调度与负载均衡中延迟尾部概率的量子估计
Quantum Estimation of Delay Tail Probabilities in Scheduling and Load Balancing
AI总结：
本文提出了一种基于截断再生模拟的量子框架，用于在具有可数无限状态空间的调度与负载均衡系统中高效估计延迟尾部概率。
摘要：
在调度和负载均衡系统中估计延迟尾部概率是一项关键但计算上极具挑战性的任务，因为违反事件非常罕见。量子振幅估计（QAE）提供了一种通用的方法，将样本复杂度从1/p减少到1/sqrt(p)，但在处理稳态排队网络时存在挑战：经典模拟涉及无界状态空间和随机再生周期，而量子电路具有固定深度和有限的寄存器。在本文中，我们开发了一个基于截断再生模拟的量子模拟框架，用于延迟尾部概率。我们证明，再生罕见事件估计器可以通过截断再生周期重新表述为有限随机种子的确定性、可逆函数。为了控制由此产生的偏差，我们使用Lyapunov漂移和集中性论证，推导出再生时间的指数尾部界。这允许截断时间范围——因此量子电路深度——被选择，使得偏差可证明地比统计误差小。所提出的框架使在具有可数无限状态空间的模型中进行量子估计成为可能，避免了确定直接有限时间跨度模拟所需的充分混合时间的挑战。我们为GI-GI-1队列、无线网络在MaxWeight调度下的情况，以及具有Join-the-Shortest-Queue（JSQ）路由的多服务器系统提供了量子比特和电路复杂度的界限。
英文摘要：
Estimating delay tail probabilities in scheduling and load balancing systems is a critical but computationally prohibitive task due to the rarity of violation events. Quantum Amplitude Estimation (QAE) offers a generic quadratic reduction in sample complexity 1/sqrt(p) vs 1/p, but applying it to steady-state queueing networks in challenging: classical simulations involve unbounded state spaces and random regeneration cycles, whereas quantum circuits have fixed depth and finite registers. In this paper, we develop a framework for quantum simulation of delay tail probabilities based on truncated regenerative simulation. We show that regenerative rare-event estimators can be reformulated as deterministic, reversible functions of finite random seeds by truncating regeneration cycles. To control the resulting bias, we use Lyapunov drift and concentration arguments to derive exponential tail bounds on regeneration times. This allows the truncation horizon--and hence the quantum circuit depth--to be chosen such that the bias is provably negligible compared to the statistical error. The proposed framework enables quantum estimation in models with countably infinite state spaces, avoiding the challenge of determining the sufficient mixing time required for direct finite-horizon simulation. We provide bounds on qubit and circuit complexity for a GI-GI-1 queue, a wireless network under MaxWeight scheduling, and a multi-server system with Join-the-Shortest-Queue (JSQ) routing.
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