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

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

Proportional fairness and its relationship with multi-class queueing networks

We consider multi-class single-server queueing networks that have a product form stationary distribution. A new limit result proves a sequence of such networks converges weakly to a stochastic flow level model. The stochastic flow level model found is insensitive. A large deviation principle for the stationary distribution of these multi-class queueing networks is also found. Its rate function has a dual form that coincides with proportional fairness. We then give the first rigorous proof that the stationary throughput of a multi-class single-server queueing network converges to a proportionally fair allocation. This work combines classical queueing networks with more recent work on stochastic flow level models and proportional fairness. One could view these seemingly different models as the same system described at different levels of granularity: a microscopic, queueing level description; a macroscopic, flow level description and a teleological, optimization description.Comment: Published in at http://dx.doi.org/10.1214/09-AAP612 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

A qualitative study of satisfaction and dissatisfaction with Jobcentre Plus; an exploration of issues identified in the 2007 Customer Satisfaction Survey with a particular focus on those most likely to be dissatisfied

This report presents the findings of qualitative research undertaken with Jobcentre Plus staff and customers to further understand the findings of the 2007 Customer Satisfaction Survey. The research took place in all 11 regions/countries between September and December 2008 and involved interviews with staff from jobcentres and Benefit Delivery Centres, and follow-up telephone interviews and focus groups with customers. The report identifies differences in the drivers of satisfaction and dissatisfaction between different benefit groups. It also explores customer satisfaction with different services and contact channels, identifies what is seen as good customer service and puts forward some suggestions for how this may be improved

A planar near-field scanning technique for bistatic radar cross section measurements

A progress report on the development of a bistatic radar cross section (RCS) measurement range is presented. A technique using one parabolic reflector and a planar scanning probe antenna is analyzed. The field pattern in the test zone is computed using a spatial array of signal sources. It achieved an illumination pattern with 1 dB amplitude and 15 degree phase ripple over the target zone. The required scan plane size is found to be proportional to the size of the desired test target. Scan plane probe sample spacing can be increased beyond the Nyquist lambda/2 limit permitting constant probe sample spacing over a range of frequencies