Two-choice regulation in heterogeneous closed networks

TL;DR

This paper analyzes a heterogeneous closed network model with finite and infinite server queues, focusing on customer incentives to optimize load balancing in bike-sharing systems, using mean-field methods for large systems.

Contribution

It introduces a mean-field analytical framework for two-choice load balancing in heterogeneous networks with finite capacities, applicable to bike-sharing system design.

Findings

Analytical expressions for the stationary distribution of queue lengths.

Approximation of empty and full queue probabilities under incentive policies.

Guidelines for system sizing to enhance performance.

Abstract

A heterogeneous closed network with one-server queues with finite capacity and one infinite-server queue is studied. A target application is bike-sharing systems. Heterogeneity is taken into account through clusters whose queues have the same parameters. Incentives to the customer to go to the least loaded one-server queue among two chosen within a cluster are investigated. By mean-field arguments, the limiting queue length stationary distribution as the number of queues gets large is analytically tractable. Moreover, when all customers follow incentives, the probability that a queue is empty or full is approximated. Sizing the system to improve performance is reachable under this policy.