80,687 research outputs found
On the flow-level stability of data networks without congestion control: the case of linear networks and upstream trees
In this paper, flow models of networks without congestion control are
considered. Users generate data transfers according to some Poisson processes
and transmit corresponding packet at a fixed rate equal to their access rate
until the entire document is received at the destination; some erasure codes
are used to make the transmission robust to packet losses. We study the
stability of the stochastic process representing the number of active flows in
two particular cases: linear networks and upstream trees. For the case of
linear networks, we notably use fluid limits and an interesting phenomenon of
"time scale separation" occurs. Bounds on the stability region of linear
networks are given. For the case of upstream trees, underlying monotonic
properties are used. Finally, the asymptotic stability of those processes is
analyzed when the access rate of the users decreases to 0. An appropriate
scaling is introduced and used to prove that the stability region of those
networks is asymptotically maximized
Instability in Stochastic and Fluid Queueing Networks
The fluid model has proven to be one of the most effective tools for the
analysis of stochastic queueing networks, specifically for the analysis of
stability. It is known that stability of a fluid model implies positive
(Harris) recurrence (stability) of a corresponding stochastic queueing network,
and weak stability implies rate stability of a corresponding stochastic
network. These results have been established both for cases of specific
scheduling policies and for the class of all work conserving policies.
However, only partial converse results have been established and in certain
cases converse statements do not hold. In this paper we close one of the
existing gaps. For the case of networks with two stations we prove that if the
fluid model is not weakly stable under the class of all work conserving
policies, then a corresponding queueing network is not rate stable under the
class of all work conserving policies. We establish the result by building a
particular work conserving scheduling policy which makes the associated
stochastic process transient. An important corollary of our result is that the
condition , which was proven in \cite{daivan97} to be the exact
condition for global weak stability of the fluid model, is also the exact
global rate stability condition for an associated queueing network. Here
is a certain computable parameter of the network involving virtual
station and push start conditions.Comment: 30 pages, To appear in Annals of Applied Probabilit
Wireless Network-Level Partial Relay Cooperation: A Stable Throughput Analysis
In this work, we study the benefit of partial relay cooperation. We consider
a two-node system consisting of one source and one relay node transmitting
information to a common destination. The source and the relay have external
traffic and in addition, the relay is equipped with a flow controller to
regulate the incoming traffic from the source node. The cooperation is
performed at the network level. A collision channel with erasures is
considered. We provide an exact characterization of the stability region of the
system and we also prove that the system with partial cooperation is always
better or at least equal to the system without the flow controller.Comment: Submitted for journal publication. arXiv admin note: text overlap
with arXiv:1502.0113
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