Abstract—We provide an analytical proof that the departure rate of a CBR flow at an overloaded link with FIFO buffers is proportional to the flow’s share of the total offered load at the link. This property of FIFO scheduling was recently validated in [1] in a series of traffic measurement experiments. An extension of the analysis to a multi-node scenario shows that the output rate of a flow in a network with many overloaded FIFO switches approaches the pessimistic values given by blind multiplexing.