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2 Probability and Mathematical Statistics

2 Kruk Ł.

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Invariant states for fluid models of EDF networks : nonlinear lifting map

100%

Kruk Ł.

Probability and Mathematical Statistics

2010

tom Vol. 30, Fasc. 2

289--315

We study fluid models of an open, subcritical multiclass queueing network with the earliest-deadline-first (EDF) service discipline and we provide a characterization of the corresponding invariant manifold. We show that the invariant states exhibit nonlinear state space collapse. Consequences of these findings for diffusion limits for EDF queueing networks are also discussed.

Stability of two families of real-time queueing networks

100%

Kruk Ł.

Probability and Mathematical Statistics

2008

tom Vol. 28, Fasc. 2

179--202

We study open multiclass queueing networks with renewal arrival streams and general service time distributions. Upon arrival to the network, customers from each class are assigned a random deadline drawn from a distribution associated with this class.We show that preemptive subcritical EDF networks with fixed customer routes are stable. We also prove that a broad class of (not necessarily subcritical) networks with reneging and Markovian routing, including EDF, FIFO, LIFO, SRPT, fixed priorities and processor sharing, is stable.