Parallel traffic service systems such as transportation, manufacturing, and computer systems typically involve feedback control (e.g., dynamic routing) to ensure stability and to improve throughput. Such control relies on connected cyber components for computation and communication. These components are susceptible to random malfunctions and malicious attacks, which motivates the design of strategic defense that are both traffic-stabilizing and cost-efficient under reliability/security failures. In this paper, we consider a parallel queuing system with dynamic routing subject to such failures. For the reliability setting, we consider an infinite-horizon Markov decision process where the system operator strategically activates the protection mechanism upon each job arrival based on the traffic state. We use Hamilton-Jacobi-Bellman equation to show that the optimal protection strategy is a deterministic threshold policy. For the security setting, we extend the model to an infinite-horizon stochastic game where the attacker strategically manipulates routing assignment. We show that a Markov perfect equilibrium of this game always exists and that both players follow a threshold strategy at each equilibrium. For both settings, we also consider the stability of the traffic queues in the face of failures. Finally, we develop approximate dynamic programming algorithms to compute the optimal/equilibrium policies and present numerical examples for validation and illustration.

翻译：并行交通服务系统（如运输、制造及计算机系统）通常依赖反馈控制（例如动态路由）来确保稳定性并提升吞吐量。此类控制依赖于互联的计算机组件进行运算与通信，而这些组件易受随机故障与恶意攻击影响，这促使我们设计一种在可靠性与安全失效下既能稳定交通流又具成本效益的战略防御方案。本文考虑一个受此类失效影响的动态路由并行排队系统。在可靠性场景下，我们构建了一个无限时域马尔可夫决策过程，其中系统操作员根据交通状态在每个作业到达时战略性地激活保护机制。利用哈密顿-雅可比-贝尔曼方程，我们证明最优保护策略为确定性阈值策略。在安全场景下，我们将模型扩展为无限时域随机博弈，其中攻击者战略性操纵路由分配。我们证明该博弈始终存在马尔可夫完美均衡，且双方参与者在每个均衡点均遵循阈值策略。针对两种场景，我们进一步研究了交通队列在故障下的稳定性。最后，我们开发了近似动态规划算法以计算最优/均衡策略，并通过数值算例进行验证与说明。