Operational Reliability of Deadline-Constrained Task Assignment: Stability Characterization and Adversarial Routing
Introduces average cost stability, combining outstanding tasks and irrecoverable deadline failures, for assessing system reliability under time constraints.
Key Findings
Methodology
This paper proposes an observable stability measure based on the number of outstanding tasks and the cumulative irrecoverable deadline failures. Under bounded arrivals and uniform deadline limits, it mathematically proves that the outstanding task count remains bounded regardless of scheduling policy, and that average failure rate is equivalent to bounded expected cumulative failures. The concept of degenerate backlog stability is introduced, showing that bounded backlog does not necessarily imply bounded failures. An adversarial pickup-and-delivery model with location spoofing attacks is used to validate the framework. The designed deadline-aware assignment algorithms and adversarial models demonstrate that traditional backlog measures can misjudge system stability, while the proposed average cost stability accurately captures persistent failures.
Key Results
- Under finite arrival and deadline constraints, the number of outstanding tasks remains bounded across all policies, and the expected cumulative irrecoverable failures are finite, ensuring long-term reliability.
- Degenerate backlog stability is identified, where backlog remains bounded but cumulative failures diverge, exposing limitations of traditional metrics.
- In adversarial pickup-and-delivery scenarios with location spoofing, despite request cancellations, backlog remains bounded, but average cost stability detects instability, confirming the metric’s robustness.
Significance
This work advances the understanding of system reliability by moving beyond traditional backlog-based stability, especially for time-sensitive tasks with potential malicious interference. It provides a rigorous, observable criterion that aligns with operational concerns, enabling better design of resilient autonomous systems. The framework addresses critical gaps in existing stability notions, offering a practical tool for industries like autonomous transportation, logistics, and robotics to ensure persistent service quality even under adversarial conditions.
Technical Contribution
The paper introduces a novel stability concept based on observable quantities, with rigorous theoretical proofs linking bounded outstanding tasks to bounded cumulative failures. It formalizes the relationship between average cost stability and failure accumulation, and extends the analysis to include degenerate regimes. The design of deadline-aware assignment algorithms and adversarial models demonstrates how the framework can be practically implemented and tested, providing a foundation for future resilient multi-agent system research.
Novelty
This is the first work to integrate average cost stability with deadline constraints, explicitly considering irrecoverable failures alongside outstanding tasks. It departs from classical backlog stability and failure rate metrics, emphasizing long-term failure accumulation control. The introduction of degenerate backlog regimes and adversarial testing with location spoofing further distinguishes this approach, offering a comprehensive and operationally relevant stability assessment framework.
Limitations
- The model assumes bounded arrivals and deadlines, which may not hold in highly dynamic or unpredictable environments, limiting direct applicability.
- The adversarial models focus on location spoofing, not covering other attack vectors like communication jamming or hardware failures.
- Computational complexity of the proposed algorithms may hinder real-time deployment in large-scale systems, requiring further optimization.
Future Work
Future research will extend the framework to unbounded or stochastic arrival processes, incorporate diverse attack models, and develop scalable algorithms. Exploring adaptive scheduling policies that optimize for both throughput and stability under adversarial conditions is also a promising direction. Additionally, validating the approach in real-world autonomous vehicle fleets and logistics networks will be crucial for industrial adoption.
AI Executive Summary
Modern autonomous systems in transportation, logistics, and manufacturing increasingly rely on task scheduling under strict deadlines. Traditional stability metrics, such as queue length or average failure rate, often fall short in these contexts because they do not account for the long-term impact of unrecoverable failures. This paper addresses this gap by proposing an average cost stability measure that combines the number of outstanding tasks with the cumulative count of irrecoverable deadline failures, providing a more comprehensive assessment of system reliability.
The core idea is that, under bounded arrivals and deadlines, the outstanding task count remains uniformly bounded regardless of the scheduling policy. Moreover, the expected total number of irrecoverable failures is finite if and only if the system is stable under this new criterion. This insight reveals that traditional backlog measures can be misleading, especially in scenarios where tasks expire or are maliciously manipulated. The concept of degenerate backlog stability is introduced, showing that backlog can be bounded even when failures accumulate infinitely.
To validate the framework, the authors develop deadline-aware assignment algorithms and adversarial models involving location spoofing attacks within a pickup-and-delivery setting. Using real-world mobility data from San Francisco, they demonstrate that traditional backlog metrics may falsely suggest stability, while the average cost stability correctly identifies persistent failure regimes. These findings have significant implications for designing resilient, time-sensitive autonomous systems, emphasizing the importance of monitoring irrecoverable failures alongside backlog.
Overall, this work provides a rigorous, observable, and operationally meaningful stability criterion that enhances the robustness of autonomous task assignment systems. It opens avenues for future research in adaptive, attack-resilient scheduling and real-world deployment in complex, adversarial environments, ultimately contributing to safer and more reliable autonomous operations.
Deep Analysis
Background
Autonomous task scheduling在交通、物流、制造等行业中扮演核心角色。早期研究关注队列长度和吞吐量，确保系统稳定。随着无人驾驶和智能调度的发展，截止时间成为关键约束。现有方法如车辆路径问题（VRP）和动态调度模型，强调路径可行性与效率，但多忽略任务失败的长期影响。传统稳定性指标如队列界限和平均失败率，虽能反映短期性能，却难以捕捉持续失败的风险。面对恶意攻击和环境扰动，亟需更全面的稳定性评估工具。本文提出结合未完成任务数和不可恢复失败数的平均成本指标，旨在弥补现有方法的不足，提升系统鲁棒性。
Core Problem
在截止时间约束下，任务可能因延迟或攻击未能及时完成，导致系统性能下降。传统指标如队列长度有限，不能反映持续失败的风险。如何定义一种既能反映任务完成情况，又能捕捉不可逆失败的稳定性指标，成为核心问题。尤其在存在恶意行为或环境干扰时，单纯依赖堆积界限可能误判系统安全性。本文试图解决这一问题，提出基于观察到的未完成任务与累计失败的指标，确保系统在长期运行中不会无限积累失败。
Innovation
1) 引入基于观察指标的平均成本稳定性，结合未完成任务数与累计不可恢复失败数，提供更全面的系统可靠性评估。2) 证明在有限到达与截止时间条件下，未完成任务数有界，且平均失败数与累计失败数等价，增强理论基础。3) 提出退化堆积概念，分析在某些策略下堆积界限满足但失败无限的情况。4) 设计截止感知调度算法，结合对抗性位置欺骗模型，验证指标在恶意环境中的实用性。这些创新突破了传统稳定性分析的局限，为复杂系统提供更可靠的评估工具。
Methodology
- �� 定义系统状态：包括未完成任务集与累计失败数。
- �� 数学分析：证明在有限到达与截止时间条件下，未完成任务数有界。
- �� 等价性证明：展示平均失败数与累计失败数的关系，确保指标的操作意义。
- �� 引入退化堆积：分析在某些策略下堆积界限满足但失败无限的情况。
- �� 对抗模型设计：模拟位置欺骗攻击，验证指标的敏感性与鲁棒性。
- �� 调度策略：设计截止感知调度算法，结合理论分析与仿真验证。
Experiments
利用真实的旧金山出行需求数据，模拟不同截止时间和车队规模。引入位置欺骗攻击模型，测试多种调度策略（贪婪、即时调度、即时调度+重调度）。评估指标包括未完成任务数、累计失败数、传统堆积指标等。通过对比分析，验证传统指标可能误判系统稳定性，而平均成本指标能准确反映持续失败风险。多场景、多模型、多参数设置确保结论的稳健性。
Results
实验显示，在请求截止时间有限的情况下，未完成任务在所有策略下均有限制，验证理论结论。对抗模型中，尽管请求未被完成，堆积仍保持有限，但累计失败无限，传统指标误判系统稳定性。平均成本指标成功识别出系统的不稳定状态，验证其在恶意环境中的实用价值。这些结果强调了引入不可逆失败数的重要性，为未来调度策略提供依据。
Applications
该指标适用于自动驾驶、物流配送、仓储管理等时间敏感系统，帮助运营者识别潜在风险，优化调度策略。特别在存在恶意行为或环境干扰时，提供更可靠的系统稳定性评估。未来可结合机器学习实现自适应调度，提升系统鲁棒性，推动智能调度在工业界的广泛应用。
Limitations & Outlook
模型假设有限到达与截止时间，实际场景可能超出界限，影响指标适用性。对抗模型主要集中在位置欺骗，未充分考虑通信干扰、硬件故障等多样性攻击。算法复杂度较高，实际部署需优化以满足实时性要求。未来需扩展模型适用范围，提升算法效率，增强多场景鲁棒性。
Plain Language Accessible to non-experts
想象你在厨房做饭，菜需要在一定时间内做好，否则就会变坏。你有很多任务（做菜），每个菜都有截止时间。如果你只看厨房里还剩多少菜（未完成任务），可能会觉得一切正常，但实际上，有些菜已经变坏（失败），你没有注意到。这个时候，只关注剩菜的数量是不够的。你还需要知道有多少菜已经变坏（不可恢复的失败），才能真正知道厨房的状况。这个方法就像是用一个特殊的计数器，不仅看剩多少菜，还看变坏了多少菜，确保厨房一直保持良好状态。这样，即使剩菜不多，但如果变坏的菜越来越多，也会被及时发现，避免整个厨房变糟糕。
ELI14 Explained like you're 14
想象你在学校准备考试，你有很多题要做，但每题都有截止时间。如果你只看还剩多少题没做，可能会觉得还挺好，但其实，有些题已经过期（不能得分了），你没有注意到。这个时候，只看剩余题数是不够的，因为你可能一直在做题，但还是会错过很多题。你需要一个更聪明的方法，不仅看还剩多少题，还要知道有多少题已经过期了。这样，你就能知道自己是不是还在稳步前进，还是已经开始掉队了。这个方法就像用一个特别的计数器，既看还剩多少题，也看过期了多少题，帮助你更好地准备考试，避免最后出问题。
Abstract
Automated task-assignment systems often serve stochastic tasks subject to finite deadlines. In these settings, conventional backlog-based stability can be misleading: finite task lifetimes may keep the number of outstanding tasks bounded even as deadline failures continue indefinitely, while average failure-rate criteria can still permit recurrent failures. We introduce average cost stability, a criterion which is particularly useful for time-sensitive tasks, combining two observable quantities: the number of outstanding tasks and the cumulative number of irrecoverable deadline failures. Under bounded arrivals and uniformly bounded service windows, we show that the outstanding-task count is uniformly bounded independently of the assignment policy and prove that our average cost stability is equivalent to bounded expected cumulative failures. We further characterize degenerate backlog stability, in which backlog remains bounded despite unbounded cumulative failures. We instantiate the framework in an adversarial pickup-and-delivery system where internal fleet agents spoof reported locations to attract assignments and leave requests unserviced. We develop deadline-aware assignment procedures and adversarial models with varying knowledge and coordination capabilities. Experiments using real mobility-on-demand request data and our proposed adversarial models demonstrate that backlog can remain bounded while cancellations persist, whereas our proposed average cost stability correctly identifies such behavior as unstable.