We consider the following network model motivated, in particular, by blockchains and peer-to-peer live streaming. Data packet flows arrive at the network nodes and need to be disseminated to all other nodes. Packets are relayed through the network via links of finite capacity. A packet leaves the network when it is disseminated to all nodes. Our focus is on two communication disciplines, which determine the order in which packets are transmitted over each link, namely {\em Random-Useful} (RU) and {\em Oldest-Useful} (OU). We show that RU has the maximum stability region in a general network. For the OU we demonstrate that, somewhat surprisingly, it does {\em not} in general have the maximum stability region. We prove that OU does achieve maximum stability in the important special case of a symmetric network, given by the full graph with equal capacities on all links and equal arrival rates at all nodes. We also give other stability results, and compare different disciplines' performances in a symmetric system via simulation. Finally, we study the cumulative delays experienced by a packet as it propagates through the symmetric system, specifically the delay asymptotic behavior as $N \to \infty$. We put forward some conjectures about this behavior, supported by heuristic arguments and simulation experiments.

翻译：我们考虑以下网络模型，其动机主要来自区块链和点对点实时流媒体。数据包流到达网络节点，并需要传播至所有其他节点。数据包通过有限容量的链路在网络中中继转发。当数据包传播至所有节点时，它便离开网络。我们聚焦于两种通信规则，即"随机有用优先"(RU)和"最旧有用优先"(OU)，这两种规则决定每个链路上数据包的传输顺序。我们证明RU在一般网络中具有最大稳定性区域。对于OU，我们令人惊讶地发现其通常并**不**具有最大稳定性区域。但我们证明，在对称网络这一重要特例中（即完全图且所有链路容量相等、所有节点到达率相等），OU确实能达到最大稳定性。我们同时给出其他稳定性结果，并通过仿真比较对称系统中不同规则的性能。最后，我们研究数据包在对称系统中传播时累积的时延，特别关注当$N \to \infty$时的时延渐近行为。基于启发式论证和仿真实验，我们提出关于该行为的若干猜想。