A note on the interpretation of the dual variables in estimating traffic capacity at signal- controlled road junctions

The values of the dual variables in a constrained optimisation problem can be used to estimate the sensitivity of the optimal value of the objective function to changes in the constraints. Allsop (1972) used standard methods of linear programming to derive expressions for the sensitivity of the reserve capacity at a signal-controlled road junction to various changes in the traffic engineering constraints. That analysis used the assumption that the maximum reserve capacity would be achieved when the cycle time used is maximal. While this normally occurs, some junctions have come to light where a reduction in the cycle time increases the capacity. Allsop's analysis is extended here to account for this possibility.