Rank-Based Stochastic Differential Inclusions and Diffusion Limits for a Load-Balancing Model

• 成果类型: Article; Early Access
• 署名作者: Atar, Rami; Ichiba, Tomoyuki
• 署名单位: Technion Israel Institute of Technology; University of California System; University of California Santa Barbara
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X; 1526-5471
• DOI: 10.1287/moor.2024.0702
• 发表日期: 2025-11-27
• 关键词: load balancing; rank-based stochastic differential equations; rank-based stochastic differential inclusions; path-wise uniqueness

摘要

Banerjee, Budhiraja and Estevez (2025) studied a randomized load balancing model in a heavy traffic asymptotic regime where the load balancing stream is thin compared to the total arrival stream. It was shown that the limit is given by a system of rankbased Brownian particles on the half-line. In this paper we extend this result from the case of exponential service time to an invariance principle, where service times have finite second moment. The main tool is a new notion of rank-based stochastic differential inclusion, which may be of interest in its own right.