Linear programming and network flows (2nd ed.)
Linear programming and network flows (2nd ed.)
An analysis of stochastic shortest path problems
Mathematics of Operations Research
Dynamic shortest paths in acyclic networks with Markovian arc costs
Operations Research
Introduction to Stochastic Dynamic Programming: Probability and Mathematical
Introduction to Stochastic Dynamic Programming: Probability and Mathematical
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This paper develops an algorithm for finding the dynamic shortest path from the source node to the sink node in stochastic dynamic networks, in which the arc lengths are independent random variables with exponential distributions. In each node there is an environmental variable, which evolves in accordance with a continuous time Markov process. The parameter of the exponential distribution of the transition time of each arc is also a function of the state of the environmental variable of its initiating node. It is also assumed that upon arriving at each node, we know the state of its environmental variable and also the states of the environmental variables of its adjacent nodes. Upon arriving at each node, we can move toward the sink node through the best outgoing arc or wait for encountering the better state of its environmental variable, which reduces the expected transition times of the outgoing arcs. In this paper, we apply the stochastic dynamic programming for finding the dynamic shortest path from the source node to the sink node by obtaining the optimal strategy of movement in each node of the network.