Travel time estimation as a function of the probability of breakdown
Travel time estimation methods have been developed in the past few years. However, for previously developed models travel times under congested conditions are underestimated due to difficulties in the calculation of vehicle queue formation and dissipation. The purpose of this study is to develop a model that can estimate travel time on a freeway as a function of a given demand. The scope of this study includes congestion due to heavy traffic, and not due to weather, accidents, incidents, or work zones. This study is divided into two phases: (i) evaluate and compare previously developed methods---shockwave analysis, queuing theory, re-scaled cumulative curves, and simulation---to field data, (ii) develop a methodology for estimating travel time for a given freeway route, consisting of several consecutive links using the concept of probabilistic breakdown for freeway links. The DTMC (Discrete Time Markov Chains) method is applied to develop this model.
Speed and flow data are used for model development, and link travel time or route travel time is applied to validate the model. Speed and volume data were obtained from Mobility Technologies. These data were originally collected by RTMS (Remote Traffic Microwave Sensor) in one-minute intervals for a 4-month period, from May to August 2004. Travel time data were collected at the TCC (Traffic Control Center) located in Philadelphia, PA.
As a result of the first phase, it was concluded that shockwave analysis cannot adequately estimate travel time. Also, queuing theory and re-scaled cumulative curves cannot be applied in this case due to the lack of data at the ramps along the freeway.
In the second phase, the following five tasks were undertaken: (i) define states and variables according to whether the link is congested or not, (ii) estimate travel time of each link both when the link is non-congested and when it is congested, (iii) estimate transition matrices considering the effects of congestion to the upstream or downstream links, (iv) estimate route travel time using the link travel time and transition matrices, (v) adjust the model to consider time of day and daily variations according to the characteristics of the traffic patterns by time of day. As a result, the developed model estimates the expected travel time for the entire route as a function of those embedded probabilities of breakdown. When compared to field data, the model estimates O-D travel time fairly well for congested conditions. The expected O-D travel time, however, is somewhat overestimated because the model considers the probability of occurrence of a breakdown, while the field-measured data are not from a representative sample with respect to breakdown probability.