In this paper, we propose a framework of traffic control to accommodate multimedia connections on an ATM wide-area network. At the lower layer, an efficient bandwidth allocation method and a constant time cell scheduling algorithm are provided in each network node. These mechanisms have the capability of multiplexing traffics and satisfying diverse delay and loss performance requirements. At the higher layer, a three-phase connection establishment procedure is applied. It transforms the end-to-end performance requirement of a connection request into local requirements for each intermediate node of a routing path. If the requirements for each intermediate node can be satisfied, the connection is accepted; otherwise, another routing path will be examined. Without resort to any complicated rate control inside the network, in our system, time distances between successive cells while they are passing through the network are maintained by imposing an upper bound on the end-to-end queueing delay of each cell. Simulation results show that the connection establishment overhead of our system is almost independent of the traffic load of the network. Its value is very small so that the proposed framework is feasible in the future ATM networks. Besides, optimally transforming end-to-end performance requirement into those for each intermediate node to maximize the saturation load of the network has been proved to be an NP-Hard problem. Two heuristic algorithms are proposed. Experiments are performed to evaluate these algorithms.