28A25 Integration with respect to measures and other set functions
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- 2011 (1)
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We consider the dynamic shortest path problem in the continuous-time model because of its importance. This problem has been extensively studied in the literature. But so far, all contributions to this problem are based on the assumption that all transit times are strictly positive. However, in order to study dynamic network flows it is essential to support negative transit times since they occur quite naturally in residual networks.
In this paper we extend the work of Philpott [SIAM Control Opt.,~1994, pp.~538--552] to the case of arbitrary (also negative and irrational) transit times. We study a corresponding linear program in a space of measures and give a full characterization of its extreme points. In particular, we show a one-to-one correspondence between extreme points and dynamic paths.