Modeling skiers flows via Wardrope equilibrium in closed capacitated networks

2025-09-16

AI Summary

This paper addresses the problem of skier route choice and queueing delays arising from capacity-constrained gondola lifts in closed-loop ski resort networks. We propose a unified modeling framework integrating Wardrop user equilibrium with endogenous queuing delays. Innovatively, we model gondola service as a finite-capacity closed Jackson network and formulate the equilibrium condition via a variational inequality (VI), which is equivalently transformed into a tractable convex optimization problem. Our approach is the first to jointly capture route choice, facility capacity constraints, and dynamic waiting-time feedback within a closed network—eliminating the inconsistency inherent in conventional two-stage methods. Numerical experiments demonstrate that the proposed algorithm converges stably and efficiently computes equilibria, accurately representing the nonlinear interplay between skier flow distribution and facility load. The framework provides a scalable theoretical tool and practical support for ski-resort operations optimization and infrastructure planning.

Technology Category

• Planning, Routing, and Scheduling: Model-Based Reasoning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Combinatorial Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We propose an equilibrium model of ski resorts where users are assigned to cycles in a closed network. As queues form on lifts with limited capacity, we derive an efficient way to find waiting times via convex optimization. The equilibrium problem is formulated as a variational inequality, and numerical experiments show that it can be solved using standard algorithms.

Problem

• Modeling skier flows using Wardrop equilibrium in networks
• Computing lift waiting times via convex optimization
• Solving variational inequality with standard algorithms

Innovation

• Closed network cycle assignment model
• Convex optimization for waiting times
• Variational inequality equilibrium formulation