Abstract
Traffic models can be very useful in the enhancement of complex transportation systems, as well as in their management and evaluation. They can help in the design and operations of traffic systems since they can predict traffic operational conditions at some time in the future under various sets of design, traffic, and control characteristics. Traffic engineers and designers can make decisions regarding facility modifications or traffic management improvements based on the expected impact of those improvements on the transportation system. Traffic models can also help in the evaluation of existing systems and in the development of priorities for improvement. Some mathematical models are based on theoretical principles. For example: Flow = Speed × Density is a mathematical model based on the fundamental principles of traffic flow. On the other hand, empirical models are those based on field observations (empirical observations) rather than on relationships that can be mathematically described. Empirical models predict how a system behaves rather than explaining how its components interact. Empirical models can be useful when the mathematical relationship is unknown or difficult to express. Examples of empirical models are the traffic stream relationships discussed in Chap. 3.
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Problems
Problems
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1.
Conduct a literature review and discuss the comparisons between shockwave analysis and queuing analysis. Do the two analysis methods provide consistent results? What are the differences between the two methods?
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2.
Traffic along a two-lane, two-way highway travels at a speed of 55 mph and the demand is 1100 vph and the density is 18 veh/m/ln. A truck with a speed of 15 mph enters the highway and travels for 3 miles. Passing is not allowed and vehicles behind the truck are forced to follow at a speed of 15 mph. Draw all shockwaves created by the presence of the truck and estimate how long it would take for the impact of the truck presence to be entirely alleviated (problem suggested in Refs. [1, 2]).
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3.
In Example 7.2, assume that the demand during the next hour (9:00 am–10:00 am) drops to 1600 vehicles/h. When will the queue dissipate, what is the total delay for the entire congested period, and what is the average delay per vehicle for all vehicles traveling through this segment over the 2-h period of analysis?
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In Example 7.3, obtain the probability that n vehicles will be in the system, where n = 0–10.
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5.
Plot the average number of customers in the system as a function of the traffic intensity for the M/M/1 system.
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6.
Identify three queuing systems for which there are closed-form equations that provide the delay and queue length estimates. List those equations for each of the three systems.
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7.
Conduct a literature review search on traffic flow prediction for freeway networks. What are the advantages and disadvantages of each method identified and are there any methods currently deployed in practice?
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8.
Conduct a literature review to document recent advancements in signal control optimization.
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Elefteriadou, L. (2024). Analytical Models and Techniques. 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_7
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