517 research outputs found
Insensitive, maximum stable allocations converge to proportional fairness
We describe a queueing model where service is allocated as a function of
queue sizes. We consider allocations policies that are insensitive to service
requirements and have a maximal stability region. We take a limit where the
queueing model become congested. We study how service is allocated under this
limit. We demonstrates that the only possible limit allocation is one that
maximizes a proportionally fair optimization problem.Comment: 9 page
Store-Forward and its implications for Proportional Scheduling
The Proportional Scheduler was recently proposed as a scheduling algorithm
for multi-hop switch networks. For these networks, the BackPressure scheduler
is the classical benchmark. For networks with fixed routing, the Proportional
Scheduler is maximum stable, myopic and, furthermore, will alleviate certain
scaling issued found in BackPressure for large networks. Nonetheless, the
equilibrium and delay properties of the Proportional Scheduler has not been
fully characterized.
In this article, we postulate on the equilibrium behaviour of the
Proportional Scheduler though the analysis of an analogous rule called the
Store-Forward allocation. It has been shown that Store-Forward has
asymptotically allocates according to the Proportional Scheduler. Further, for
Store-Forward networks, numerous equilibrium quantities are explicitly
calculable. For FIFO networks under Store-Forward, we calculate the policies
stationary distribution and end-to-end route delay. We discuss network
topologies when the stationary distribution is product-form, a phenomenon which
we call \emph{product form resource pooling}. We extend this product form
notion to independent set scheduling on perfect graphs, where we show that
non-neighbouring queues are statistically independent. Finally, we analyse the
large deviations behaviour of the equilibrium distribution of Store-Forward
networks in order to construct Lyapunov functions for FIFO switch networks
Large deviations of the stationary measure of networks under proportional fair allocations
We address a conjecture introduced by Massouli\'e (2007), concerning the
large deviations of the stationary measure of bandwidth-sharing networks
functioning under the Proportional fair allocation. For Markovian networks, we
prove that Proportional fair and an associated reversible allocation are
geometrically ergodic and have the same large deviations characteristics using
Lyapunov functions and martingale arguments. For monotone networks, we give a
more direct proof of the same result relying on stochastic comparisons that
hold for general service requirement distribution. These results comfort the
intuition that Proportional fairness is 'close' to allocations of service being
insensitive to the service time requirement
Large deviations for the stationary measure of networks under proportional fair allocations
We address a conjecture introduced by Massouli´e (2007), concerning the large deviations of the stationary measure of bandwidth-sharing networks functioning under the Proportional fair allocation. For Markovian networks, we prove that Proportional fair and an associated reversible allocation are geometrically ergodic and have the same large deviations characteristics using Lyapunov functions and martingale arguments. For monotone networks, we give a more direct proof of the same result relying on stochastic comparisons that hold for general service requirement distribution. These results comfort the intuition that Proportional fairness is ´close´ to allocations of service being insensitive to the service time requirement.Fil: Jonckheere, Matthieu Thimothy Samson. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires; ArgentinaFil: Lopez, S.. Universidad Nacional Autónoma de México; Méxic
Active Queue Management for Fair Resource Allocation in Wireless Networks
This paper investigates the interaction between end-to-end flow control and MAC-layer scheduling on wireless links. We consider a wireless network with multiple users receiving information from a common access point; each user suffers fading, and a scheduler allocates the channel based on channel quality,but subject to fairness and latency considerations. We show that the fairness property of the scheduler is compromised by the transport layer flow control of TCP New Reno. We provide a receiver-side control algorithm, CLAMP, that remedies this situation. CLAMP works at a receiver to control a TCP sender by setting the TCP receiver's advertised window limit, and this allows the scheduler to allocate bandwidth fairly between the users
Proportional Switching in First-in, First-out Networks
We consider a family of discrete time multihop switched queueing networks where each packet moves along a fixed route. In this setting, BackPressure is the canonical choice of scheduling policy; this policy has the virtues of possessing a maximal stability region and not requiring explicit knowledge of traffic arrival rates. BackPressure has certain structural weaknesses because implementation requires information about each route, and queueing delays can grow super-linearly with route length. For large networks, where packets over many routes are processed by a queue, or where packets over a route are processed by many queues, these limitations can be prohibitive. In this article, we introduce a scheduling policy for first-in, first-out networks, the ProportionalScheduler, which is based on the proportional fairness criterion. We show that, like BackPressure, the ProportionalScheduler has a maximal stability region and does not require explicit knowledge of traffic arrival rates. The ProportionalScheduler has the advantage that information about the network's route structure is not required for scheduling, which substantially improves the policy's performance for large networks. For instance, packets can be routed with only next-hop information and new nodes can be added to the network with only knowledge of the scheduling constraints
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