Elevator Optimization: Application of Spatial Process and Gibbs Random Field Approaches for Dumbwaiter Modeling and Multi-Dumbwaiter Systems

TL;DR

This paper explores mathematical models using spatial process and Gibbs random field techniques to optimize multi-dumbwaiter elevator systems, aiming to improve efficiency and practical application in industry.

Contribution

It introduces novel analytical models for multi-dumbwaiter systems using spatial process and Gibbs random field approaches, providing solutions for elevator optimization.

Findings

Successful development of basic dumbwaiter models

Effective strategies for multi-dumbwaiter system optimization

Potential industrial applications demonstrated

Abstract

This research investigates analytical and quantitative methods for simulating elevator optimizations. To maximize overall elevator usage, we concentrate on creating a multiple-user positive-sum system that is inspired by agent-based game theory. We define and create basic "Dumbwaiter" models by attempting both the Spatial Process Approach and the Gibbs Random Field Approach. These two mathematical techniques approach the problem from different points of view: the spatial process can give an analytical solution in continuous space and the Gibbs Random Field provides a discrete framework to flexibly model the problem on a computer. Starting from the simplest case, we target the assumptions to provide concrete solutions to the models and develop a "Multi-Dumbwaiter System". This paper examines, evaluates, and proves the ultimate success of such implemented strategies to design the basic elevator's optimal policy; consequently, not only do we believe in the results' practicality for industry, but also their potential for application.