# Meeting Details

Title: Gaussian Limits for A Fork-Join Network with Non-Exchangeable Synchronization in Heavy Traffic Probability and Financial Mathematics Seminar Hongyuan Lu, PSU, Industr. & Manufact. Engineering We study a fork-join network of stations with multiple servers and non-exchangeable synchronization in heavy traffic under the FCFS discipline. Each arriving job forks into $K$ parallel tasks, which are processed simultaneously in $K$ parallel service stations. After service completion, each task will wait in a buffer associated with its service station for synchronization. Tasks are only synchronized if all the tasks associated with the same job are completed. We develop a new approach to show a functional central limit theorem for the number of tasks in each waiting buffer for synchronization, jointly with the number of tasks in each parallel service station and the number of synchronized jobs, under general assumptions on the arrival and service processes. Specifically, we represent the aforementioned processes as functionals of a sequential empirical process driven by the sequence of service vectors for each job's parallel tasks. As a consequence, all the limiting processes are functionals of two independent processes - the limiting arrival process and a generalized Kiefer process driven by the service vector of each job. We characterize the transient and stationary distributions of those limit processes.