A switching device is able to route the arriving data packets according to data packet destination information to dedicated output ports. The switching arrangement has, for each set of input ports in the switching device, a set of output buffers with an output buffer for storing the payload of each data packet at an address in the output buffer which pertains to the same set of output buffers and belongs to the dedicated output ports. At least one of the output buffers has a set of output queues with an output queue for each output port for storing the address of each payload stored in the corresponding output buffer. An arbiter controls a readout order of the stored addresses. For the output buffers which pertain to the same set of output ports a multiplexer multiplexes according to the readout order the payloads from the output buffers to the output ports.