PRINCIPLE OF MODELING THE URBAN STREET NETWORK

E. B. Khilazhev, V. I. Malyshkin, N. P. Baida

(Presented by the Department of Computer Engineering)

The choice of a quasi-optimal strategy for regulating street traffic for a specific situation by means of a natural experiment on a street network is difficult for several reasons. The principal ones are: high cost; considerable expenditure of time; the impossibility of using a given strategy for another network without modification; the random nature of changes in the traffic flow in time and space. It is more expedient to choose and investigate regulation strategies on a mathematical model of traffic flows in a street network. The random nature of the flows can be taken into account by using the method of statistical trials. The large volume of computations in this method makes it necessary to resort to the use of a digital computer. At the same time, use of the model and the introduction into it of corrections and improvements are also facilitated, especially if automatic programming is used to describe the model.

It becomes possible to investigate, one after another, several regulation strategies on a given network and to evaluate them according to selected criteria.

By restoring the initial numbers in the random-number generator (RNG), one can repeat a single situation the desired number of times. By entering other values of the geometric dimensions of the network or of the flow parameters, one can investigate the effect of one regulation strategy on various street networks and on different flow distributions. Proceeding from the aims of modeling, the requirements for the model can be formulated. It must:

1) take into account the random nature of traffic flows, the pulsed character of flows leaving intersections, the effect of the breakup of platoons of vehicles on long sections between intersections, and the possibility of any intersection operating according to a fixed cycle or a self-regulation algorithm;

2) describe intersections of any complexity; as far as possible, a large number of intersections, i.e., a more extensive network;

3) allow rapid replacement of the regulation strategy, the parameters of traffic flows, the geometric dimensions of the street network, and the algorithms of intersections.

Several ways of constructing such a model are possible. According to the representation of traffic flows, three methods of construction can be distinguished [1]:

1. Modeling the behavior of each vehicle separately along the entire route in the network; here greater time expenditures are required, but high model accuracy is ensured.

2. Modeling the traffic flow as continuous, without distinguishing individual vehicles; the time expenditures are relatively small, but the model’s accuracy deteriorates.

3. A combined method: at intersections individual vehicles are considered, while on streets—platoons, characterized by the number of vehicles in them. The time expenditures, compared with the first method, are reduced, while the model’s accuracy decreases only slightly.

Such a combined model was proposed and developed by Siemens [1—3].

Disadvantages of the model:

a large amount of memory is required to represent intersections in the computer;

the time expenditures remain unjustifiably large;

the effect of platoons breaking up on long streets is not taken into account.

It is proposed to construct a model with flows represented by their density, without distinguishing individual vehicles throughout the entire network. The accuracy of the model can be increased by using statistical data and the results of mathematical modeling of the microstructure of the traffic flow, in which the behavior of individual vehicles on an element of the street network was investigated [2, 3].

Description of the Model

All input streets of the network being modeled have zero length and adjoin the corresponding intersections. The TSC generates the density of the vehicle flow on input streets for a unit modeling cycle (3—10 sec). All internal streets have arbitrary length; they are assigned the numbers of the initial and terminal intersections. If a street is longer than 500 m, the flow emerging from it may be considered purely random; therefore such a street may be replaced by an input street, the flow intensity on which is a function of the input flow of the initial intersection. With a shorter street length, there may be located on it at the same time no more than 10 platoons of vehicles in both directions (average speed—10 m/sec, minimum cycle—20 sec). The routing of vehicles is carried out in platoons, which are determined by the density of vehicles in it, the distance from the exit point, and a width that is a function of distance. Each street is assigned a maximum capacity; when it is exceeded, a queue is recorded. An intersection has 4 input and 4 output cells; intersections formed by the crossing of 5 or more streets are broken down into a number of simpler ones. Two-phase intersections with low intensity (up to 10% of the total traffic vol—

Fig. 1. Layout of a simple two-phase intersection

Fig. 2. Layout of a complex intersection

of movement) for left turns are considered simple; crews are routed through them along routes fixed in space and by phase in accordance with the mock-up (Fig. 1). Intersections with a high intensity of left turns or with more than two phases are considered complex. Crews are routed through them along routes fixed in space (Fig. 2), with indication of the phase numbers in which movement along these routes is permitted. Such a modeling scheme makes it possible to model up to 12 phases with, theoretically, any combination of routes for passing through the intersection. The operation of traffic lights according to a rigid cycle is specified by a fixed phase duration; under automatic regulation, only the minimum value of the green phase is rigidly specified, and the extension of the phase is set by means of a GSC, whose parameters depend on the flow density in the corresponding input cells of the intersection. The exit of crews from the network is modeled by periodic (once per unit modeling cycle) clearing of the corresponding output cells of boundary intersections.

By adding to the program a simple district-communication block, which processes and stores flows at some boundary of a district, it is possible to model the joining of two districts controlled from different dispatch centers.

The enlarged block diagram of the model is presented in Fig. 3.

Fig. 3. Block diagram of the model

1 — input of initial data, preparation of working cells, 2 — generation of flows on input streets, 3 — counter of input streets, 4 — check of the criterion of intersection complexity, 5 — modeling of a complex intersection, 6 — modeling of a simple intersection, 7 — intersection counter, 8 — modeling of internal streets, 9 — counter of internal streets, 10 — increment of the internal time of the model, 11 — check of completion of modeling, 12 — preparation and printing of results, 13 — stop, 14 — district-communication block.

The program makes it possible to investigate strategies for controlling traffic on street networks of the desired type at various prescribed flow intensities.

REFERENCES

1. U. Gross et al. Simulation und Steuerung von Verkehrsnetzen, Electronische Rechenanlagen, No. 4, 1965.

2. R. Böttger. Simulation von Strassenverkehr mit Datenverarbeitungsanlagen, Neue Technik, No. 4, 1968.

3. R. Böttger, G. Bretschneider. Simulation von Strassenverkehr auf einem Digitalrechner, Nachrichtentechnische Zeitschrift, Heft 1, T-1, 1965.