Strategic Defense of Feedback-Controlled Parallel Queues against Reliability and Security Failures

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.