Abstract
How much traffic can a facility carry? This is one of the fundamental questions designers and traffic engineers have been asking since highways were constructed. The term “capacity” has been used to quantify the traffic-carrying ability of transportation facilities. The value of capacity is used when designing or rehabilitating highway facilities to determine their geometric design characteristics such as the desirable number of lanes; it is used to design the traffic signalization schemes of intersections and arterial streets; it is used in evaluating whether an existing facility can handle the traffic demand expected in the future; it is also used in the operations and management of traffic control systems (ramp metering algorithms, congestion pricing algorithms, signal control optimization, incident management, etc.).
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References
Highway Capacity Manual, 7th Edition, Transportation Research Board, National Academies, Washington DC, 2022
Airport Capacity and Delay, US DOT, FAA, Advisory Circular No 150.5060-5, 1983
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Problems
Problems
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1.
Conduct a literature review to identify previous studies that quantify capacity-related measures. Provide five numerical values of freeway capacity estimates at locations around the United States. How were these values obtained (provide a definition) and how much do they vary from each other and from the HCM7 recommended values?
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2.
Using Fig. 4.2 and assuming that capacity is defined to occur when the probability of breakdown is 0.25, determine the following: (a) What is the capacity of the ramp if the demand from the mainline is 4500 vph? (b) What is the capacity of the mainline freeway if the metered ramp supplies 1380 vph? Can you relate the numbers in the graph to the capacities provided in the HCM7 method for freeways?
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3.
Two “critical” freeway-ramp junctions (1 and 2) experience breakdown events independently. Assume that the ramps are metered but there are no data available regarding ramp metering rates. Assume also that based on the freeway data collected at the two segments, the breakdown volume is Weibull-distributed with parameters.
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(a)
Α1 = 18.36 β1 = 2269
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(b)
Α2 = 17.85 β2 = 2105
Find the expected value E(q) and the standard deviation (σ) of the estimated Weibull breakdown volume. For any time interval i, what is the probability of breakdown at each ramp junction if the mainline volume exceeds 2000 veh/h/ln?
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(a)
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4.
Conduct a literature review on the two-capacity phenomenon. What is a recent estimate of the capacity drop that has been reported in the literature, and what was the procedure used to measure it?
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5.
Your State Department of Transportation is interested in estimating the implications of the two-capacity phenomenon. Assuming that the per lane capacity is 2300 pcph before the breakdown and the maximum throughput drop is 10%, calculate the following: (a) What is the difference in throughput under the two scenarios over an hour for a three-lane facility? (b) If the expected demand of the facility is 2500 pcph over the peak hour, what is the expected difference in the maximum queue length, total delay, and average delay per vehicle at the end of the hour? (c) What is the percent difference in the average delay per vehicle between the two scenarios?
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Elefteriadou, L. (2024). Capacity. In: An Introduction to Traffic Flow Theory. Springer Optimization and Its Applications, vol 84. Springer, Cham. https://doi.org/10.1007/978-3-031-54030-1_4
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DOI: https://doi.org/10.1007/978-3-031-54030-1_4
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