Throughput-Optimal Scheduling via Rate Learning

TL;DR

The paper tackles throughput-optimal scheduling under unknown arrival statistics by proposing Schedule as You Learn (SYL), which learns an average service rate vector within the convex hull of feasible schedules and then selects randomized schedules to realize that rate in expectation. Using Nesterov's dual averaging, SYL ensures queue stability by driving the expected service to exceed the arrival rate in the long run, with convergence guarantees for the learned rate vector $\\bar{\\mu}_k$ to a throughput-supporting target $\\mu^*$. It provides two formulations (known vs unknown arrival rate) and proves strong stability under Slater-type conditions, while highlighting practical trade-offs like the cost of decomposing $\\bar{\\mu}_k$ into schedules and the static connectivity assumption. Numerical experiments on a 3\\times 3 cross-bar demonstrate that SYL can offer latency improvements for prioritized flows while preserving throughput, and a biased-SYL variant shows further latency reductions at some cost to others. Overall, the work introduces a flexible, learning-based scheduling paradigm that decouples decision-making from backlog size and opens avenues for latency-aware throughput optimization in complex networks.

Abstract

We study the problem of designing scheduling policies for communication networks. This problem is often addressed with max-weight-type approaches since they are throughput-optimal. However, max-weight policies make scheduling decisions based on the network congestion, which can be sometimes unnecessarily restrictive. In this paper, we present a ``schedule as you learn'' (SYL) approach, where we learn an average rate, and then select schedules that generate such a rate in expectation. This approach is interesting because scheduling decisions do not depend on the size of the queue backlogs, and so it provides increased flexibility to select schedules based on other criteria or rules, such as serving high-priority queues. We illustrate the results with numerical experiments for a cross-bar switch and show that, compared to max-weight, SYL can achieve lower latency to certain flows without compromising throughput optimality.

Figures (5)

• Figure 1: Server with two queues. The server can only serve one packet from the queues at a time. Flow 1 and 2 are directed to nodes 1 and 2, respectively.
• Figure 2: Probability distribution of the packets waiting times for the network in Fig. \ref{['fig:toy_network']}. The waiting times are normalized to the frequency in which the server selects schedules. The packet arrivals of flow 1 and flow 2 are Bernoulli with mean $(1-\epsilon)0.8$ and $(1-\epsilon) 0.2$ respectively, where $\epsilon = 5\cdot 10^{-5}$.
• Figure 3: Schematic illustration of the convergence result in Lemma \ref{['th:dual_dual_averaging']}. Vector $\bar{\mu}_k$ is within a ball of radius $B(\log(k) + 1)/(\sigma m \sqrt{k})$ centered at $\mu^\star$. By construction, $\mu^\star$ is strictly larger than $\lambda$.
• Figure 4: Aggregated backlogs in the $3 \times 3$ cross-bar switch example in Sec. \ref{['sec:num_validation_capacity']} for different arrival rates $\tau(\lambda/0.9)$, where $\lambda$ is given in Eq. \ref{['eq:lambda']}.
• Figure 5: Comparative histograms of delay distributions across the four scheduling policies (max-weight, delay max-weight, SYL, and SYL-variant) and three different flows, showcasing the probability density of delays for pairs of nodes under three different traffic flows. For the SYL-variant we used $100$ tokens for the schedules that serve the sensitive flow 1-2 (see Sec. \ref{['sec:num_improved_performance']}).

Theorems & Definitions (6)

• Proposition 1
• Lemma 1
• Example 1
• Lemma 2
• Lemma 3
• Theorem 1