类通信网络中具有优先级的随机游动
Random walk with priorities in communication-like networks
摘要：
我们研究了两类粒子（A和B）的随机游动模型。当两个物种都出现在同一地点时，A的运动优先于B的运动。该模型最初由Maragakis等人提出并分析，Phys. Rev. E 77，020103（2008）;这里我们提供了额外的结果。我们解析地解决了两个物种的扩散系数在晶格中的一些协议。在网络中，我们发现B粒子自由的概率随节点度呈指数下降。在无标度网络中，这导致B在枢纽的局部化，并阻止它们的运动。为了解决这个问题，我们研究了几种策略，以避免捕获的B的：移动A，而不是受阻的B;允许一个被困的B跳的概率很小;偏向步行对非枢纽节点;和限制节点的容量。我们得到了格和网络的解析结果，并讨论了可能的策略的优点和缺点。
英文摘要：
We study a model for a random walk of two classes of particles (A and B). Where both species are present in the same site, the motion of A's takes precedence over that of B's. The model was originally proposed and analyzed in Maragakis et al., Phys. Rev. E 77, 020103 (2008); here we provide additional results. We solve analytically the diffusion coefficients of the two species in lattices for a number of protocols. In networks, we find that the probability of a B particle to be free decreases exponentially with the node degree. In scale-free networks, this leads to localization of the B's at the hubs and arrest of their motion. To remedy this, we investigate several strategies to avoid trapping of the B's: moving an A instead of the hindered B; allowing a trapped B to hop with a small probability; biased walk towards non-hub nodes; and limiting the capacity of nodes. We obtain analytic results for lattices and networks, and discuss the advantages and shortcomings of the possible strategies.
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