount of the resource. The method and system of the present invention is highly efficient and provides Quality of Service guarantees for multimedia traffic.