Proceedings of the ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems 2010
DOI: 10.1145/1811039.1811071
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Randomized load balancing with general service time distributions

Abstract: 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 equilibr… Show more

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Cited by 119 publications
(163 citation statements)
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“…Such independence holds at any finite time and also at the equilibrium, provided that the initial server occupancies satisfy certain assumptions. This is formally known as the propagation of chaos [11,36] or asymptotic independence property [5,6] in the literature.…”
Section: Propagation Of Chaosmentioning
confidence: 99%
See 1 more Smart Citation
“…Such independence holds at any finite time and also at the equilibrium, provided that the initial server occupancies satisfy certain assumptions. This is formally known as the propagation of chaos [11,36] or asymptotic independence property [5,6] in the literature.…”
Section: Propagation Of Chaosmentioning
confidence: 99%
“…This is because (10)- (11) show that du ( j) k /dt is nondecreasing in u (i) n for n = k and i = j [8]. Since this implies that 5 Recall that the generator A of the semigroup {T(t)} t≥0 acting on functions f : U → R having bounded partial derivatives is given by A f (g) = lim t↓0…”
Section: Appendix 2: Proof Of Propositionmentioning
confidence: 99%
“…This allows computation of queue size distributions and other quantities of interest. Employing the ansatz, it is shown in Bramson et al [6] that the limiting equilibrium distribution will sometimes have a doubly exponential tail, but that other behavior is also possible, depending on the service discipline and the tail of the service distribution F (·).…”
Section: Foss and Chernovamentioning
confidence: 99%
“…We next consider SQ(N) policies, which we are only able to analyze when the service discipline is FIFO and the service time distribution has a decreasing hazard rate (DHR). This includes heavy-tailed service distributions and is shown in [6] to lead to interesting phenomena. Last, we show the ansatz holds for a sufficiently small arrival rate, with no assumptions on the policy for selecting a queue, as long as the service distribution has 2 moments.…”
Section: Foss and Chernovamentioning
confidence: 99%
“…Luczak and McDiarmid [33] showed that the length of the longest queue scales as ðlog log NÞ=log d þ Oð1Þ. Certain generalization of the supermarket model has been explored in studying various variations, for example, modeling more crucial factors by Vvedenskaya and Suhov [51], Mitzenmacher [38], Mitzenmacher et al [39], Bramson et al [10][11][12], Li and Lui [30,31], Li et al [32,29] and Li [27,28]; fast Jackson networks by Martin and Suhov [35], Martin [34] and Suhov and Vvedenskaya [46].…”
Section: Introductionmentioning
confidence: 99%