Application of linear quadratic modelling and optimization in urban traffic control

The increasing congestion on urban streets demands traffic control signal timing to be well co-ordinated and optimized even during the transition between timing patterns used in different periods of time-of-day (TOD). The TOD timing plans, defined by fixed-time co-ordination parameters, need to change from one TOD period to another. The current methods used in transitioning are aimed at achieving quick transition rather than optimizing traffic flow during the transition period. As a result, they generally cause increased vehicle delays during the transition period particularly for vehicles on the minor street, which face lengthened red times. This paper proposes a quadratic optimization method that can be used to reduce disutility measures to motorists during the transition period. The transition is modeled as a linear dynamic process, and the disutility measures are modeled as the sum of squares of the deviations of the co-ordination parameters – that is, cycle length, phase split, and offset – from the optimal values during the transition. A linear quadratic (LQ) optimization technique of optimal control is used to determine the step size and the number of steps necessary to complete the transition with minimum disutility. The proposed transition period optimization method has the advantage that the user need not specify minimum and maximum cycle length to achieve optimization, as is the case with current methods. Simulation results for three co-ordinated intersections showed that the proposed method reduces total vehicle delay when compared to the immediate transition method embedded in CORSIM traffic simulation software. This is due to the fact that vehicles on the minor street approaches get proportional green time without significantly affecting green times on the major street approach green phase. However, the method showed a slight increase in total delay for vehicles on the major street.