The Merlin-Randell problem of train journeys
type: Item
instance of: scholarly article
title: The Merlin-Randell problem of train journeys
zbMATH Open document ID: 0573.90094
DOI: 10.1007/BF00267866
author: Maciej Koutny
published in: Acta Informatica
publication date: 1986-01-01T00:00:00Z
review text: The following synchronization problem is studied: ''There is a finite set of trains, a finite set of stations, and the engine house. Each station can hold only one train. Each train has a route to follow starting and ending at the engine house. The route may be repeated one or more times. A train may leave a station (or the engine house) only when its immediate destination is an empty station or the engine house. At the beginning all trains are placed at the engine house. The problem is to find a synchronization among train movements which allows parallel movements of trains where possible and enables the completion of each train journey.'' A formal model of the train system is proposed assuming that each train route is deterministic and contains no repeated stations. The model is based on the notion of a movement graph being a labeled directed multigraph, the nodes of which represent stations, the arcs of which represent possible train movements. The solution proposed is based on a characterization of inadmissible situations by means of some subgraphs of the movement graph. The properties of these subgraphs, called minimal critical patterns, are investigated. Optimal and suboptimal synchronization strategies are defined. A specification of the optimal strategy in the basic COSY notation is included, and its correctness is demonstrated.
Mathematics Subject Classification ID: 90C35
Mathematics Subject Classification ID: 90B35
Mathematics Subject Classification ID: 05C35
zbMATH DE Number: 3916046
zbMATH Keywords: Merlin-Randell problem of train journeys
zbMATH Keywords: synchronization
zbMATH Keywords: train system
zbMATH Keywords: movement graph
zbMATH Keywords: labeled directed multigraph
zbMATH Keywords: optimal strategy
zbMATH Keywords: train scheduling
MaRDI profile type: Publication
cites work: Q3879197
cites work: Q3725542
cites work: Q3939202
cites work: COSY - a system specification language based on paths and processes
cites work: Q3867194
full work available at URL: https://doi.org/10.1007/bf00267866
OpenAlex ID: W2018146264
description: scientific article; zbMATH DE number 3916046