In this paper we study the combined assignment-intersection control problem and show that it descends from the more general Equilibrium Network Design Problem (ENDP) in the case of locally optimized control systems (e.g. adaptive traffic-lights). Previous studies deal with this problem using Deterministic User Equilibrium (DUE) assignment models; in this paper we propose a Stochastic User Equilibrium (SUE) model with asymmetric delay functions. In the paper theoretical properties of the model are investigated. Moreover we propose and test some algorithms to solve the problem, with different locally optimized signal control rules, and we estimate their convergence speed.
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