Abstract
Increasing the throughput by balancing the traffic load through the whole network is important for the transportation system. User optimal routing service usually results in congestions in the bottleneck links. On the other hand, individual travelers typically have delay constraints to satisfy, which might be ignored in the system optimum. In this work, we look into the traffic assignment problem in the stochastic network, considering the maximum delay constraint, so that any route suggested by the system optimal traffic assignment does not incur a delay longer than the constraint in most cases. We formulate the Stochastic Delay Constrained Maximum Flow problem (SDCMF), and prove that it is NP- Complete. The delay aware algorithms are proposed to solve the SDCMF problem, which not only find a set of paths with maximum flow, but also consider the delay of each path.
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