A fast exact simulation method for a class of Markov jump processes

TL;DR

The paper introduces the Hashing-Leaping Method (HLM), a new exact simulation algorithm for Markov jump processes that maintains constant computational cost per event, outperforming existing methods in large-scale scenarios.

Contribution

The paper presents the HLM, a novel SSA that uses hash-table-like bucket sorting to achieve efficient, exact simulation of Markov jump processes with scalable performance.

Findings

HLM has constant cost per event regardless of the number of clocks.

HLM outperforms three existing SSA methods in large-scale problems.

Performance tests show HLM's efficiency and scalability.

Abstract

A new method of the stochastic simulation algorithm (SSA), named the Hashing-Leaping method (HLM), for exact simulations of a class of Markov jump processes, is presented in this paper. The HLM has a conditional constant computational cost per event, which is independent of the number of exponential clocks in the Markov process. The main idea of the HLM is to repeatedly implement a hash-table-like bucket sort algorithm for all times of occurrence covered by a time step with length $\tau$. This paper serves as an introduction to this new SSA method. We introduce the method, demonstrate its implementation, analyze its properties, and compare its performance with three other commonly used SSA methods in four examples. Our performance tests and CPU operation statistics show certain advantage of the HLM for large scale problems.