Stability of multiclass queueing networks under first-in-first-out service discipline

In this paper, we first formally identify a first-in first-out (FIFO) fluid network that corresponds to the queueing network under a FIFO service discipline, thus complementing the result of Dai for the use of the fluid model for the stability of a multiclass queueing network under a FIFO service discipline. Then we established two sufficient conditions for the stability of a multiclass FIFO queueing network. The results extend the previous work on the single class network, the single station network and a network studied by Rybko and Stolyar. Finally we establish a fluid approximation theorem for the queueing network under FIFO service discipline.