Study of a Dynamic Cooperative Trading Queue Routing Control Scheme for Freeways and Facilities with Parallel Queues

TL;DR

This paper proposes a novel cooperative control scheme for freeway and parallel queue management that ensures stable, cost-efficient lane switching among agents with different values of time, validated through simulations.

Contribution

It introduces a new coalition-based control policy using a partition function game and strong-core stability analysis for dynamic queue routing.

Findings

The control scheme is stable in static queue settings.

Simulation shows the scheme maintains strong-core stability.

Coalitional instabilities are minimal in dynamic queue scenarios.

Abstract

This article explores the coalitional stability of a new cooperative control policy for freeways and parallel queuing facilities with multiple servers. Based on predicted future delays per queue or lane, a VOT-heterogeneous population of agents can agree to switch lanes or queues and transfer payments to each other in order to minimize the total cost of the incoming platoon. The strategic interaction is captured by an n-level Stackelberg model with coalitions, while the cooperative structure is formulated as a partition function game (PFG). The stability concept explored is the strong-core for PFGs which we found appropiate given the nature of the problem. This concept ensures that the efficient allocation is individually rational and coalitionally stable. We analyze this control mechanism for two settings: a static vertical queue and a dynamic horizontal queue. For the former, we first characterize the properties of the underlying cooperative game. Our simulation results suggest that the setting is always strong-core stable. For the latter, we propose a new relaxation program for the strong-core concept. Our simulation results on a freeway bottleneck with constant outflow using Newell's car-following model show the imputations to be generally strong-core stable and the coalitional instabilities to remain small with regard to users' costs.