优先排队网络的等待时间动力学
Waiting time dynamics of priority-queue networks
摘要：
我们研究了优先级队列网络的动力学，Oliveira和Vazquez [Physica A { \bf 388}，187（2009）]引入的二元交互优先级队列模型的推广。我们发现，原来的AND型协议的互动任务是不可扩展的队列网络与循环，因为动态成为冻结由于优先级冲突。然后，我们考虑一个可扩展的交互协议，OR型的，并检查网络拓扑结构和排队的数量的影响的优先级队列网络的等待时间分布，发现它们表现出幂律尾在所有情况下考虑，但与模型相关的幂律指数。我们还表明，在任务执行的同步性，引起优先级队列网络中的优先级冲突，是一个相关因素的队列动态，可以改变幂律指数的等待时间分布。
英文摘要：
We study the dynamics of priority-queue networks, generalizations of the binary interacting priority queue model introduced by Oliveira and Vazquez [Physica A {\bf 388}, 187 (2009)]. We found that the original AND-type protocol for interacting tasks is not scalable for the queue networks with loops because the dynamics becomes frozen due to the priority conflicts. We then consider a scalable interaction protocol, an OR-type one, and examine the effects of the network topology and the number of queues on the waiting time distributions of the priority-queue networks, finding that they exhibit power-law tails in all cases considered, yet with model-dependent power-law exponents. We also show that the synchronicity in task executions, giving rise to priority conflicts in the priority-queue networks, is a relevant factor in the queue dynamics that can change the power-law exponent of the waiting time distribution.
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