Contention resolution with heterogeneous job sizes

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 V2^⊖(√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(Vlog V) with high probability. Finally, we introduce a new protocol, size-hashed backoff, specifically designed for jobs of multiple sizes that achieves makespan O(Vlog³ log V). The error probability of the first two bounds is polynomially small in n and the latter is polynomially small in log V.