Before revision:  Although QPS-r builds upon an existing add-on technique called Queue-Proportional Sampling (QPS), we are the first to discover and prove this nice property of such matchings.
After revision:  Although QPS-r builds upon an existing add-on technique called Queue-Proportional Sampling (QPS), in this paper, we provide analytical guarantees on its throughput and delay under i.i.d. traffic as well as a Markovian traffic model which can model many realistic traffic patterns.