Insensitivity in processor-sharing networks
Performance Evaluation
How Asymmetry Helps Load Balancing
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
The power of two choices in randomized load balancing
The power of two choices in randomized load balancing
Studying Balanced Allocations with Differential Equations
Combinatorics, Probability and Computing
Theory, Volume 1, Queueing Systems
Theory, Volume 1, Queueing Systems
On the power of (even a little) centralization in distributed processing
Proceedings of the ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems
On the power of (even a little) centralization in distributed processing
ACM SIGMETRICS Performance Evaluation Review - Performance evaluation review
Join-Idle-Queue: A novel load balancing algorithm for dynamically scalable web services
Performance Evaluation
A matrix-analytic solution for randomized load balancing models with PH service times
PERFORM'10 Proceedings of the 2010 IFIP WG 6.3/7.3 international conference on Performance Evaluation of Computer and Communication Systems: milestones and future challenges
Asymptotic independence of queues under randomized load balancing
Queueing Systems: Theory and Applications
Heavy traffic optimal resource allocation algorithms for cloud computing clusters
Proceedings of the 24th International Teletraffic Congress
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 in a number of applications while being simple to implement. One model that has been extensively used to study randomized load balancing schemes is the supermarket model. In this model, jobs arrive according to a rate-nλ Poisson process at a bank of n rate-1 exponential server queues. A notable result, due to Vvedenskaya et.al. (1996), showed that when each arriving job is assigned to the shortest of d ≥ 2 randomly chosen queues, the equilibrium queue sizes decay doubly exponentially in the limit as n to ∞. This is a substantial improvement over the case d=1, where queue sizes decay exponentially. The method of analysis used in the above paper and in the subsequent literature applies to jobs with exponential service time distributions and does not easily generalize. It is desirable to study load balancing models with more general, especially heavy-tailed, service time distributions since such service times occur widely in practice. This paper describes a modularized program for treating randomized load balancing problems with general service time distributions and service disciplines. The program relies on an ansatz which asserts that any finite set of queues in a randomized load balancing scheme becomes independent as n to ∞. This allows one to derive queue size distributions and other performance measures of interest. We establish the ansatz when the service discipline is FIFO and the service time distribution has a decreasing hazard rate (this includes heavy-tailed service times). Assuming the ansatz, we also obtain the following results: (i) as n to ∞, the process of job arrivals at any fixed queue tends to a Poisson process whose rate depends on the size of the queue, (ii) when the service discipline at each server is processor sharing or LIFO with preemptive resume, the distribution of the number of jobs is insensitive to the service distribution, and (iii) the tail behavior of the queue-size distribution in terms of the service distribution for the FIFO service discipline.