Description and evaluation of controlled freeway merging

This dissertation involves the mathematical modeling of the operation of a freeway entrance ramp merging control system. A renewal process was utilized to develop expressions for the statistical moments of the time a vehicle waits at the entrance ramp signal for gap acceptance control. The moments so developed were compared to moments previously developed by combinatorial analysis. A Poisson input-arbitrary service queuing approach produced expressions for the expected queue at the signal, the expected wait in the queue and the expected time a vehicle would spend in the control system before being released at the signal. The basic queueing model was applied to fixed rate metering entrance ramp control with a constant service rate introduced into the model. The capacity-demand system of ramp control was modeled in terms of a generalized Poisson process for freeway outside lane vehicular arrivals. Probabilities of failure to meet freeway control system criteria were developed from the mathematical expressions. ..