Minimum Number Of Arcs In Conditional Monte Carlo Sampling Of Stochastic Networks

1986 ◽  
Vol 24 (1) ◽  
pp. 33-44 ◽  
Author(s):  
Bajis Dodin
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Sampling ◽  
Stochastic Networks ◽  
Minimum Number ◽  
Conditional Monte Carlo

Approximating the Stochastic Network by its M Shortest Paths

1989 ◽  
Vol 3 (3) ◽  
pp. 435-451
Author(s):  
Bajis Dodin
Keyword(s):  
Monte Carlo ◽  
Shortest Path ◽  
Probability Distributions ◽  
Shortest Paths ◽  
Monte Carlo Sampling ◽  
Stochastic Networks ◽  
Mean Value ◽  
Stochastic Network ◽  
Distributional Properties ◽  
Deterministic Methods

Given a stochastic activity network in which the length of some or all of the arcs are random variables with known probability distributions. This paper concentrates on identifying the shortest path and the M shortest paths in the network and on using the M paths to identify surrogate stochastic networks which are amenable for deriving analytical solutions. First, it identifies the M shortest paths using a certain form of stochastic dominance. Second, it identifies the M shortest paths by applying the deterministic methods to the network resulting from replacing the random length of every arc by its mean value. The two sets of the M paths are compared with those obtained by Monte Carlo sampling. Finally, the paper investigates how the distributional properties of the shortest path in the surrogate network compare with those of the shortest path in the original stochastic network.

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