带老化的最短作业优先的流体极限

具有重尾处理时间分布的最短剩余处理时间队列的高流量标度极限

Heavy Traffic Scaling Limits for shortest remaining processing time queues with heavy tailed processing time distributions

该研究针对具有有限二阶矩、正则变化重尾处理时间分布的SRPT单服务器队列，证明非标准标度下测度值过程依分布收敛且无状态空间坍缩，还建立了工作量与队列长度过程的收敛性及尾部变轻时的坍缩趋近特性。

Optimal Load Balancing in Bipartite Graphs

Applications in cloud platforms motivate the study of efficient load balancing under job-server constraints and server heterogeneity. In this paper, we study load balancing on a bipartite graph where left nodes correspond to job types and right nodes correspond to servers, with each edge indicating that a job type can be served by a server. Thus edges represent locality constraints, i.e., each job can only be served at servers which contained certain data and/or machine learning (ML) models. Servers in this system can have heterogeneous service rates. In this setting, we investigate the perfor…

Steady-State Analysis of Load Balancing with Coxian-$2$ Distributed Service Times

This paper studies load balancing for many-server ($N$ servers) systems. Each server has a buffer of size $b-1,$ and can have at most one job in service and $b-1$ jobs in the buffer. The service time of a job follows the Coxian-2 distribution. We focus on steady-state performance of load balancing policies in the heavy traffic regime such that the normalized load of system is $λ= 1 - N^{-α}$ for $0<α<0.5.$ We identify a set of policies that achieve asymptotic zero waiting. The set of policies include several classical policies such as join-the-shortest-queue (JSQ), join-the-idle-queue (JIQ), i…

基于排名的路由在极端拥堵下的大型服务器系统中

Rank Based Routing in Large Server Systems under Extreme Congestion

本文研究了在极端重载条件下，基于排名的路由策略如何通过减少通信成本、提高负载均衡并为高级作业提供加入较短队列的机制，从而在大规模服务器系统中实现更优的性能。

On Universal Scaling of Distributed Queues under Load Balancing

This paper considers the steady-state performance of load balancing algorithms in a many-server system with distributed queues. The system has $N$ servers, and each server maintains a local queue with buffer size $b-1,$ i.e. a server can hold at most one job in service and $b-1$ jobs in the queue. Jobs in the same queue are served according to the first-in-first-out (FIFO) order. The system is operated in a heavy-traffic regime such that the workload per server is $λ= 1 - N^{-α}$ for $0.5\leq α<1.$ We identify a set of algorithms such that the steady-state queues have the following universal s…

Sensitivity of Mean-Field Fluctuations in Erlang loss models with randomized routing

In this paper, we study a large system of $N$ servers each with capacity to process at most $C$ simultaneous jobs and an incoming job is routed to a server if it has the lowest occupancy amongst $d$ (out of N) randomly selected servers. A job that is routed to a server with no vacancy is assumed to be blocked and lost. Such randomized policies are referred to JSQ(d) (Join the Shortest Queue out of $d$) policies. Under the assumption that jobs arrive according to a Poisson process with rate $Nλ^{(N)}$ where $λ^{(N)}=σ-\fracβ{\sqrt{N}}$, $σ\in\mb{R}_+$ and $β\in\mb{R}$, we establish functional c…

重交通下随机负载均衡的不变性原理与McKean-Vlasov极限

Invariance principle and McKean-Vlasov limit for randomized load balancing in heavy traffic

研究重交通下含部分幂次选择策略的随机负载均衡系统，在服务器数与重交通参数渐近增长的临界负载下，建立扩散归一化队列长度经验测度的流体极限，并证明两种初值假设下的不变性原理，得到McKean-Vlasov SDE极限及混沌传播性质。

大规模系统中负载均衡原理的均场分析

Mean-field analysis of load balancing principles in large scale systems

本文提出一个均场数学框架，用于分析大规模异构服务器集群中 JSQ 等负载均衡原理的瞬态与稳态极限，并比较作业系统时间等性能指标。

Join-the-Shortest-Queue的多服务器渐近性：大偏差与稀有事件

Many-Server Asymptotics for Join-the-Shortest-Queue: Large Deviations and Rare Events

本文研究了处理器数量随到达率变化的Join-the-Shortest-Queue路由策略，在无限维路径空间中建立了占用过程的大偏差原理，并推导出长队列概率的显式指数衰减率。

Diffusion Approximations for Load Balancing Mechanisms in Cloud Storage Systems

In large storage systems, files are often coded across several servers to improve reliability and retrieval speed. We study load balancing under the Batch Sampling routing scheme for a network of $n$ servers storing a set of files using the Maximum Distance Separable (MDS) code (cf. Li, Ramamoorthy, and Srikant (2016)). Specifically, each file is stored in equally sized pieces across $L$ servers such that any $k$ pieces can reconstruct the original file. When a request for a file is received, the dispatcher routes the job into the $k$-shortest queues among the $L$ for which the corresponding s…

Asymptotic Optimality of Speed-Aware JSQ for Heterogeneous Systems

The Join-the-Shortest-Queue (JSQ) load-balancing scheme is known to minimise the average delay of jobs in homogeneous systems consisting of identical servers. However, it performs poorly in heterogeneous systems where servers have different processing rates. Finding a delay optimal scheme remains an open problem for heterogeneous systems. In this paper, we consider a speed-aware version of the JSQ scheme for heterogeneous systems and show that it achieves delay optimality in the fluid limit. One of the key issues in establishing this optimality result for heterogeneous systems is to show that …