Store-Forward and its implications for Proportional Scheduling

TL;DR

This paper analyzes the Store-Forward allocation as an approximation to the Proportional Scheduler in multi-hop networks, providing explicit equilibrium calculations, delay analysis, and conditions for product-form distributions.

Contribution

It introduces the Store-Forward allocation as a tool to understand the equilibrium and delay properties of the Proportional Scheduler, including explicit calculations and independence results.

Findings

Store-Forward asymptotically allocates according to the Proportional Scheduler.

Explicit stationary distribution and delay calculations for FIFO Store-Forward networks.

Identification of conditions for product-form resource pooling and independence in certain network topologies.

Abstract

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.