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## Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2019 | 73 | 2 |
Tytuł artykułu

### Stability of preemptive EDF queueing networks

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EN
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EN
We show stability of preemptive, strictly subcritical EDF networks with Markovian routing. To this end, we prove that the associated fluid limits satisfy the first-in-system, first-out (FISFO) fluid model equations and thus, by an extension of a result of Bramson (2001), the corresponding fluid models are stable. We also demonstrate that in a preemptive multiclass EDF network, after a time large enough to process all the initial customers to completion, the maximal number of partially served customers in the system over a finite time horizon converges to zero in $$L^1$$ under fluid scaling.
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2019
online
2020-01-16
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Bibliografia
• Billingsley, P., Probability and Measure, 2nd Edition, Wiley, New York, 1986.
• Bramson, M., Convergence to equilibria for fluid models of FIFO queueing networks, Queueing Syst. Theory Appl. 22 (1996), 5–45.
• Bramson, M., Convergence to equilibria for fluid models of head-of-the-line proportional processor sharing queueing networks, Queueing Syst. Theory Appl. 23 (1996), 1–26.
• Bramson, M., State space collapse with application to heavy traffic limits for multiclass queueing networks, Queueing Syst. Theory Appl. 30 (1998), 89–148.
• Bramson, M., Stability of earliest-due-date, first-served queueing networks, Queueing Syst. Theory Appl. 39 (2001), 79–102.
• Dai, J. G., On positive Harris recurrence of multiclass queueing networks: a unified approach via fluid limit models, Ann. Appl. Probab. 5 (1995), 49–77.
• Dai, J. G., Weiss, G., Stability and instability for fluid models of reentrant lines, Math. Oper. Res. 21 (1996), 115–134.
• Davis, M. H. A., Piecewise-deterministic Markov processes: a general class of nondiffusion stochastic models, Journal of the Royal Statistical Society. Series B 46 (1984), 353–388.
• Doytchinov, B., Lehoczky, J. P., Shreve, S. E., Real-time queues in heavy traffic with earliest-deadline-first queue discipline, Ann. Appl. Probab. 11 (2001), 332–379.
• Getoor, R. K., Transience and recurrence of Markov processes, Seminaire de Probabilites XIV 284, 397–409, Springer, New York, 1979.
• Kruk, Ł, Stability of two families of real-time queueing networks, Probab. Math. Stat. 28 (2008), 179–202.
• Kruk, Ł, Invariant states for fluid models of EDF networks: nonlinear lifting map, Probab. Math. Stat. 30 (2010), 289–315.
• Kruk, Ł, Lehoczky, J. P., Shreve, S. E., Yeung, S.-N., Earliest-deadline-first service in heavy traffic acyclic networks, Ann. Appl. Probab. 14 (2004), 1306–1352.
• Meyn, S. P., Down, D., Stability of generalized Jackson networks, Ann. Appl. Probab. 4 (1994), 124–148.
• Rybko, A. N., Stolyar, A. L., Ergodicity of stochastic processes describing the operations of open queueing networks, Probl. Inf. Transm. 28 (1992), 199–220.
• Williams, R. J., Diffusion approximations for open multiclass queueing networks: sufficient conditions involving state space collapse, Queueing Syst. Theory Appl. 30 (1998), 27–88.
• Yeung, S.-N., Lehoczky, J. P., Real-time queueing networks in heavy traffic with EDF and FIFO queue discipline, working paper, Department of Statistics, Carnegie Mellon University.
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