Geodesic
Resource relocation on asymmetric networks
Journal of Graph Algorithms and Applications, Tome 14 (2010) no. 2, pp. 149-163.

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The necessary information to optimally serve sequential requests at the vertices of an undirected, unweighted graph with a single mobile resource is a known result of Chung, Graham, and Saks; however, generalizations of this concept to directed and weighted graphs present unforeseen and surprising changes in the necessary lookahead for strategic optimization. A pair of edges of unequal weights and opposite orientation can serve to simulate a communication or transportation connection with asymmetric costs, as may arise in a transportation network from prevailing winds or elevation changes, or in a communication network from aDSL or a similar technology. This research explores the complications introduced by asymmetric connections within even very small networks. We consider the dynamic relocation problem on a two-vertex system and find that, even in this simplest possible asymmetric graph, the necessary lookahead for optimal relocation may be arbitrarily large. This investigation also gives rise to a linear-time algorithm to determine the optimizing real-time response to any request sequence which uniquely determines an optimal response. 
@article{JGAA_2010_14_2_a1,
     author = {D. Jacob Wildstrom},
     title = {Resource relocation on asymmetric networks},
     journal = {Journal of Graph Algorithms and Applications},
     pages = {149--163},
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     volume = {14},
     number = {2},
     year = {2010},
     doi = {10.7155/jgaa.00202},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00202/}
}
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D. Jacob Wildstrom. Resource relocation on asymmetric networks. Journal of Graph Algorithms and Applications, Tome 14 (2010) no. 2, pp. 149-163. doi : 10.7155/jgaa.00202. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00202/

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