Heavy Traffic Limit with Discontinuous Coefficients via a Nonstandard Semimartingale Decomposition

• 成果类型: Article; Early Access
• 署名作者: Atar, Rami; Miyazawa, Masakiyo
• 署名单位: Technion Israel Institute of Technology; Tokyo University of Science
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X; 1526-5471
• DOI: 10.1287/moor.2025.0924
• 发表日期: 2026-05-26
• 关键词: semimartingale decomposition; single server queue; level-dependent arrival and service rates; heavy traffic; diffusion approximation; diffusion-approximation

摘要

This paper studies a single server queue in heavy traffic, with general interarrival and service time distributions, where arrival and service rates vary discontinuously as a function of the (diffusively scaled) queue length. It is proved that the weak limit is given by the unique-in-law solution to a stochastic differential equation in [0, infinity) with discontinuous drift and diffusion coefficients. The main tool is a semimartingale decomposition for point processes introduced by Daley and Miyazawa in 2019, which is distinct from the Doob-Meyer decomposition of a counting process. Although the use of this tool is demonstrated here for a particular model, we believe it may be useful for investigating the scaling limits of queueing models very broadly.