Contention resolution with heterogeneous job sizes

Authors:
Michael A. Bender;Jeremy T. Fineman;Seth Gilbert
Affiliations:
Dept. of Computer Science, Stony Brook University, NY;CSAIL, Massachusetts Institute of Technology, Cambridge, MA;CSAIL, Massachusetts Institute of Technology, Cambridge, MA
Venue:
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Year:
2006

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Abstract

We study the problem of contention resolution for different-sized jobs on a simple channel. When a job makes a run attempt, it learns only whether the attempt succeeded or failed. We first analyze binary exponential backoff, and show that it achieves a makespan of V2Θ(√logn) with high probability, where V is the total work of all n contending jobs. This bound is significantly larger than when jobs are constant sized. A variant of exponential backoff, however, achieves makespan O(V logV) with high probability. Finally, we introduce a new protocol, size-hashed backoff, specifically designed for jobs of multiple sizes that achieves makespan O(V log3logV). The error probability of the first two bounds is polynomially small in n and the latter is polynomially small in logV.