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Capacity of a road facility as an important characteristic in transportation and traffic studies is defined as the maximum rate of flow that could be held by that facility, which has been supposed to have a constant and certain value. This assumption, although necessary for most traffic studies, has also caused some problems, like that of demand exceeding capacity in many road facilities. Researchers have recently shown that capacity is not necessarily the maximum flow rate held by a facility. They have also demonstrated that capacity has a stochastic nature rather than a constant and deterministic value. Stochastic approach to capacity is more complicated and comprehensive. In this approach, capacity is treated as a random variable generated from a population, and having corresponding distribution function. Knowing more about breakdown phenomenon, as transition from acceptable to unacceptable flow, plays a key role in this approach. To obtain breakdown flow rates, threshold speed as the quantitative measure is used to distinguish congested and non-congested flow rates. Flow rates occurring immediately before decrease of average speed below the threshold speed, are regarded as breakdown flow rates and their value in addition to non-congested flow rates are used to estimate the distribution function. Product Limit Method with analogy to life time data is used to estimate non-parametric function. The main advantage of this method is that it considers censoring data. In capacity estimation, if a time interval is followed by a breakdown, it will be regarded as uncensored interval; if it is non-congested it will be regarded as censored interval, meaning that capacity of the road is bigger than incoming demand. If it is located in a congested area, it would not be used in the estimation process. Two common parametric estimation methods are (OLS) ordinary least squares and (MLE) maximum likelihood estimation. Since binary data is used to estimate capacity distribution function, the ordinary least squares method is not useful with such data. Maximum likelihood estimation with a presumption about the type of distribution is used to estimate the parameters. Distribution function with the maximum log-likelihood value would be the function that has most likely produced the sample, and is known as the capacity of the freeway. In this paper, both non-parametric and parametric capacity distribution functions of Tehran-Karaj freeway as the oldest and the busiest freeway in Iran, serving and average of 100,000 passenger cars a day, are estimated. Threshold speed is found to be respectively 70 km/h and 75 km/h in two sections under investigation located in the direction to Karaj. Based on the data gathered for four months by traffic cameras; and refining to meet standard criteria, a sample of 229 and 169 breakdowns were detected at each section. Different distribution functions are fitted to the data, and with trial about different kinds of functions, Gumbel distribution is found to be the best distribution fitting the observed data.

Keywords: Freeway Capacity, Stochastic Approach, Maximum Likelihood Estimation, Product Limit Method, Distribution Function, Gumbel Distribution

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