Longest-Queue Policies in Dynamic Matching with Abandonments
Abstract
We study a dynamic two-way matching market in which agents of heterogeneous types arrive over time, wait to be matched according to a compatibility network, and abandon the system if their random patience expires. The decision maker collects match rewards and pays holding and abandonment costs, and seeks to maximize the expected net value over a finite horizon. We evaluate policies by their approximation ratio against a fluid benchmark, the optimal value of a linear-programming relaxation that upper bounds the expected net value of every policy. Under a general position gap (GPG) condition, which requires the unique optimal dual solution of this linear program to remain optimal under small perturbations of the arrival rates, we propose a longest-queue policy. The policy first uses this dual solution to identify a set of good match types and a set of critical agent types. Upon each arrival, it considers only good matches and matches the arrival to the critical partner with the longest queue subject to availabilities. In the high-volume regime, in which arrival rates are scaled by s, we prove that the policy attains an approximation ratio of at least 1-O(1/s) at every scale s >= 1 and every horizon T >= 1, so the ratio tends to 1 as s goes to infinity.
Related
BibTeX
@misc{he2026longestqueue,
title = {{Longest-Queue Policies in Dynamic Matching with Abandonments}},
author = {Siqi He and Yehua Wei and Jiaming Xu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01431},
eprint = {2611.01431},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01431},
}
RIS
TY - UNPB
TI - Longest-Queue Policies in Dynamic Matching with Abandonments
AU - Siqi He
AU - Yehua Wei
AU - Jiaming Xu
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01431
UR - https://arxiv.org/abs/2611.01431
AB - We study a dynamic two-way matching market in which agents of heterogeneous types arrive over time, wait to be matched according to a compatibility network, and abandon the system if their random patience expires. The decision maker collects match rewards and pays holding and abandonment costs, and seeks to maximize the expected net value over a finite horizon. We evaluate policies by their approximation ratio against a fluid benchmark, the optimal value of a linear-programming relaxation that upper bounds the expected net value of every policy. Under a general position gap (GPG) condition, which requires the unique optimal dual solution of this linear program to remain optimal under small perturbations of the arrival rates, we propose a longest-queue policy. The policy first uses this dual solution to identify a set of good match types and a set of critical agent types. Upon each arrival, it considers only good matches and matches the arrival to the critical partner with the longest queue subject to availabilities. In the high-volume regime, in which arrival rates are scaled by s, we prove that the policy attains an approximation ratio of at least 1-O(1/s) at every scale s >= 1 and every horizon T >= 1, so the ratio tends to 1 as s goes to infinity.
ER -