Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
Minimum cost-reliability ratio path problem
Computers and Operations Research
Lower bounds on two-terminal network reliability
Discrete Applied Mathematics
Computers and Operations Research
An algorithm for finding the k quickest paths in a network
Computers and Operations Research
The all-pairs quickest path problem
Information Processing Letters
Finding the k quickest simple paths in a network
Information Processing Letters
Algorithms for the constrained quickest path problem and the enumeration of quickest paths
Computers and Operations Research
Minimum time paths in a network with mixed time constraints
Computers and Operations Research
A heuristic technique for generating minimal path and cutsets of a general network
Computers and Industrial Engineering
Extend the quickest path problem to the system reliability evaluation for a stochastic-flow network
Computers and Operations Research
Flow reliability of a probabilistic capacitated-flow network in multiple node pairs case
Computers and Industrial Engineering
A label-setting algorithm for finding a quickest path
Computers and Operations Research
An algorithm for ranking quickest simple paths
Computers and Operations Research
Reliability Evaluation for an Information Network With Node Failure Under Cost Constraint
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
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The quickest path problem involving two attributes, the capacity and the lead time, is to find a single path with minimum transmission time. The capacity of each arc is assumed to be deterministic in this problem. However, in many practical networks such as computer networks, telecommunication networks, and logistics networks, each arc is multistate due to failure, maintenance, etc. Such a network is named a multistate flow network. Hence, both the transmission time to deliver data through a minimal path and the minimum transmission time through a multistate flow network are not fixed. In order to reduce the transmission time, the data can be transmitted through k minimal paths simultaneously. The purpose of this paper is to evaluate the probability that d units of data can be transmitted through k minimal paths within time threshold T. Such a probability is called the transmission reliability. A simple algorithm is proposed to generate all lower boundary points for (d,T), the minimal system states satisfying the demand within time threshold. The transmission reliability can be subsequently computed in terms of such points. Another algorithm is further proposed to find the optimal combination of k minimal paths with highest transmission reliability.