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Routing in dynamic and stochastic network is to provide adaptive 'best' route guidance where the link/route travel times are modelled as a time-varying stochastic process. Typical approaches for routing when travel times are both dynamic and stochastic assume that link travel times are independent and travellers are seeking for expected shortest paths. It is observed in many applications that providing the single least-expected travel time path is not adequate and appropriate to help diverse travellers make travel decision. Given the stochastic link attributes, the accumulated uncertainty of those attributes over any given route can easily make many routes statistically indistinguishable from the expected shortest path. In this paper, we investigate the dependences between link and path attributes, derive the exact path travel time distribution from link travel time distributions with consideration of their interrelationship, and employ an efficient simulation method to determine a set of adaptive 'best' paths. Given certain reference function of travel time, the individual turning decision at each branching point is made accordingly.
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