Travel Time Models: Macroscopic Traffic Flow Model

There are a lot of ways to improve the traffic flow, such as traffic signal timing optimization. But the challenge is the evaluation of traffic performance with various traffic and geometric configurations [Chandler et al. 1958]. So the development of traffic models extend traffic flow theory into the network level. This section will view macroscopic traffic flow.

3.2.1. Travel Time Models. Travel time provides an overview of how well a traffic network is working at a specific time. A vehicle can come into network from a road and pass through one or more intersections, finally leave at a road. The travel time of the vehicle is represented the interval of it traveling through the network. However, the information is limited as the travel time

General Network Models. Besides speed based evaluation, a number of performance measures have been proposed. Two models are represented in this chapter, the α-relationship and two-fluid theory [Zahavi et al. 1972a; Zahavi et al. 1972b]. In α-relationship [Zahavi et al. 1972a; Zahavi et al. 1972b], Zahavi selected three principals variables, I (the traffic density), R (the road density) and v (the weighted space mean speed). The relationship between I and v/R was given by Eq. (29): (29) where α and m are parameters.

Two-fluid theory model is based on two assumptions:

(1) The average running speed of moving vehicles in a street network is proportional.

(2) The stop time of a vehicle in a network is equal to the average stopped time during the same period.

So for the first assumption, the average speed V is defined as: V = Vm(1 − fs)n+1 (30) where Vm is the average running speed, fs is the fraction of average vehicles stopped time. T is the average travel time, Tr is the moving time, and Ts represents the average stop time, we can see T = Tr + Ts (31) (32)

3.3. Traffic Impact Flow

In the centralized model, there is a central agent that collects all local data from distributed agents, then it makes decisions based on the preset algorithms and assigns decisions back to each of local agents. Centralized model has three common issues in different areas: first one is that it is less robustness. In general, central agent is a single agent that controls all actions of the system. It will affect entire traffic network when it has failures or physical problems. Second, the curse of dimensionality becomes critical at the central agent as it has to analyze all data from all local agents. Third, this model requires high computing ability and throughput capacity, which means central agent have to response decisions back within a small delay [Komisarczuk et al.