The marvelous thing about traffic flow is the fact that one vehicle might act as the last straw, drawing the urban network into congestion. This can be avoided with traffic management systems, which exhibit a structure, a traffic model, with the objective of optimizing the traffic characteristic and facing congestion by controlling the traffic.

Advanced traffic management systems play a role to control the traffic congestion in the urban network. Both traffic signal control and routing aim at enhancing the traffic performance of urban networks with technology advancement. In addition to traffic signal control, the current thesis includes traffic routing as another control measure in the traffic management system. 

Combined model of traffic routing and traffic signal control has a long history.  In this thesis, similar to previous works, both traffic routing and signal control are coupled in a continuous-time model for a simple traffic network. The network consists of two routes between specific origin and destination, and connected by a signalized intersection. The routing control inputs split the inflow between the two routes and the signal control inputs split the green duration between the two routes. The presented simplified model yet captures the control interaction, and is utilized to derive analytical solution within a form of queue feedback control.

Unlike previous works, (i) the developed model considers dynamic transient periods, rather than steady-state periods or equilibrium conditions, and (ii) system optimum via optimal control is found analytically.  

The optimal control analytical solutions, which are derived based on Pontryagin’s Maximum Principle, are found under the objective function of minimizing total delay by manipulating traffic routing- and signal-control inputs. The results of the analysis show that three different cases of optimal solution exist depending on the parameters and initial  values of the state variables. Feasible state region for each case is formed, wherein every region there are different control inputs for traffic routing and signal. The derived optimal analytical solutions are verified via numerical solutions. A feedback routing and signal control policy based on link queue lengths is presented. The suggested policy can be further developed to an optimal control algorithm for more complex structure for an urban traffic network.

Full thesis PDF File