Study of Parameterized-Chain networks

TL;DR

This paper introduces Parameterized-Chain Networks (PCN) for modeling large linear networks, providing a dependency graph-based method to analyze deadlocks despite the undecidability of some properties.

Contribution

The paper develops a novel PCN framework and a dependency graph approach to analyze deadlocks in parameterized linear networks, addressing undecidability issues.

Findings

Dependency graph characterizes deadlocks in PCN

Partial and total deadlocks correspond to specific subgraphs

Application demonstrated on traffic network example

Abstract

In areas such as computer software and hardware, manufacturing systems, and transportation, engineers encounter networks with arbitrarily large numbers of isomorphic subprocesses. Parameterized systems provide a framework for modeling such networks. The analysis of parameterized systems is a challenge as some key properties such as nonblocking and deadlock-freedom are undecidable even for the case of a parameterized system with ring topology. In this paper, we introduce \textit{Parameterized-Chain Networks} (PCN) for modeling of networks containing several linear parameterized segments. Since deadlock analysis is undecidable, to achieve a tractable subproblem we limit the behavior of subprocesses of the network using our previously developed mathematical notion `weak invariant simulation.' We develop a dependency graph for analysis of PCN and show that partial and total deadlocks of the proposed PCN are characterized by full, consistent subgraphs of the dependency graph. We investigate deadlock in a traffic network as an illustrative example. This document contains all the details and proofs of the study.