[Paper Review] Robust Scheduling for Flexible Processing Networks

Ramtin Pedarsani, Jean Walrand+1 more|arXiv (Cornell University)|Oct 12, 2016

Advanced Wireless Network Optimization17 references3 citations

TL;DR

This paper proposes a robust scheduling framework for flexible processing networks that uses stochastic gradient projection based on queue-length changes to dynamically allocate service capacity without relying on prior knowledge of arrival or service rates. The method ensures rate stability in flexible fork-join and queueing networks under mild assumptions, achieving optimal resource balancing using only real-time queue state information.

ABSTRACT

Modern processing networks often consist of heterogeneous servers with widely varying capabilities, and process job flows with complex structure and requirements. A major challenge in designing efficient scheduling policies in these networks is the lack of reliable estimates of system parameters, and an attractive approach for addressing this challenge is to design robust policies, i.e., policies that do not use system parameters such as arrival and/or service rates for making scheduling decisions. In this paper, we propose a general framework for the design of robust policies. The main technical novelty is the use of a stochastic gradient projection method that reacts to queue-length changes in order to find a balanced allocation of service resources to incoming tasks. We illustrate our approach on two broad classes of processing systems, namely the flexible fork-join networks and the flexible queueing networks, and prove the rate stability of our proposed policies for these networks under non-restrictive assumptions.

Motivation & Objective

• To address the challenge of unreliable or unknown system parameters—such as arrival and service rates—in large-scale processing networks like data centers, healthcare systems, and manufacturing lines.
• To design scheduling policies that depend only on observable system states (e.g., queue sizes) rather than estimated parameters, enhancing adaptability and robustness.
• To develop a general, parameter-free framework applicable to flexible processing networks with overlapping server capabilities and interdependent task workflows.
• To prove rate stability of the proposed policy under non-restrictive assumptions, ensuring long-term system efficiency and scalability.

Proposed method

• Uses a stochastic gradient projection method that updates service allocation based on changes in queue lengths over time intervals.
• Applies a recursive update rule: $ p^{n+1} = [p^n + \beta^n \tilde{E}^n (I - R^T)^{-1} \Delta Q^n]_{\mathcal{C}_{\varepsilon_0}} $, where $ \tilde{E}^n $ indicates non-empty queues.
• Estimates the imbalance between effective service and demand using $ \Delta Q^n $, the change in queue sizes, which serves as an unbiased estimator of $ \nu_k - \mu_k p_k^n $ when $ Q_k^n > 0 $.
• Implements a projection onto a feasible set $ \mathcal{C}_{\varepsilon_0} $ to maintain stability and ensure convergence.
• Leverages the structure of the routing matrix $ R $ and the inverse of $ (I - R^T) $ to propagate queue changes across the network and estimate flow imbalances.
• Relies solely on current and past queue sizes, avoiding any dependence on arrival rates, service rates, or routing probabilities.

Experimental results

Research questions

• RQ1 Can a scheduling policy be designed that ensures system stability without requiring knowledge of arrival or service rates in flexible processing networks?
• RQ2 How can service capacity be adaptively allocated across competing queues using only queue-length observations?
• RQ3 What conditions ensure that a stochastic gradient-based policy converges to a balanced allocation in flexible fork-join and queueing networks?
• RQ4 Is it possible to achieve rate stability using only local queue state information, even when service rates are unknown or time-varying?
• RQ5 Can the proposed method be generalized to networks with non-factorizable service rates or non-cooperative servers?

Key findings

• The proposed robust scheduling policy ensures almost sure convergence of the service allocation vector $ p^n $ to the optimal allocation $ p^* = \nu_k / \mu_k $, which balances flow demands across the network.
• The flexible queueing network achieves rate stability under the proposed policy, meaning $ \lim_{n \to \infty} \frac{Q_k^n}{n} = 0 $ for all queues $ k $, indicating that queue sizes grow sublinearly.
• The algorithm uses only queue size changes $ \Delta Q^n $ and routing structure $ R $ to estimate flow imbalances, making it fully adaptive and parameter-free.
• The use of $ \tilde{E}^n $ ensures that updates are only applied to non-empty queues, preserving the unbiasedness of the gradient estimator.
• The convergence and stability results hold under mild conditions on the step size sequence $ \beta^n $, without requiring knowledge of system parameters.
• The framework is general and applicable to a wide class of processing networks, including cloud computing, manufacturing, and healthcare systems with complex task dependencies and resource flexibility.