Abstract:
In this paper the authors pursue the effect of volatility on the probability of highway breakdown. Because daily aggregated flow values exhibit dissimilar levels of variability throughout the day, a stochastic volatility (SV) model was pursued. Under this format, assuming traffic flow volatility follows an autoregressive process of order one, volatility was estimated at each 15-minute time step per day during the collection period of 205 days. A computational Bayesian format was used to fit parameters of 205 SV models to data collected from one bottleneck site along Interstate 93 in Salem, NH. Fitted results show that volatility estimates successfully capture flow variability observed from the traffic data. To evaluate the effect of SV on breakdown, a sampling scheme was created in which sampled demands and capacities were compared. To estimate demand, a signal was first extracted from the flow aggregates using a Functional Data Analysis (FDA) model and then combined with a sampled SV estimate. For stochastic capacity, daily flow maxima were used as either censored or uncensored estimates of capacity based on breakdown occurrence. By extreme value theory, these capacity values are distributed as a Generalized Extreme Value (GEV) distribution. From a GEV model fitted to this data, capacity estimates are sampled and compared to SV-based demand to produce breakdown probabilities by time of day. Finally, the breakdown probabilities are compared to those estimated by the sample data only to illustrate the effect of SV on breakdown.
