Extend the quickest path problem to the system reliability evaluation for a stochastic-flow network
From the point of view of quality management, it is an important issue to reduce the transmission time in the network. The quickest path problem is to find the path in the network to send a given amount of data from the source to the sink such that the transmission time is minimized. Traditionally, this problem assumed that the capacity of each arc in the network is deterministic. However, the capacity of each arc is stochastic due to failure, maintenance, etc. in many real-life networks. This paper proposes a simple algorithm to evaluate the probability that d units of data can be sent from the source to the sink through the stochastic-flow network within T units of time. Such a probability is called the system reliability. The proposed algorithm firstly generates all lower boundary points for (d,T) and the system reliability can then be computed in terms of such points. The shortest path problem is a well-known problem in operations research, computer science, etc. Chen and Chin have proposed a variant of the shortest path problem, termed the quickest path problem. It is to find a path in the network to send a given amount of data from the source to the sink with minimum transmission time. More specifically, the capacity of each arc in the network is assumed to be deterministic. However, in many real-life networks such as computer systems, telecommunication systems, etc., the capacity of each arc is stochastic due to failure, maintenance, etc. Such a network is named a stochastic-flow network. Hence, the minimum transmission time is not a fixed number. This paper proposes a simple algorithm to evaluate the probability that the specified amount of data can be sent from the source to the sink through the network within a given time. Such a probability is called the system reliability.
quickest path system reliability stochastic-flow network lower boundary point minimal path time constraint