Stability of RYNSORD-a decentralized algorithm for railway networks under perturbations

RYNSORD, a novel, decentralized algorithm with soft reservation for efficient scheduling and congestion mitigation in railway networks, has been introduced in the literature. It is a specific instance of the asynchronous distributed decision-making (ADDM) class of systems, a fundamental property of which is stability. Stability refers to their behavior under representative perturbations to their environments, given that ADDM systems are intended to be real, complex, and, to some extent, mission critical systems, and are subject to unexpected changes in their operating conditions. This paper introduces an intuitive definition of stability for RYNSORD, that reflects those used in control systems and physics, and presents an in-depth stability analysis of RYNSORD. The analysis utilizes three types of stability-strongly stable, marginally stable, and unstable. The perturbations are classified as either changes in the input pattern or changes in one or more characteristics of the system, such as hardware failures. The study utilizes a large-scale simulation of a subset of the eastern United States railroad network. Trains are initiated at stochastically generated times at each of the stations and are bound for randomly selected destinations. In the study, first a steady-state operating point is identified. Second, the system is perturbed by increasing the rate of trains inserted into the system temporarily, i.e., for a finite interval. Third, an examination of whether and when the system returns to the previous steady-state, yields the results of stability analysis. Performance results indicate that while RYNSORD is strongly stable with respect to input traffic rate perturbations of finite durations, it is marginally stable to unstable under permanent track segment and communications link failures, reflecting a balanced assessment of the strengths and weaknesses of RYNSORD.