OVERALL CENTRAL MOMENTS OF TRAFFIC DELAY AT A SIGNALIZED INTERSECTION

Abstract

Overall traffic delay model for estimating the mean and variance at a signalized intersection is discussed. The model was developed under basis of two delay components, namely deterministic and stochastic components. The latter component was put under D/D/1 framework and therein mean and its variance derived. While the stochastic component was put under the M/G/1 framework, mean and variance derived. Extension on stochastic component and M/G/1 framework was discussed with the usage of compressed queueing processes. Harmonization of the moments of deterministic and stochastic components to obtain the overall central moments of traffic delay has been discussed. Illustration of the model on real traffic data has been carried out. Simulation was performed using statistical software for traffic intensities ranging from 0.1 to 1.9. The simulated results indicate that both deterministic and stochastic components are incompatible as the traffic intensity approaches capacity. Also, the simulation shows that variance of overall traffic delay drops linearly when the traffic intensity is less than 3 because of increasing rate of random arrivals. This variance decreases slowly as the traffic intensity approaches capacity and slowly increases as the traffic intensity goes beyond capacity. This confirms the results that exist in literature that oversaturated conditions and random delay renders the stochastic component in traffic delay models unrealistic.