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Randomized load-balancing algorithms play an important role in improving performance in large-scale networks at relatively low computational cost. A common model of such a system is a network of $N$ parallel queues in which incoming jobs with independent and identically distributed service times are routed on arrival using the join-the-shortest-of-$d$-queues routing algorithm. Under fairly general conditions, it was shown by Aghajani and Ramanan that as $Nrightarrowinfty$, the state dynamics converges to the unique solution of a countable system of coupled deterministic measure-valued equations called the hydrodynamic equations. In this article, a characterization of invariant states of these hydrodynamic equations is obtained and, when $d=2$, used to construct a numerical algorithm to compute the queue length distribution and mean virtual waiting time in the invariant state. Additionally, it is also shown that under a suitable tail condition on the service distribution, the queue length distribution of the invariant state exhibits a doubly exponential tail decay, thus demonstrating a vast improvement in performance over the case $d=1$, which corresponds to random routing, when the tail decay could even be polynomial. Furthermore, numerical evidence is provided to support the conjecture that the invariant state is the limit of the steady-state distributions of the $N$-server models. The proof methodology, which entails analysis of a coupled system of measure-valued equations, can potentially be applied to other many-server systems with general service distributions, where measure-valued representations are useful.
Randomized load balancing networks arise in a variety of applications, and allow for efficient sharing of resources, while being relatively easy to implement. We consider a network of parallel queues in which incoming jobs with independent and identi
We introduce a general framework for the mean-field analysis of large-scale load-balancing networks with general service distributions. Specifically, we consider a parallel server network that consists of N queues and operates under the $SQ(d)$ load
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
We consider a system of N queues with decentralized load balancing such as power-of-D strategies(where D may depend on N) and generic scheduling disciplines. To measure the dependence of the queues, we use the clan of ancestors, a technique coming fr
In the load balancing problem, each node in a network is assigned a load, and the goal is to equally distribute the loads among the nodes, by preforming local load exchanges. While load balancing was extensively studied in static networks, only recen