2020/04/20 by Xingyu Zhou, Ness B. Shroff, Zhou, Xingyu +1
Business, Management and Accounting · Computer Science · #Advanced Queuing Theory Analysis #Age of Information Optimization #Distributed #Distributed systems and fault tolerance #FOS: Computer and information sciences #FOS: Mathematics #Parallel #Probability (math.PR) #and Cluster Computing (cs.DC)
paper · pdf · doi:10.48550/arxiv.2004.09574
openalex publication_date 2020/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note, we apply Stein's method to analyze the performance of general load balancing schemes in the many-server heavy-traffic regime. In particular, consider a load balancing system of N servers and the distance of arrival rate to the capacity region is given by N1-α with α> 1. We are interested in the performance as N goes to infinity under a large class of policies. We establish different asymptotics under different scalings and conditions. Specifically, (i) If the second moments linearly increase with N with coefficients σa2 and νs2, then for any α> 4, the distribution of the sum queue length scaled by N-α converges to an exponential random variable with mean (σa2 + νs2)/(2). (3) If the second moments quadratically increase with N with coefficients σa2 and νs2, then for any α> 3, the distribution of the sum queue length scaled by N-α-1 converges to an exponential random variable with mean (σa2 + νs2)/(2). Both results are simple applications of our previously developed framework of Stein's method for heavy-traffic analysis in \citezhou2020note.