Shirdel Gholam H, Abdolhosseinzadeh Mohsen
Department of Mathematics, Faculty of Basic Science, University of Qom, Qom, Iran.
Springerplus. 2016 Sep 13;5(1):1529. doi: 10.1186/s40064-016-3180-7. eCollection 2016.
The stochastic shortest path length is defined as the arrival probability from a given source node to a given destination node in the stochastic networks. We consider the topological changes and their effects on the arrival probability in directed acyclic networks. There is a stable topology which shows the physical connections of nodes; however, the communication between nodes does not stable and that is defined as the unstable topology where arcs may be congested. A discrete time Markov chain with an absorbing state is established in the network according to the unstable topological changes. Then, the arrival probability to the destination node from the source node in the network is computed as the multi-step transition probability of the absorption in the final state of the established Markov chain. It is assumed to have some wait states, whenever there is a physical connection but it is not possible to communicate between nodes immediately. The proposed method is illustrated by different numerical examples, and the results can be used to anticipate the probable congestion along some critical arcs in the delay sensitive networks.
随机最短路径长度被定义为随机网络中从给定源节点到给定目的节点的到达概率。我们考虑有向无环网络中的拓扑变化及其对到达概率的影响。存在一种稳定拓扑，它展示了节点的物理连接；然而，节点之间的通信并不稳定，这被定义为不稳定拓扑，其中弧可能会拥塞。根据不稳定拓扑变化在网络中建立一个具有吸收状态的离散时间马尔可夫链。然后，将网络中从源节点到目的节点的到达概率计算为所建立马尔可夫链最终状态下吸收的多步转移概率。假设存在一些等待状态，每当存在物理连接但节点之间无法立即通信时。通过不同的数值例子说明了所提出的方法，其结果可用于预测延迟敏感网络中一些关键弧上可能的拥塞情况。
