Rejection-Based Simulation of Non-Markovian Agents on Complex Networks

TL;DR

This paper introduces a rejection-based, event-driven simulation method for non-Markovian agents on complex networks, enabling efficient modeling of systems with arbitrary residence time distributions.

Contribution

It presents a novel simulation algorithm that overcomes computational challenges in non-Markovian network models by using rejection sampling to handle arbitrary waiting time distributions.

Findings

Efficient simulation of epidemic and information spreading models.

Reduced computational costs compared to traditional methods.

Accurate modeling of non-Markovian dynamics in complex networks.

Abstract

Stochastic models in which agents interact with their neighborhood according to a network topology are a powerful modeling framework to study the emergence of complex dynamic patterns in real-world systems. Stochastic simulations are often the preferred - sometimes the only feasible - way to investigate such systems. Previous research focused primarily on Markovian models where the random time until an interaction happens follows an exponential distribution. In this work, we study a general framework to model systems where each agent is in one of several states. Agents can change their state at random, influenced by their complete neighborhood, while the time to the next event can follow an arbitrary probability distribution. Classically, these simulations are hindered by high computational costs of updating the rates of interconnected agents and sampling the random residence times from arbitrary distributions. We propose a rejection-based, event-driven simulation algorithm to overcome these limitations. Our method over-approximates the instantaneous rates corresponding to inter-event times while rejection events counterbalance these over-approximations. We demonstrate the effectiveness of our approach on models of epidemic and information spreading.