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

Abstract

RYNSORD, a novel, decentralized algorithm with soft reservation for ecient scheduling and congestion mitigation in railway networks, has been recently introduced in the literature. It is a speci®c instance of the asynchronous distributed decision-making (ADDM) class of systems, a fundamental property of which is stability. Stability refers to the behaviour of systems 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 de®nition of stability for RYNSORD that re¯ects 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 classi®ed 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, ®rstly, a steady-state operating point is identi®ed. Secondly, the system is perturbed by increasing the rate of trains inserted into the system temporarily, i.e. for a ®nite interval. Thirdly, 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 trac rate perturbations of ®nite durations, it is marginally stable to unstable under permanent track segment and communication link failures, re¯ecting a balanced assessment of the strengths and weaknesses of RYNSORD.

A Review of Online Dynamic Models and Algorithms for Railway Traffic Management

“…Most dispatching rules, including the first-come-first-served (FCFS) evaluated in [16] and distributed approaches [43], [52], [53], [55], [74], are considering prediction only to a limited extent. Those approaches are dynamic in nature (i.e., they take decision only at present time regardless of future evolution) but they provide in suboptimal decisions.…”

Impact of a stochastic and dynamic setting on the stability of railway dispatching solutions

“…For example, Meng and Zhou [10] consider a rolling horizon framework to study the robustness of a meet-pass plan against random variations both in train running times and the duration of the disruption for a single track line. Lee and Ghosh [11] instead analyze the stability of a decentralized algorithm (RYNSORD) with soft reservation for efficient traffic scheduling and congestion rmtIgation. The major shortcoming with the approaches in literature is that they refer to macroscopic, deterministic, and/or approximate models unable to accurately reproduce system dynamics (resulting from the interaction of train speed profiles, delays and the signaling system) and neglecting most stochastic phenomena that are inherently present in the real system and responsible for solution instability.…”