Bede, Zsuzsanna - Péter, Tamás
3. Real traffic network
We chose Üllői Road in Budapest for a real presentation of the system since this is one radial main road of the city. The larger quantity of vehicles moving towards the centre in the morning and moving outwards in the afternoon is typical of this section. The other reason for this designation was the geometric condition. 3 lanes are available in both directions on this section. (Fig. 2.) These are constricted to only 2-2 lanes on the overpass.
If we take away one lane from either direction, at least one lane would still remain for the length of the full section.
Our model was prepared from a map, so we gave the length of the sections proportionally, according to reality. Firstly, we modelled the current state and then we reversed the controlling of a lane from north to south in the morning hours (from Kálvin Square to Ecseri Street). We examined the arrival times in the course of two kinds of simulations. We make the below mentioned statement on the basis of the preliminary measurements: if in the morning peak time we help the inwards moving traffic with plus one lane, then the journey time decreases by 50% on average, if we take away one lane in the opposite direction, then the journey time of the outgoing
Figure 2. The simulation of Üllői Street
Usually it is hard to get unique vehicle data from large traffic network models.
However, if the speed profiles belonging to different routes are available, then the optimal routes can be easily calculated. The model describing large traffic networks can be converted to a real-time track recommender, which calculates the best route with respect to the variation of the traffic. Based on the unique speed processes extracted from the macro models, it is possible to examine the single vehicle’s power demand and emission [EJJT; 2009].
The used model [(Péter, Bokor; 2007),(Péter, et al.; 2008)] is validated by the examination of a real section of Budapest [Bede, Péter; 2010]. Before starting the examination we have to take into consideration, that the simulated variation of traffic is based on statistical data. Because of this the acceptance of the simulated diagrams depends on the values measured on the road network.
Figure 4. Velocities and performances distribution
So we drove along the examined route and stored the real speed profiles using a GPS.
Comparing the speed diagrams stored during different runs showed that it is impossible to get twice the same profile. The drive cycles must be handled as different realizations of a stochastic process, and can only be examined with a statistical analysis. Keeping this in mind, we compared the simulated and measured data, as shown on Fig. 3. (we indicated the running-time on the horizontal axis). So in the course of the validation of the model we get the velocity profiles as the result of the traffic simulation, and we drove along the route nine times. We fixed the current position every second with GPS. We compared these data with the velocity profiles obtained from the simulation and we analysed the distribution of velocity and
Figure 3. Example of a speed profile obtained from the simulation together with measured GPS profile [Bede, Péter; 2010].
to the overall performance claims.
4.1. The results and the examination of accelerations
We began the comparison of the received speed values with the examination of the vehicle-based speed and power demand distributions. The model is validated and provides unique speed processes that are identical to the real measured ones. We analysed the simulated speed profiles with respect to the acceleration. The acceleration profiles show extreme values over the capabilities of vehicle in 10 - 15 points during the examined 4 kilometre long section. This phenomenon shows that the speed – density based macroscopic model does not contain an acceleration criterion.
Based on this result, it is necessary to apply a new criterion to the extreme values of the speed change in the model, providing that the accelerations remain in the permissible range.
x(t)’(n x 1) = <1/li>(n x n) [ K(n x n) x(t)(n x 1) + Kinp(n x m) s(t)(m x 1)] (3) The new criterion in a discreet model applying ∆t step:
If vi(t)’> amax, then: vi(t+∆t) = vi(t)+ amax∆t (i=1,2,…,n) (4) If vi(t)’< amin, then: vi(t+∆t) = vi(t)+ amin∆t (i=1,2,…,n) (5) Where: vi(t) on the ith section is the calculated speed of traffic, amin ≈ -3,5…-4 m/s2, amax ≈ 1,8 m/s2
Based on the acceleration profiles it can be stated, that our simulation model gives bad values only in case of sudden acceleration or deceleration. A speed profile sampled every second and the acceleration profile calculated from it consists 600-1200 points, while bad values occur in 5 - 25 points only, which is about 2 - 4%.
4.2. Resume
We filtered out the unreal acceleration and deceleration values, and recalculated the speed- and acceleration profiles. We experienced that there is an insignificant difference between the original and filtered speed profiles (the calculated difference is 0,46 % for the full time; 5,68 % for the critical points). The conclusion is that the effect of the filtering on the statistician processes examined by the macroscopic traffic model is insignificant.
However, when obtaining optimal routes (optimal trajectory) from the model it is important to ensure that there are no unreal acceleration values in the calculated speed and acceleration profiles! So, filtering is important when switching to microscopic models.
The phenomenon recognized here points out an interesting new problem connected to the macroscopic traffic models. The elimination of this phenomenon resulted the development of the model. We changed the model so, that it examines the acceleration values in every time point, and if one of them is outside the permissible range then the acceleration value will be limited. The model will process this modified speed function.
We examined a general mathematical model describing the Reversible Lane System.
Our descriptive mathematical network model is a positive non-linear dynamic system, and it is also important that it is a macroscopic model. The function of every element and the contacts between the elements can cease in case of direction change in any part of the network, and then new contacts and new functional elements are activated.
We examined how probable the availability of the optimal control in a sample network would be depending on the traffic density, using a new principle, which responds to the dynamic change of the structure of the network graph. It can be shown that the results from our model are in harmony with the real traffic values based on measurements made in road traffic systems working with Reversible Lane System, included in our literature references.
Acknowledgement
The project presented in this article is supported by OTKA CNK 78168.
This work is connected to the scientific program of the " Development of quality-oriented and harmonized R+D+I strategy and functional model at BME" project. This project is supported by the New Hungary Development Plan (Project ID: TÁMOP-4.2.1/B-09/1/KMR-2010-0002).
The work reported in the paper has been developed in the framework of the project „Talent care and cultivation in the scientific workshops of BME" project. This project is supported by the grant TÁMOP-4.2.2.B-10/1-2010-0009.
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