Dynamics of Taxi-like Logistics Systems: Theory and Microscopic Simulations

TL;DR

This paper develops an analytical and simulation-based framework to understand the dynamics of bi-agent logistics systems, exemplified by taxi networks, revealing universal features and optimal resource levels for system efficiency.

Contribution

It introduces a combined analytical and simulation approach to study complex bi-agent logistics systems, identifying universal dynamical features and optimal agent numbers for improved system performance.

Findings

Identification of two distinct dynamical phases in taxi systems.

Derivation of the optimal number of taxis for efficiency.

Emergent behaviors explained by analytical models.

Abstract

In this paper we study the dynamics of a class of bi-agent logistics systems consisting of two types of agents interacting on an arbitrary complex network. By approximating the system with simple microscopic models and solving them analytically, we reveal some universal dynamical features of such logistics systems, and propose the applications of such features for system optimisations. Large scale agent-based numerical simulations are also carried out to explore more realistic and complicated systems, with interesting emergent behaviours that can be well understood from our analytical studies. Using the taxi system as a typical logistics system with commuters and empty taxis as two types of agents, we illustrate two dynamical phases with distinct behaviours, separated by a phase boundary that can be identified as the optimal number of taxis for a particular taxi system. We show that these features, and the tuning of the optimal number of taxis, can be applied to various situations, including taxi systems allowing real-time dynamical ride-sharing. Our studies could lead to a theoretical basis for the understanding of a large class of bi-agent logistics systems, that can be useful for systematic optimisations via judicious benchmarking of routing and resource allocation strategies.