2019/12/25 by Dennis Schol, Schol, Dennis, Maria Vlasiou +3
Business, Management and Accounting · Decision Sciences · Mathematics · Social Sciences · #Advanced Queuing Theory Analysis #FOS: Computer and information sciences #FOS: Mathematics #Performance (cs.PF) #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics #Transportation Planning and Optimization
paper · pdf · doi:10.48550/arxiv.1912.11661
openalex publication_date 2019/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study an N server fork-join queue with nearly deterministic arrival and service times. Specifically, we present a fluid limit for the maximum queue length as N→∞. This fluid limit depends on the initial number of tasks. In order to prove these results, we develop extreme value theory and diffusion approximations for the queue lengths.