## What is meant by travel flow?

Travel flow is a major area of transportation engineering specially studied in civil engineering. The travel flow is a mathematical approach with general concepts of science to study and estimate the interactions between travelers and infrastructures. The travelers here mean pedestrians, cyclists, drivers, motorists, and other vehicles. The infrastructures include highways, traffic devices, and highway signs. Travel flow is also known as traffic flow, whose main target is to establish an optimum and efficient traffic network that permits smooth traffic flow with minimum traffic congestions.

The flow of traffic follows non-linear randomized propagations. It primarily depends on the individual driver's reaction and travel experiences that lead to travel propagations not following the principles of mechanics, instead, it follows shock wave propagation and cluster formation approach. This leads to a harmonic trajectory consisting of both forward and backward motions depending on the density of vehicles, which significantly increases the vehicle travel time.

In this article, a brief introduction has been provided regarding the travel flow and its associated theories and principles.

## Traffic flow theory

Traffic flow targets in studying the individual driver movements and vehicles from one point to another point and the interactions they make with other vehicles during the course of travel. Studying traffic flow is a difficult task as it is not a steady analysis, but rather it is an unsteady analysis, as the flow does not follow a constant pattern. The flow keeps on changing continuously with respect to time, as the behavior of an individual driver is different. The traffic flow in a straight highway and expressway with fewer vehicles can be assumed to be steady and can be analyzed and studied easily.

## Traffic flow terminologies

To better represent the flow, the traffic flow is generally constrained along a one-dimensional pathway, like a travel lane and various relationships have been established, some of the relationships are outlined below.

### Time-space diagram

The time-space diagram is a fundamental diagram used in transportation engineering. It is a two-dimensional diagram, where the abscissa of the diagram denotes the time and the ordinate represents the vehicle position or distance traveled. Transportation engineers use this diagram to point out vehicle position and trajectory with respect to a specific time. This diagram can be used to establish the traffic flow characteristics at a certain area or space, as it permits multiple vehicle flow characteristics on a single diagram.

### Flow

The flow is the number of vehicles passing through a fixed point at a given time. The empirical formula of flow is mathematically given by,

$f=\frac{3600\times N}{{t}_{\mathrm{hw}}}$, where, $f$ represents the flow, $N$ represents the number of vehicles, and ${t}_{\mathrm{hw}}$ represents time headway

### Density

The ratio between the number of vehicles and the length of the roadway represents the density. Mathematically the density concentration is given as,

$D=\frac{N}{Q}$, where, $D$ represents the density concentration, and $Q$ represents the length of the roadway.

The inverse of density is termed spacing. Spacing is referred to as the center to center distance between two vehicles on the roadway.

### Speed

According to elementary physics, speed is the ratio between the distance covered by a vehicle and the time taken. But measurement of the speed of every vehicle on the roadways is not possible. Hence, the approach of average speed is considered. There are two speeds generally considered in a travel flow, they are:

**Time mean speed**: Time mean speed is based on a reference point on the roadway by loop detectors. It is expressed as

${V}_{t}=\left(\frac{1}{g}\right)\sum _{i=1}^{g}{V}_{i}$

where ${V}_{t}$ represents the time mean speed, $g$ denotes the number of vehicles passing through a fixed point, and ${V}_{i}$ represents the velocity of the ${i}^{\mathrm{th}}$ vehicle on the roadway.

**Space mean speed**: The space mean speed is calculated over the entire roadway. It is calculated by taking consecutive pictures from satellites, or cameras. It is given as

${V}_{s}={\left(\left(\frac{1}{r}\right)\sum _{i=1}^{r}\left(\frac{1}{{V}_{i}}\right)\right)}^{-1}$

where ${V}_{s}$ represents the space mean speed, $r$ represents the number of vehicles passing the roadway.

## Macroscopic and microscopic model of analysis

The traffic flow models are studied into two categories which are outlined below.

### Microscopic model

The work of the macroscopic model is to study the behavior of vehicles such as cars like change in speed and distance with respect to the leading vehicle, i.e., which is ahead of the traffic in a roadway.

### Macroscopic model

The macroscopic model works by performing an analogy by establishing traffic streamflow. It is generally related to density, flow, and density. One of which is the fundamental diagram of the traffic flow, which represents the flow f varies linearly with velocity V of the vehicle. It is given as,

f=kV

where k is the traffic density which is the slope.

Another familiar model like the Greenshields model is popularly used. The Greenshields model assumes that speed and density follow a linear relationship. It was developed and used extensively before the applications of computers, and the calculation was general arithmetic calculations performed manually.

## Context and Applications

This topic is majorly taught in different undergraduate and postgraduate degree courses of:

- Bachelors in Technology (Civil Engineering)
- Masters in Technology (Civil Engineering)
- Masters in Technology (Highway Engineering)
- Masters in Technology (Transportation Engineering)

## Practice Problems

1. Which of the following is true for the time-space diagram?

- The abscissa is time and the ordinate is the distance traveled.
- The abscissa is the distance traveled while the ordinate is time.
- The abscissa is work done while the ordinate is time.
- The abscissa is time while the ordinate is work done.

Answer: Option a

Explanation: In a time-space diagram, the abscissa is the time and the ordinate is the distance traveled by the vehicle.

2. Who are the people behind the application of travel flow theory for traffic estimation and development?

- Project management team
- Building construction and management team
- The team of civil engineers and transportation engineers
- None of these

Answer: Option c

Explanation: The application of travel flow theory and traffic estimation and development is primarily handled by civil engineers and transportation engineers.

3. What is meant by traffic flow?

- It means the number of vehicles taking a left-turn.
- It means the number of vehicles passing through a fixed point.
- It signifies the number of vehicles performing a specific work, like lane changing and inter-vehicle interactions.
- Both a and c.

Answer: Option b

Explanation: Flow means the number of vehicles passing through a fixed point.

4. Which model assumes that speed and density follow a linear relationship?

- Greenshields model
- Travel flow management model
- Newell-Daganzo Merge model
- Microscopic model

Answer: Option a

Explanation: The Greenshields model assumes speed and density follows a linear relationship.

5. What is time spacing?

- It is the inverse of flow.
- It is the inverse of time headway.
- It is the inverse of density.
- It is the inverse of speed.

Answer: Option c

Explanation: Spacing is referred to as the inverse of density.

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