Separation of Circulating Tokens

TL;DR

This paper addresses the problem of maintaining minimum distances between circulating tokens in distributed systems, proposing protocols for different scenarios with unknown parameters, ensuring safety and optimal spacing.

Contribution

It introduces simple, formalized protocols for controlling circulating tokens in distributed systems, including uniform and non-uniform solutions for unknown system parameters.

Findings

Protocol for fixed distance with unknown m and n

Non-uniform protocol with a corrective process for maximizing distance

Formal Petri net representation of the token separation protocol

Abstract

Self-stabilizing distributed control is often modeled by token abstractions. A system with a single token may implement mutual exclusion; a system with multiple tokens may ensure that immediate neighbors do not simultaneously enjoy a privilege. For a cyber-physical system, tokens may represent physical objects whose movement is controlled. The problem studied in this paper is to ensure that a synchronous system with m circulating tokens has at least d distance between tokens. This problem is first considered in a ring where d is given whilst m and the ring size n are unknown. The protocol solving this problem can be uniform, with all processes running the same program, or it can be non-uniform, with some processes acting only as token relays. The protocol for this first problem is simple, and can be expressed with Petri net formalism. A second problem is to maximize d when m is given, and n is unknown. For the second problem, the paper presents a non-uniform protocol with a single corrective process.