Standard Deviation of Travel Time in a Freeway Network--A Mathematical Quantifying Tool for Reliability Analysis

Abstract

Travel time reliability is a new way of looking at congestion and unpredictable variation of travel time. The standard deviation of travel time is a good indicator for investigating reliability of a network. This paper presents a mathematical model dealing with the standard deviation of the total travel time within a freeway network. In general, the distribution of the travel time of links and the distribution of delays at bottlenecks can be described by different probability distributions. The parameters of those distributions can be calibrated by measurements or simulation studies. However, it is hard to calculate the standard deviation or variance of travel time of a route consisting of several consecutive links or bottlenecks. The presented paper shows that, under some assumptions, the variance of the total route travel time can be calculated as the sum of the variances of the single links or bottlenecks in case that the travel times and the delays are independent of each other. In reality the independency between the consecutive links or bottlenecks may not be satisfied. In this case the variance of the total travel time can also be estimated given the correlation coefficient between the two consecutive links or bottlenecks. Again, this correlation coefficient can be calibrated by measurements or by simulation studies. Once the variance in the travel time is known, the standard deviation is also known. Using the proposed model, the standard deviation of travel time - and, thus, the reliability of a freeway network - can be quantitatively estimated given the geometric design of the freeway network and the traffic demand.