Simple analytical models for estimating the queue lengths from probe vehicles at traffic signals

As mobile traffic sensor technology gets more attention, mathematical models are being developed that utilize this new data type in various intelligent transportation systems applications. This study introduces simple analytical estimation models for queue lengths from tracked or probe vehicles at traffic signals using stochastic modeling approach. Developed models estimate cycle-to-cycle queue lengths by using primary parameters such as arrival rate, probe vehicle proportions, and signal phase durations. Valuable probability distributions and moment generating functions for probe information types are formulated. Fully analytical closed-form expressions are given for the case ignoring the overflow queue and approximation models are presented for the overflow case. Derived models are compared with the results from VISSIM-microscopic simulation. Analytical steady-state and cycle-to-cycle estimation errors are also derived. Numerical examples are shown for the errors of these estimators that change with probe vehicle market penetration levels, arrival rates, and volume-to-capacity ratios. © 2013 Elsevier Ltd.