A Simple proof for the stability of global FIFO queueing networks

Bramson, M. Instability of FIFO queueing networks. Annals of Applied Probability, 4: 414–431 (1994)

Bramson, M. Convergence to equilibria for fluid models of FIFO queueing networks. Queueing Systems, 22: 5–45 (1996)

Bramson, M. Convergence to equilibria for fluid models of head-of-the-line proportional process sharing queueing networks. Queueing Systems, 23: 1–26 (1996)

Bramson, M. Stability of earlist-due-date, first-served queueing networks. Queueing Systems, 39: 79–102 (2001)

Chen, H., Zhang, H. Stability of multiclass queueing networks under FIFO service discipline. Mathematics of Operations Research, 22: 691–725 (1997)

Chen, H., Zhang, H. Stability of multiclass queueing networks under priority service disciplines. Operations Research, 48: 26–37 (2000)

Dai, J.G. On the positive Harris recurrence for multiclass queueing networks. Annals of Applied Probability, 5: 49–77 (1995)

Dai, J.G., Weiss, G. Stability and instability of fluid models for re-entrant lines. Mathematics of Operations Research, 21: 115–134 (1996)

Lu, S.H., Kumar, P.R. Distributed sheduling based on due dates and buffer priorities. IEEE Trans. Autom. Control, 36: 1406–1416 (1991)

Rybko, S., Stolyar, A. Ergodicity of stochastic processes that discribe the functioning of open queueing networks. Problem of Information Transmission, 28: 3–26 (1992) (in Russian)

Seidman, T.I. First come, first served can be unstable! IEEE Trans. Automat. Control, 39: 2166–2171 (1994)

Stolyar, A. On the stability of multiclass queueing networks. In: Proc. 2nd Conf. on Telecommunication Systems-Modeling and Analysis, Nashiville, 1994, 1020–1028