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A Framework for Predicting Runtime Savings from Discrete-Event Simulation Model Simplification Operations

Mohd Shoaib, Navonil Mustafee, Varun Ramamohan

TL;DR

The paper tackles the challenge of predicting runtime savings (RS) from discrete-event simulation (DES) model simplification at the conceptualisation stage. It introduces a queueing-theoretic RS prediction framework that links reductions in the total instructions per arrival (RIE) to RS, across DES with $M/M/n$, $M/G/n$, and $G/G/n$ subsystems. The methodology unfolds in two stages: first, deriving occupancy-dependent instructions-per-arrival relationships $ heta^{m}_{k}( ho)$ for subsystems in $igrace 2s,1s,ms igrace$ and queue disciplines $igrace M/M/1, M/G/1, G/G/1 igrace$, and then mapping reductions in instructions to RS via a regression $ hoz^{m}=g(ar{I}^{m}|oldsymbol{eta}^{m},oldsymbol{ u}^{m})$. Validation across two-stage, three-stage, and real-world PHC DES scenarios shows high fidelity (typically $R^2 o 0.99$, low MAPEs) and demonstrates the framework’s potential to guide whether to pursue simplification before executing the parent model. The work offers a practical path toward integrating RS prediction into DES tools, enabling pre-emptive assessment of simplification benefits and informing resource allocation during model development.

Abstract

Abstraction or substitution and aggregation are the most widely used simulation model simplification operations. Abstraction involves replacing subsystems within a discrete-event simulation (DES) with one or more quantities - typically random variables - representing the lengths of stay in the subsystems(s) in question to create a `simplified' system comprising only of subsystems of interest to the analysis at hand. Aggregation involves replacing more than one subsystem of the original `parent' simulation with a single subsystem. However, the model simplification process itself can be expensive, in terms of the computational runtime and effort required to collect the data required to estimate the distributions of the length of stay variables, the distribution-fitting process, and testing and validation of the simplified model. Moreover, the savings in simulation runtime that the simplification process yields is \textit{a priori} unknown to the modeller. In this context, a method that predicts the runtime savings (RS) from DES model simplification operations before their execution - at the conceptualisation stage of the simplified model development process - may help judge whether its development is indeed worth undertaking. In this paper, we present a queueing-theoretic framework for the prediction of RS from model simplification operations. Our framework is applicable for DES models comprising $M/M/, M/G/ \text{ and } G/G/$ subsystems. The performance of the RS prediction framework is demonstrated using multiple computational experiments. Our proposed framework contributes to the literature around DES model complexity and more broadly to DES runtime prediction.

A Framework for Predicting Runtime Savings from Discrete-Event Simulation Model Simplification Operations

TL;DR

The paper tackles the challenge of predicting runtime savings (RS) from discrete-event simulation (DES) model simplification at the conceptualisation stage. It introduces a queueing-theoretic RS prediction framework that links reductions in the total instructions per arrival (RIE) to RS, across DES with , , and subsystems. The methodology unfolds in two stages: first, deriving occupancy-dependent instructions-per-arrival relationships for subsystems in and queue disciplines , and then mapping reductions in instructions to RS via a regression . Validation across two-stage, three-stage, and real-world PHC DES scenarios shows high fidelity (typically , low MAPEs) and demonstrates the framework’s potential to guide whether to pursue simplification before executing the parent model. The work offers a practical path toward integrating RS prediction into DES tools, enabling pre-emptive assessment of simplification benefits and informing resource allocation during model development.

Abstract

Abstraction or substitution and aggregation are the most widely used simulation model simplification operations. Abstraction involves replacing subsystems within a discrete-event simulation (DES) with one or more quantities - typically random variables - representing the lengths of stay in the subsystems(s) in question to create a `simplified' system comprising only of subsystems of interest to the analysis at hand. Aggregation involves replacing more than one subsystem of the original `parent' simulation with a single subsystem. However, the model simplification process itself can be expensive, in terms of the computational runtime and effort required to collect the data required to estimate the distributions of the length of stay variables, the distribution-fitting process, and testing and validation of the simplified model. Moreover, the savings in simulation runtime that the simplification process yields is \textit{a priori} unknown to the modeller. In this context, a method that predicts the runtime savings (RS) from DES model simplification operations before their execution - at the conceptualisation stage of the simplified model development process - may help judge whether its development is indeed worth undertaking. In this paper, we present a queueing-theoretic framework for the prediction of RS from model simplification operations. Our framework is applicable for DES models comprising subsystems. The performance of the RS prediction framework is demonstrated using multiple computational experiments. Our proposed framework contributes to the literature around DES model complexity and more broadly to DES runtime prediction.

Paper Structure

This paper contains 14 sections, 8 figures, 21 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Relevant Literature
  3. Runtime Savings Prediction Methodology
  4. Runtime Savings Mechanism Associated with Model Simplification Operations
  5. Runtime Savings Prediction Model Development
  6. Runtime Savings Prediction Model Development: Computational Implementation
  7. Runtime Savings Prediction Model: Deployment and Validation
  8. Discussion and Conclusion
  9. Example Outputs from Parent and Simplified Models
  10. Validation Experiment 2: Additional Results
  11. Additional validation experiment 2 results for the $M/G/$ case.
  12. Validation experiment 2: results for the $M/M/$ case.
  13. Validation experiment 2: results for the $G/G/$ case.
  14. Details Regarding the Study Code on Github.

Figures (8)

  • Figure 1: Top: a two-stage tandem queuing system (parent model). Bottom: A simplified version model of the parent model developed by substituting the second subsystem with a random variable representing the length of stay in the second subsystem.
  • Figure 2: Top: a three-stage tandem queuing system (parent model). Bottom: a simplified version of the parent model developed by aggregating the second and third subsystems into a single subsystem.
  • Figure 3: The effect of the number of servers on the computational runtime for simulations of $M/M/n$ and $M/G/n$ systems.
  • Figure 4: Average waiting time versus server occupancy for $M/M/1$, $M/G/1$, and $G/G/1$ queueing systems.
  • Figure 5: The relationship between the average number of instructions per arrival and server occupancy for the second subsystem within two-stage systems with $M/M/$, $M/G/$ and $G/G/$ systems.
  • ...and 3 more figures