Balanced allocations (extended abstract)
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
The Power of Two Choices in Randomized Load Balancing
IEEE Transactions on Parallel and Distributed Systems
On the stability of a partially accessible multi-station queue with state-dependent routing
Queueing Systems: Theory and Applications
Randomized load balancing with general service time distributions
Proceedings of the ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Diffusion approximations for large-scale buffered systems
ACM SIGMETRICS Performance Evaluation Review
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Randomized load balancing greatly improves the sharing of resources while being simple to implement. In one such model, jobs arrive according to a rate-驴N Poisson process, with 驴D, D驴2, randomly chosen queues, the equilibrium queue sizes decay doubly exponentially in the limit as N驴驴. This is a substantial improvement over the case D=1, where queue sizes decay exponentially.The reasoning in Vvedenskaya et al. (Probl. Inf. Transm. 32:15---29, 1996) does not easily generalize to jobs with nonexponential service time distributions. A modularized program for treating randomized load balancing problems with general service time distributions was introduced in Bramson et al. (Proc. ACM SIGMETRICS, pp. 275---286, 2010). The program relies on an ansatz that asserts that, for a randomized load balancing scheme in equilibrium, any fixed number of queues become independent of one another as N驴驴. This allows computation of queue size distributions and other performance measures of interest.In this article, we demonstrate the ansatz in several settings. We consider the least loaded balancing problem, where an arriving job is assigned to the queue with the smallest workload. We also consider the more difficult problem, where an arriving job is assigned to the queue with the fewest jobs, and demonstrate the ansatz when the service discipline is FIFO and the service time distribution has a decreasing hazard rate. Last, we show the ansatz always holds for a sufficiently small arrival rate, as long as the service distribution has 2 moments.