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.

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