18 research outputs found
On performance bounds for balanced fairness
International audienceWhile Erlang's formula has helped engineers to dimension telephone networks for over eighty years, such a three-way " performance-demand-capacity " relationship is still lacking for data networks. It may be argued that the enduring success of Erlang's formula is essentially due to its simplicity: the call blocking rate does not depend on the distribution of call duration but on overall demand only. In this paper, we consider data networks and characterize those capacity allocations which have the same insensitivity property, in the sense that performance of data transfers does not depend on precise traffic characteristics such as the distribution of data volume but on overall demand only. We introduce the notion of " balanced fairness " and prove some key properties satisfied by this insensitive allocation. It is shown notably that the performance of balanced fairness is always better than that obtained if flows are transmitted in a " store and forward " fashion, allowing simple formula applying to the latter to be used as a conservative evaluation for network design and provisioning purposes
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
Fluid flow models in performance analysis
We review several developments in fluid flow models: feedback fluid models, linear stochastic fluid networks and bandwidth sharing networks. We also mention some promising new research directions
Throughput Performance in Networks with Linear Capacity Contraints
International audienceWe consider a network whose resources are shared by a dynamic number of data flows according to balanced fairness. We give explicit bounds on the mean throughput that results from this stochastic resource sharing when the capacity constraints are linear. We illustrate the results on a few examples of wireline and wireless networks
Proportional switching in FIFO networks
We consider a family of discrete time multihop switched queueing networks where each packet movesalong a xed route. In this setting, BackPressure is the canonical choice of scheduling policy; this policy hasthe virtues of possessing a maximal stability region and not requiring explicit knowledge of tra c 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 manyroutes are processed by a queue, or where packets over a route are processed by many queues, these limitationscan be prohibitive.In this article, we introduce a scheduling policy for FIFO networks, the Proportional Scheduler, which isbased on the proportional fairness criterion. We show that, like BackPressure, the Proportional Scheduler hasa maximal stability region and does not require explicit knowledge of tra c 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 routedwith only next-hop information and new nodes can be added to the network with only knowledge of thescheduling constraintsThe research of the rst author was partially supported by NSF grants DMS-1105668 and DMS-1203201.
The research of the second author was partially supported by the Spanish Ministry of Economy and Competitiveness Grants
MTM2013-42104-P via FEDER funds; he thanks the ICMAT (Madrid, Spain) Research Institute that kindly hosted him while
developing this project
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