Traffic model (traffic planning)

Traffic model is a technical term in traffic planning and deals with the mapping of traffic processes in models . Depending on the depth of detail considered, there are microscopic , mesoscopic and macroscopic traffic models that consider traffic demand or traffic flow .

Traffic flow model

These models serve to make statements about the traffic flow and the traffic density on a given infrastructure. They are mostly limited to ( motorized , less often non-motorized ) road traffic . Various models are used for the traffic flow models.

The microscopic models depict individual driver / vehicle units with their respective individual characteristics. Because of the computational effort involved, these microscopic models are particularly suitable for small study areas. They are used, among other things, in traffic planning to simulate the effects of individual infrastructure measures and in adaptive cruise control to calculate a safe reaction to changes in speed of the vehicle in front. Well-known representatives of the microscopic models are the Nagel-Schreckenberg model or the vehicle follow-up model by Rainer Wiedemann, which is one of the most frequently used in planning practice due to its use in VISSIM .

The Cell Transmission Model (CTM) allows calculations in the microscopic, mesoscopic and macroscopic range. This depends on the size of the traffic cells used .

The macroscopic models only depict the traffic in its mass, individual driver / vehicle units are not considered. These models allow statements to be made about traffic flow and traffic density. Such statements can be interpreted with a fundamental diagram. The traffic status (i.e. whether the traffic is flowing freely or is stowed ) can thus be described. Areas of application for these models are, for example, the congestion forecast in large transport networks such as the German motorway network. These models include, for example, the Section Based Model and the Sasonal autoregressive cross-validated model (SARIMA), which is based on the autoregressive integrated moving average (ARIMA).

Transport demand model

These models mostly work on a macroscopic level and are mainly used to forecast traffic .

For this it is necessary to divide the planning area into equivalent traffic cells / traffic districts. Their size, homogeneity and availability of sociodemographic data influence the accuracy of the later model results. The traffic cells are connected to one another by traffic lines. Traffic cells and traffic lines together make up the network model.

Four calculation steps can be carried out within the traffic model to determine the traffic demand:

Traffic generation

The traffic planner determines the degree of traffic generation of a traffic cell via the existence function of a cell. Different amounts of traffic are generated depending on whether a cell is used as a place to live or work . This data can be taken from the statistics or calculated. Common calculation models for this are the characteristic value model, regression analysis or the increase factor model . The result is information on the source - and target traffic . ${\ displaystyle Q_ {i}}$ ${\ displaystyle Z_ {j}}$

Traffic distribution (traffic destination selection)

By calculating the generation of traffic, it remains unclear to which other traffic cells the traffic is distributed.

There are different target dialing models. The so-called random model is used for small study areas and areas in which spatial resistance does not play a major role . The source and destination traffic calculated in traffic generation are distributed to the traffic cells proportionally to the total traffic volume. ${\ displaystyle Q_ {i}}$ ${\ displaystyle Z_ {j}}$ ${\ displaystyle V}$ ${\ displaystyle v _ {\ text {i, j}} = {\ frac {Q_ {i} \ cdot Z_ {j}} {V}}}$

One of the first models that also took distances into account was the so-called gravitation model, which was used in Lill's travel time law as early as 1889 . With this calculation of the traffic distribution one assumes the assumption that a traffic cell behaves like a gravitational point, i. H. a cell gets more attraction, the more mass it has. As the distance increases, the attraction force of the cell decreases. This gravity model comes from mechanics and reproduces the traffic distribution within the planning area relatively precisely. ${\ displaystyle R = {\ frac {Q * Z} {D ^ {2}}}}$

The logit model assumes that the destination selection consists of a deterministic and a stochastic part. A natural exponential function is used as the evaluation function for the traffic .

In the basic model of target selection , evaluation functions such as those mentioned above are multiplied by source and target-side as well as modifine factors. These factors are determined so that the traffic distribution corresponds to the previously determined individual traffic volumes. with the boundary conditions: ${\ displaystyle v _ {\ text {i, j, k}} = B _ {\ text {i, j, k}} * fq_ {i} * fz_ {j} * fa_ {k}}$

${\ displaystyle Q_ {i} ^ {\ text {min}} \ leq Q_ {i} = \ sum _ {j} \ sum _ {k} {v _ {\ text {i, j, k}}} \ leq Q_ {i} ^ {\ text {max}}}$ , With ${\ displaystyle Q_ {i} ^ {\ text {min}} \ leq Q_ {i} ^ {\ text {max}}}$

${\ displaystyle Z_ {j} ^ {\ text {min}} \ leq Z_ {j} = \ sum _ {i} \ sum _ {k} {v _ {\ text {i, j, k}}} \ leq Z_ {j} ^ {\ text {max}}}$ , With ${\ displaystyle Z_ {j} ^ {\ text {min}} \ leq Z_ {j} ^ {\ text {max}}}$

${\ displaystyle A_ {k} ^ {\ text {min}} \ leq A_ {k} = \ sum _ {i} \ sum _ {j} {v _ {\ text {i, j, k}}} \ leq A_ {k} ^ {\ text {max}}}$ , With ${\ displaystyle A_ {k} ^ {\ text {min}} \ leq A_ {k} ^ {\ text {max}}}$

One possible calculation of these factors is the so-called Furness algorithm .

One of the problems with the aforementioned models is that they react strongly to small changes when the costs are close together. The so-called EVA-1 function compensates for this disadvantage, so that the traffic flow distribution only differs significantly when there are major differences.

The result is recorded in a square traffic flow or source-destination matrix (also known as OD matrix (origin-destination)).

Choice of mode of transport (traffic distribution)

When choosing the means of transport, the distribution of traffic between individual (MIV = motorized individual transport, NIV = non-motorized individual transport) and public transport (ÖV) - the so-called modal split - is determined. Pedestrian and cyclist traffic (NIV) must also be considered in order to enable the later calibration of the collected data. In order to obtain realistic values for the calculation, the correct selection of influencing variables must be made. When choosing a means of transport, a distinction is made between three use cases:

Choice Riders can choose between public and private transportation.
Captive riders have to use public transport (e.g. due to the lack of a car)
Captive drivers must use private transport (e.g. to transport cargo)

Trip End / Trip Interchange

The two previous work steps can be used both in this order (so-called trip interchange model (TIM)) and vice versa (so-called trip end model (TEM)). With the TIM method, the traffic volumes are first distributed between the traffic cells and then distributed to the individual modes. With the TEM method, the entire traffic volume is first divided into the individual modes and only later distributed to the individual traffic relationships. Depending on the chosen distribution method, these procedures can lead to different results.

Traffic allocation (choice of traffic route)

The values determined in the above calculation methods can be displayed in a matrix . Traffic reassignment determines which route traffic will take to get from source to destination. The traffic planner can choose between four calculation models:

Bestweg method
The traffic always chooses the route with the shortest journey time.
Simultaneous assignment
The probability of the route choice is distributed over all possible routes
Stochastic procedure
Calculation like simultaneous assignment, only with the influence of an error size due to incorrect behavior of road users.
Limited capacity procedure
Realistic mapping of the route choice under the influence of all factors such as B. Speed, phase plans of traffic lights and risk of traffic jams.

literature

Henning Natzschka: Road construction: design and construction technology. With 178 tables. BG Teubner Verlag, Stuttgart 1996, ISBN 3-519-05256-3 .
Schnabel / Lohse: Basics of road traffic engineering and traffic planning. Verlag für Bauwesen, Berlin, 1997, ISBN 3-345-00567-0 .

References and comments

^ Rauch / Hübner / Denter / Babitsch (2019): Improving the Prediction of Emergency Department Crowding: A Time Series Analysis Including Road Traffic Flow. Studies in health technology and informatics, 260, pages 57-64
↑ see en: Autoregressive integrated moving average

[1] Rauch / Hübner / Denter / Babitsch (2019): Improving the Prediction of Emergency Department Crowding: A Time Series Analysis Including Road Traffic Flow. Studies in health technology and informatics, 260, pages 57-64

[2] see en: Autoregressive integrated moving average