Stability of Multiclass Queueing Networks Under FIFO Service Discipline

In this paper, we first formally identify a FIFO fluid network that corresponds to the queueing network under a first-in first-out (FIFO) service discipline, thus complementing the result of Dai (Dai, J. G. 1995a. On positive Harris recurrence of multiclass queueing networks: A unified approach via fluid limit models. Ann. Appl. Probab.5 49–77.) for the use of the fluid model for the stability of a multiclass queueing network under a FIFO service discipline. Then we establish 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 (Rybko, A. N., A. L. Stolyar. 1992. Ergodicity of stochastic processes describing the operations of open queueing networks. Problemy Peredachi Informatsii28 2–26.). Finally we establish a fluid approximation theorem for the queueing network under FIFO service discipline.