Sustained Flow Index: A Stochastic Measure of Freeway Performance

The capacity of a road addresses its quantitative traffic carrying ability. The estimation of capacity as a parameter to assess traffic flow performance on freeway facilities has received considerable attention in the literature. Research into the traffic operation at high volumes reveals that the capacity of freeways is not a fixed number, but rather a random variable. Thus, in a stochastic approach to freeway capacity of estimation, the capacity is treated as a random variable generated from a population of flow observations, stemmed from a certain distribution function. Since the type of capacity distribution function is generally not known with certainty, it needs to be modeled. The Normal and the Weibull distributions have been among the most common function types that were suggested for freeway capacity. In this research, different capacity distribution types were tested for freeway facilities by applying the models for censored data on empirical observations of United States (U.S.) freeways. Based on the findings of this research and the results of previous studies on German freeways, it was suggested that the capacity distribution function may be characterized with left-skewedness. Since traditional operational performance measures for the analysis of traffic flow on freeways typically disregard the randomness of capacity, new approaches to make use of the concept of randomness within freeway operation analysis are necessary. To address this need, this research introduces a new indicator of freeway performance based solely on a stochastic approach to capacity estimation. This new indicator, the Sustained Flow Index (SFI), was defined as the product of the traffic volume and the probability of survival of this volume (as the probability that the acceptable traffic operation can be sustained). By maximizing the SFI, the optimum volume that can be carried by a freeway over prolonged time periods was derived from parameters of different capacity distribution functions. The breakdown probability (the probability that the acceptable traffic operation fails) corresponding to the optimum volume may be used as a benchmark to select a single value from the capacity distribution function. To validate the optimum volumes as design capacity values, an empirical comparison was made between the conventional capacity estimates and optimum volumes for 19 freeway sections in the U.S. The results show that, on average, optimum volumes obtained by maximizing the SFI corresponded well to conventional capacity values. To illustrate the application of the SFI, a ramp metering algorithm was modified to enhance performance of a