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It has been long recognized that to minimize the system total travel cost is one of the major objectives for transport managers. Meanwhile, from a traveler’s perspective, her objective is to reduce her own travel cost as much as possible; therefore, the deterministic user equilibrium is widely assumed to model a traveler’s rational route choice behavior. A bi-level programming formulation has been proposed for some transportation problems such as the network design problem and the (second-best) road pricing problem. In a bi-level formulation, the upper level is to minimize the system total cost and the lower level is to solve the corresponding parametric deterministic user equilibrium, where the parameter might stand for toll charge or the road capacity expansion.

The lower level deterministic user equilibrium, however, ignores a traveler’s stochastic route choice behavior and the stochastic nature of traffic flow pattern. Indeed, the significant amount of variation of traffic flow pattern has been observed in both traffic count field data and commuter’s route choice lab experiment. Therefore, it should be more appropriate to model the traffic flow pattern in the lower level as a flow probability distribution on the flow space, rather than single deterministic equilibrium. Since traffic link (route) flow should be modeled as a random vector, the system total cost should be regarded as a random variable. Hence the stochastic system optimum (SSO) problem is defined to solve the mean and variance optimization problem of the random system total travel cost.

This research aims at reformulating the SSO bi-level problem in such a way that in the lower level the traffic flow follows a stationary distribution in a Markov chain of driver’s day-to-day stochastic route choice adjustment process, and the upper level is to solve the mean and variance optimization of the system total cost. Given any toll charge pattern or road capacity expansion condition, an efficient algorithm is expected to be developed to solve the first- and second- order moments of the route flow stationary distribution in the lower level. Furthermore, an iterative method will be proposed to solve the upper level SSO problem. The completion of this research will provide new insight in solving the more realistic stochastic version of the network design and road pricing problems, which in turn benefit both academic literature and practical applications in the New York Metropolitan area.