A stochastic flow network composed of multistate arcs can be utilized to describe several practical systems such as computer networks, where transmission time taken for sending data to a sink is an important index. Determining a path with minimum transmission time is known as the quickest path problem (QPP). All algorithms addressing the QPP assume that the determined minimal paths (MPs) are disjoint. Further, for the general case of intersectional MPs, if a congestion phenomenon occurs during the transmission process, these algorithms will lead to an incorrect outcome. Moreover, in practical scenarios, as a budget limit is considered, spare routing is applied to consolidate the system. The objective is to develop an algorithm based on Monte Carlo simulations (MCSs) for evaluating the system reliability while considering the congestion phenomenon. The system reliability is the probability that a specific amount of data can be transmitted successfully through multiple MPs under both time and budget constraints. Furthermore, spare routing to increase the system reliability is established in advance to specify the main and spare MPs. Experiments validate the evaluation of system reliability based on MCSs. The credibility and efficiency of the proposed algorithm are also discussed.

可以使用由多状态电弧组成的随机流网络来描述几种实用的系统，例如计算机网络，其中将数据发送到接收器所花费的传输时间是重要的指标。确定传输时间最短的路径称为最快路径问题（QPP）。解决QPP的所有算法均假定所确定的最小路径（MP）不相交。此外，对于交叉MP的一般情况，如果在传输过程中发生拥塞现象，则这些算法将导致错误的结果。此外，在实际情况下，由于考虑了预算限制，因此应用了备用路由来巩固系统。目的是开发一种基于蒙特卡洛模拟（MCS）的算法，以在考虑拥塞现象的同时评估系统可靠性。系统可靠性是在时间和预算约束下，特定数量的数据可以通过多个MP成功传输的概率。此外，预先建立了备用路由以提高系统可靠性，以指定主MP和备用MP。实验验证了基于MCS的系统可靠性评估。还讨论了所提算法的可信度和效率。