Abstract
In the classical balls-and-bins model, m balls are allocated into n bins one by one uniformly at random. In this note, we consider the d-thinning variant of this model, in which the process is regulated in an on-line fashion as follows. For each ball, after a random bin has been selected, an overseer may decide, based on all previous history, whether to accept this bin or not. However, one of every d consecutive suggested bins must be accepted. The maximum load of this setting is the number of balls in the most loaded bin. We show that after Θ(n) balls have been √ allocated, the least maximum load achievable with high probability is (Forumala Prsrnted). This should be compared log log n with the related d-choice setting, in which the optimal maximum load achievable with high probability is (Forumala Prsrnted).
Original language | English |
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Article number | 1 |
Journal | Electronic Communications in Probability |
Volume | 25 |
DOIs | |
State | Published - 2020 |
Bibliographical note
Publisher Copyright:© 2020, Institute of Mathematical Statistics. All rights reserved.
Keywords
- Balls and bins
- Load balancing
- Thinning
- Two-choice