FIFO Queues Are Bad for Rumor Spreading

The two most intensively studied communication paradigms for spreading rumors are the so-called PUSH and PULL algorithms. The previous analysis of these protocols assumed that every node could process all such push/pull operations within a single step, which could be unrealistic in practical situations. We propose a new framework for the analysis of rumor spreading accommodating buffers, in which a node can process only few push/pull messages at a time. We develop time complexity upper and lower bounds for randomized rumor spreading in the new framework, and compare the results with analogous ones in the classical setting. Our results highlight that there might be a very significant performance loss if messages are processed at each network node in first-in first-out order.