In this paper, we present a routing mechanism and buffer allocation mechanism for an ATM switching fabric. Since the fabric will be used to transfer multimedia traffic, it should provide a guaranteed throughput and a bounded latency. We focus on the design of a suitable routing mechanism that is capable of fulfilling these requirements and is free of deadlocks. We will describe two basic concepts that can be used to implement deadlock-free routing. Routing of messages is closely related to buffering. We have organized the buffers into parallel FIFO's, each representing a virtual line. In this way, we not only have solved the problem of head of line blocking, but we can also give real-time guarantees. We will show that for local high-speed networks, it is more advantageous to have a proper flow control than to have large buffers. Although the virtual line concept can have a low buffer utilization, the transfer efficiency can be higher. The virtual line concept allows adaptive routing. The total throughput of the network can be improved by using alternative routes. Adaptive routing is attractive in networks where alternative routes are not much longer than the initial route(s). The network of the switching fabric is built up from switching elements interconnected in a Kautz topology.