Modeling Vehicle Interactions and the Movement of Groups of Vehicles

Abstract

Chapter 1 discussed the movement of an individual vehicle and provided the equations of motion assuming there are no other vehicles around. This chapter examines the interactions between vehicles, which is at the heart of traffic flow theory. It is these interactions that produce the observed traffic operational conditions, including crashes and congestion. Traffic operational characteristics of interest include capacity (i.e., the maximum amount of traffic that can pass through a point or section in vehicles or other units of traffic per unit time), prevailing speed (i.e., the speed at which the facility operates under a given set of prevailing conditions, including the demand, the highway design, etc.), delay, and travel time. These characteristics are discussed in more detail in Part II.

Problems

• 1. Solve Example 2.1 assuming the following: desired maximum speed of the following vehicle, v(n + 1)_DES, is 80 mph, the maximum acceleration which the following vehicle wishes to undertake, a(n + 1)_MAX, is 8 ft/s², the actual most severe deceleration that the follower wishes to undertake, b(n + 1), is −10.5 ft/s², the most severe deceleration rate that vehicle n + 1 estimates for vehicle n, $\hat{b_n}$, is −12.5 ft/s², and the effective vehicle length, L(n), is 25 ft. How do the results differ from those of Example 2.1. Explain any differences observed.

• 2. Solve Example 2.1 assuming that the car-following model is GHR with parameters m = 1, l = 1, and λ_m,l = 2.6. How do the results compare to those of Example 2.1?

• 3. Conduct a literature review of car-following models. What parameters are used in addition to the ones described in this chapter?

• 4. Conduct a literature review of lane-changing models for freeways and arterials.

• 5. The following utility functions have been developed using data from four-lane freeways to indicate driver preference for truck drivers for each of the four lanes:

  • U_{x, L1} = 181.25 – 0.18 F_L1 + 1.27 v_L1

  • U_{x, L2} = 341.3 – 0.27 F_L2 + 1.35 v_L2

  • U_{x, L3} = 40.53 – 0.05 F_L3 + 0.35 v_L3

  • U_{x, L4} = 18.26 – 0.02 F_L4 + 0.07 v_L4

  where

  • U_{x, L1}, U_{x, L2}, U_{x, L3}, and U_{x, L4} are the utilities of each of the four lanes;

  • F_L1, F_L2 F_L3, and F_L4 are the passenger vehicle flows of each of the four lanes; and

  • v_L1, v_L2, v_L3, and v_L4 are the prevailing speeds of each of the four lanes.

  If during the peak hour, the passenger vehicle flows are F_L1 = 1380 vph, F_L2 = 1560 vph, F_L3 = 1250 vph and F_L4 = 1320 vph and the speeds are v_L1 = 55 mph, v_L2 = 60 mph, v_L2 = 62 mph, and v_L4 = 62 mph, estimate the probabilities that truck drivers will select each of the four lanes.

• 6. Conduct a literature review of gap acceptance models for unsignalized intersections.

• 7. Conduct a literature review of gap acceptance models for merging at freeway junctions.