Zanjan University, Zanjan, Iran
Optimisation of urban traffic flow at a four by four network
M. Ebrahim Foulaadvand and Somayyeh Belbaasi
Within Nagel-Schreckenberg cellular automata, we model the traffic flow in a small city network comprising of two south to north and two east to west streets. The network is composed of four intersections each carrying unidirectional traffic flow. Cyclic boundary conditions are applied to the streets. Signalised traffic lights control the traffic flow at each intersection. The control parameters of the problem consist of density of cars in streets, cycle lengths of the traffic lights and the green times distribution at each signal. By extensive Monte Carlo simulations, we obtain the flux of each street and correspondingly the total network throughput in terms of parameters. It is shown that total current of the network exhibits nontrivial dependences on the value of the network's parameters. Our results shed more lights on the problem of city traffic optimisation.

HU Mao-Bin
School of Engineering Science, Hefei, China
Traffic dynamics based on local routing strategy in a weighted scale-free network
Mao-Bin Hu, Rui Jiang, Wen-Xu Wang, and Qing-Song Wu
Summary: The paper is about traffic dynamics on network such as internet.

Ever since the small world and the scale-free properties were identified, the complex networks have received much attention of the physicists. Due to the importance of large communication networks such as the Internet and WWW in modern society, dynamics of information flow have drawn more and more attention from physical and engineering fields.
In most of the real cases, a complex topology is often associated with a large heterogeneity in the capacity and intensity of the connections, i.e., most networks are weighted networks. However, to our knowledge, the traffic dynamics have been investigated only in unweighted networks so far. Therefore, in this paper, we carry out a study of traffic dynamics in a weighted scale-free network.
To this end, the weighted scale-free network model proposed by Wang et al. is used as a framework to investigate the traffic dynamics. This model, by introducing a general strength-coupling mechanism under which the traffic and topology mutually interact, gives power-law distributions of degree, weight, and strength.
We assume that node $i$ can deliver at most $s_i$ packets per time step towards their destinations, where $s_i$ denotes strength of node $i$. If a packet's destination is found within the immediate neighbors of $l$, the packets will be delivered from $l$ directly to its target and then removed from the system. Otherwise, the probability of a neighbor node $i$, to which the packet will be delivered is as follows: $$ P_{l\rightarrow i} = \frac{w_{li}^{\alpha}}{\sum_j w_{lj}^{\alpha}} ,$$ where the sum runs over the immediate neighbors of the node $l$. $\alpha$ is an introduced tunable parameter. Furthermore, we set the capacity of link connecting nodes $i$ and $j$ as $\max(\beta w_{li},1)$, where $w_{li}$ is weight of the link connecting nodes $i$ and $j$.
Our simulations show that when $\beta\rightarrow \infty$, i.e., the capacity of every link is very large, the network capacity is reached at $\alpha=\alpha_c$ larger than $1$. Both the network capacity and the value of $\alpha_c$ remain unchanged with the decrease of $\beta$ provided $\beta$ is larger than a threshold $\beta_{c1}$. When $\beta$ is less than $\beta_{c1}$, the capacity of some links will be reached from time to time. As a result, some packets are delayed, accordingly the network capacity decreases. Furthermore, we find that $\alpha_c$ increases with the decrease of $\beta$ when $\beta$ is less than $\beta_{c1}$. Nevertheless, when $\beta$ becomes smaller than the second threshold $\beta_{c2}$, $\alpha_c$ begins to decrease with the decrease of $\beta$.
In addition, we find $R_c$ tends to be a constant with the decrease of $\alpha$. This constant decreases with the decrease of $\beta$ for $\beta$ is less than $\beta_{c1}$ . When $\alpha$ is negative and $|\alpha|$ is very large, the probability that links with large weight are chosen to deliver packets is very small. This implies that even if we cut off the links with large weight, the network capacity will remain essentially unchanged.
Furthermore, the average number of packets on nodes and delivered through links, the travel time and travel distance of packets are also investigated. Finally, a comparison with the results from unweighted network traffic is made.

Moscow Institute of Physics and Technology, Russia
About one model of road flow interactions for heavy traffic in big cities
Yaroslav A. Kholodov, Alexander S. Kholodov, Nikolai V. Kovshov
We present a model of traffic flow in a system of roads in big cities. Depending on the volume of the traffic the topology of the flow is changing by switching direction of lines and traffic control signal operation.
Our model utilizes solution of the corresponding boundary-value problem for the hyperbolic partial differential equations. This underlying physical model is based on the barotropic gas equation analog for the graph edges (roads). As the boundary conditions in the branch points (the crossroads) we used an analog of the Poiseuille's law in gasdynamics together with the law of vehicle flux conservation. The road net is described as a set of separate roads (graph edges) connected by the crossroads (graph branching points). The entrances and exits of the road net are the edges with the boundary conditions specified at one end. The key problem is to set up correctly the equation of the state of the traffic flow by using experimental data.
The existing experience for such net computational models [1-2] proves that on the state-of-the-art computers this approach allows solving efficiently the sufficiently complicated ?global? problems for traffic flows on graphs with flexible topology.
To verify our model we made simulations of the entire Moscow city district within ?Sadovoe? transport ring. The distribution of the road flux velocities and the road flux values in the Central District of Moscow City were obtained for 3 hours interval after the start of the road traffic. Values of the road fluxes were set in accordance with the experimental measurements at the entrances, while free boundaries conditions were set on the exits. As the result the essentially nonuniform road flux distribution was found with traffic congestions in the appropriate places. Results of the calculated road flux values on the graph exits matched experiment data.
[1] Alexander S. Kholodov, Yaroslav A. Kholodov, Computational models on graphs for nonlinear hyperbolic system of equations, ASME 2004 PVP, Volume 476, No. PVP 2004-2580, P. 161-167, 2004.
[2] Kholodov Y.A, Kholodov A.S., Kovshov N.V., Simakov S.S., Severov D.S., Bordonos A.K., Bapaev A.Z., Computational models on graphs for nonlinear hyperbolic and parabolic systems of equations. Proceedings of the III European Conference on Computational Mechanics, Springer, eds. C. A. Mota Soares et, al., P. 2279.1-2279.19, 2006.

A.M. Prokhorov General Physics Institute, Russia
Three-frame algorithm of car path reconstruction from airborne traffic data
Dmitry Klochkov, Namik Gusein-zade, Ihor Lubashevsky, Sergey Zuev
The airborne traffic monitoring system form a novel technology of detecting the main characteristics of traffic flow on highways as well as transport network of mega cities. Currently it is under development and, it seems, will have unique capabilities for determining the flow rate, the vehicle velocity, and density simultaneously as well as for detecting spatial structure of traffic flow on road fragments with complex topology.
The optical digital camera located on an airborne platform produces a series of images which then are processed to single out the detected vehicles. In this way the video data are converted into the time sequence of frames containing the vehicle coordinates. At the next step it is necessary to reconstruct the observed vehicle motion by identification of succeeding positions of individual vehicles in the frame sequence. Exactly this reconstruction is the main objective of the given work.
A three-frame algorithm is developed to identify the succeeding vehicle positions and implemented in software. It is mainly based on choosing the neighboring points in the frame sequence characterized by a minimal acceleration. The virtual road was created to verify and optimize the developed algorithm for the noised data. Using the virtual road the feasibility of reconstructing the individual vehicle paths is analyzed depending on the noise properties. In particular, it is demonstrated that the found vehicle paths can be used to calculate the mean traffic flow characteristics for rather noisy data. Finally recent empirical data collected during pilot helicopter flights are analyzed using the given algorithm.

Université Paris Sud - IEF
Performance evaluation of VANET under realistic vehicular traffic assumption
Muriel Mabiala, Anthony Busson, Veronique Veque
Vehicle-to-vehicle communication has become a very challenging topic in recent years. Vehicles equipped with devices capable of short-range wireless connectivity can form a mobile ad hoc network, called a Vehicular Ad-hoc NETwork (VANET). In such networks, two vehicles which are not in the radio scope of each other can communicate by using other vehicles as relay.
In this work, we investigate two aspects of these particular networks: topological properties of VANET and routing protocol comparison. The originality of this work is that we use an analytical model and a vehicle traffic simulator which allow us to take into account realistic vehicular traffic patterns in the evaluation of the network aspect.
We first study the properties of the VANET in terms of topology and connection lifetime. More precisely, we study the probability that there exists a path (a vehicle subset which can be used as relay to reach the destination) between a source and a destination as function of the vehicle density and the source-destination distance. When there is a path, we study the lifetime of this path. These two quantities allow us to envisage the kind of applications which could be supported by the VANET. It appears that when the density of vehicles is small the network is often disconnected and communication between distant vehicles becomes impossible. When the path exists, the connection lifetime is generally less than a couple of minutes. Therefore, for user oriented applications (advertising, chat, VoIP, etc.), a hybrid network would be more efficient. It would help the network to be connected and would increase its capacity.
The second part of our work focuses on the efficiency of the routing algorithm in the VANET. A routing algorithm is a distributed algorithm used by the nodes to learn the route to the potential destinations. There exist standardized routing protocols designed for ad-hoc networks. But VANET is a particular ad hoc network where the nodes (vehicles) move very fast. This introduces a high dynamism in the topology of the network which is difficult to manage. So, we compare the performances of different existing routing protocols in this context. We use two different simulators. The first one is a traffic simulator which emulates the vehicular traffic on a highway. It uses microscopic simulations. The second one is a network simulator (NS2) which simulates all the protocols (wifi, IP, UDP and the routing protocols) used by the nodes to communicate. The simulations show that reactive protocols are the most efficient in a VANET.

TADAKI Shin-ichi
Saga University, Japan
Packet flow and its temporal properties on networks
Shin-ichi Tadaki
The Internet is one of the most important modern media for daily communication. It gathers research interests from engineering and social viewpoints. It also attracts scientific interests recently in viewpoints of statistical physics. The structure of the Internet and its services such as WWW have been unveiled observationally and theoretically as small-world and scale-free network structures. The temporal properties of the packet flow on the Internet also have been reported to show power-law fluctuations.
The power-law fluctuations in the packet flow have been observed in shorter time scales than one day for avoiding the periodicity of human activities. Exclusion and queuing mechanisms in the Internet are thought to be an origin of the power-law fluctuations in the packet flow. The power-law fluctuations are found in longer time scales than months. The origin have not been clearly understood. Scale-free structures of the Internet are sometimes thought to be their origins.
We observe temporal properties of modeled packet flow in various types of networks by simulations. We will observe temporal properties of random packet flow on regular, random and scale-free networks. The scale-free structure of a network itself can not be the origin of power-law fluctuations. We will discuss the exclusion effects of packets and the effect of queuing at routers. We will discuss the effects of routing mechanisms.