Extending Causal Metamodeling to a non-Markovian Queue

2026-05-30

AI Summary

Existing causal meta-models are confined to Markovian systems and struggle to represent non-Markovian queueing systems with non-exponential service times. This work proposes the first causal meta-modeling framework tailored for non-Markovian systems: it approximates general distributions using phase-type distributions, extends modular dynamic Bayesian networks to the discrete-time domain, and introduces corresponding parameter learning and time discretization strategies. The approach is validated on systems such as G/M/1, achieving inference speeds several orders of magnitude faster than direct simulation while preserving high accuracy in both probabilistic and causal queries.

Abstract

Metamodels for discrete-event simulations approximate the behavior of simulation models without running expensive simulations. Prior work introduced modular dynamic Bayesian networks (MDBNs) -- a class of metamodels that can estimate a range of probabilistic and causal queries (PCQs) using a single, trained model -- but the method was limited to Markovian systems. In this paper, we initiate an extension of MDBNs to non-Markovian queues by approximating non-exponential distributions using phase-type distributions. This approach raises novel challenges, including balancing metamodeling accuracy and tractability when choosing the number of phases, efficiently learning metamodel parameters, and choosing the sampling interval that is used to approximate a continuous-time simulation by a discrete-time MDBN. We provide preliminary solutions to these challenges, yielding the first causal metamodeling technique for non-Markovian systems. Experiments on a G/M/1 queue demonstrate that the MDBN can produce accurate answers to PCQs with orders-of-magnitude speedup of inference times relative to direct simulation.

Problem

• causal metamodeling
• non-Markovian queue
• phase-type distributions
• probabilistic and causal queries
• discrete-event simulation

Innovation

• causal metamodeling
• non-Markovian queues
• modular dynamic Bayesian networks
• phase-type distributions
• probabilistic and causal queries