Continuous-time flows in networks
Mathematics of Operations Research
Faster Algorithms for the Quickest Transshipment Problem
SIAM Journal on Optimization
Approximating earliest arrival flows with flow-dependent transit times
Discrete Applied Mathematics
SIAM Journal on Computing
Earliest Arrival Flows with Multiple Sources
Mathematics of Operations Research
An enhanced 0-1 mixed-integer LP formulation for traffic signal control
IEEE Transactions on Intelligent Transportation Systems
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The cell-transmission model-based single-destination system optimal dynamic traffic assignment problem proposed by Ziliaskopoulos was mostly solved by standard linear programming (LP) methods, e.g., simplex and interior point methods, which produce link-based flows involving vehicle-holding phenomenon. In this paper we present a network flow algorithm for this problem. We show that the problem is equivalent to the earliest arrival flow and then solve the earliest arrival flow on a time-expanded network. In particular, a scaled flow scheme is proposed to deal with the situation in which the ratio of backward wave speed to forward wave speed is less than one. The proposed algorithm produces path-based flows exhibiting realistic nonvehicle-holding properties. Complexity and numerical analyses show that the algorithm runs more efficiently than LP.