This paper compares the continuous network design problem formulations using system-optimal (SO) and user-optimal (UO) dynamic traffic assignment when the following independent stochastic parameters with known discrete probability distributions are considered: time-dependent origin-destination demands, time-varying saturation flow rates and jam density, and network improvement unit costs. These models propagate traffic according to Daganzo's cell transmission model. Two Monte Carlo bounding techniques, common random numbers (CRN) and independent random numbers (IRN) strategies, are used to solve the stochastic models. The results show that the CRN strategy outperforms IRN on a simple test network resembling a freeway corridor. The network size is sacrificed to gain higher confidence probabilistic behavior and to understand intuitively the effects of different network improvement policies. Although the findings may not necessarily be generalized, they provide interesting and insightful information. First, the SO and UO models allocate investment differently for certain budgets, and the stochastic models may lead to an erroneous solution (i.e., a bottleneck) for some budgets. Subsequently, the results of three comparison cases are discussed: (a) for the SO models, it should be more valuable to solve the stochastic than the deterministic models, but it is not always the case for the UO models; (b) the SO models appear more desirable than the UO models for single-level analysis; and (c) it should be more valuable to solve the stochastic model accounting for more randomness.
Abstract