A Divide-and-Conquer Approach for Modeling Arrival Times in Business Process Simulation

TL;DR

This paper tackles the challenge of accurately modeling case arrivals in Business Process Simulation (BPS) by moving beyond static inter-arrival distributions. It introduces Auto Time KDE (AT-KDE), a divide-and-conquer framework that learns an ensemble of KDEs across global segments, weekday patterns, and intraday bins to capture multi-level temporal dynamics. The method yields a five-step pipeline—global segmentation, weekday clustering, intraday binning, inter-arrival KDE learning, and arrival generation—and demonstrates superior accuracy and robustness across 20 diverse logs, with favorable runtimes compared to baselines. By producing realistic arrival patterns, AT-KDE enhances simulation reliability for evaluating process changes and resource planning, and its core ideas may generalize to other time-dependent domains where arrivals are non-stationary.

Abstract

Business Process Simulation (BPS) is a critical tool for analyzing and improving organizational processes by estimating the impact of process changes. A key component of BPS is the case-arrival model, which determines the pattern of new case entries into a process. Although accurate case-arrival modeling is essential for reliable simulations, as it influences waiting and overall cycle times, existing approaches often rely on oversimplified static distributions of inter-arrival times. These approaches fail to capture the dynamic and temporal complexities inherent in organizational environments, leading to less accurate and reliable outcomes. To address this limitation, we propose Auto Time Kernel Density Estimation (AT-KDE), a divide-and-conquer approach that models arrival times of processes by incorporating global dynamics, day-of-week variations, and intraday distributional changes, ensuring both precision and scalability. Experiments conducted across 20 diverse processes demonstrate that AT-KDE is far more accurate and robust than existing approaches while maintaining sensible execution time efficiency.

Figures (4)

• Figure 1: 7-Day rolling average of arrival count in the loan application process.
• Figure 2: Workflow of the modeling methodology of our AT-KDE approach.
• Figure 3: Distribution of arrivals of BPIC12 per hour of each day of the week.
• Figure 4: Comparison of arrivals between AT-KDE, LSTM and Best Distribution.