Rank-based stochastic differential inclusions and diffusion limits for a load balancing model

2024/09/23 by Rami Atar, Tomoyuki Ichiba, Atar, Rami +1
Engineering · Business, Management and Accounting · Decision Sciences · #Scheduling and Optimization Algorithms #Advanced Queuing Theory Analysis #Simulation Techniques and Applications

paper · pdf · doi:10.48550/arxiv.2409.15121

Abstract

In an earlier paper, a randomized load balancing model was studied 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 rank-based Brownian particles on the half-line. This paper extends these results 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.

Related

• Invariance principle and McKean-Vlasov limit for randomized load balancing in heavy traffic
• Heavy traffic limit with discontinuous coefficients via a non-standard semimartingale decomposition
• Load Balancing in Parallel Queues and Rank-based Diffusions
• Diffusion approximation of the stationary distribution of a two-level single server queue
• Robust heavy-traffic approximations for service systems facing\n overdispersed demand