AU2005100125B4 - Scale free network of urban traffic - Google Patents

Description

2 Description [0001] Random graphs have been the traditional means in studying the traffic networks. The defining feature of random graphs is that they are statistically homogenous and their degree distribution has an exponential form.

[0002] From studies undertaken by Mojarrabi et al [4a,4b], It has become clear that the simple statistical model of random graphs is inadequate for describing the topology of the real traffic network. The real traffic network shows the small world phenomena and is highly clustered.

[0003] In addition, the evolution dynamics of the real traffic network undergo topological phase transitions, which is different from that of random graphs.

[0004] Mojarrabi et al proposed the origin of this class of network within urban traffic is due to the competitive nature of the nodes. The competition between nodes is the origin of the gradient within the traffic network [4a and its listed references].

[0005] Toroczkai and Bassler (2004) in an important paper have shown that a network with gradient induced flows will generate a certain structural hierarchy in which a small but significant number of the nodes assume a far greater role in the shape and functioning of the network. i.e. the gradient networks are scale free networks with the power law distribution of the form k-Y (k=degree). An important result of their findings is that the traffic jamming is limited in scale free networks.

[0006] Scale free networks have attracted a considerable amount of interest among scientific communities in recent years. In fact, many real graphs in biology, sociology, Internet and telecommunication have found to exhibit scale free characteristics NASA has recommended the scale free network modeling as the future state of art for air transportation systems [0007] The scale free networks performance parameters would enable the traffic engineers to quantify the vulnerability, resilience and robustness compared to random traffic networks. This shows the importance of scale free network for future urban traffic design and management [0008] There have been many attempts to infer scale free network within the traffic network. However, the scaling exponent of the power law that governs the network architecture is initially unknown and difficult to find by traditional methods of traffic engineering based on random graph generalisation methods.

[0009] As a result, all research into the topological properties of traffic network have been failed to show the scale free properties.

[0010] In 1994, Mojarrabi et al succeeded in the first empirical evidence of the existence of scale free network within the traffic network [4b].

[0011] The present invention accordingly provides a method of improving a traffic network by: inferring, within the traffic network, a scale free network having a power law distribution; identifying properties of the scale free network, including the exponent of the power law; characterising the scale free network; and selecting one or more modifications to the traffic network, based on the characterisation, to more closely conform the traffic network to the identified properties of the scale free network.

[0012] Embodiments of the present invention comprise steps in which one can infer the properties of the scale free network within the urban traffic network and in particular, how to translate the result of such findings to the algorithm solution to measure the clustering coefficient and small world phenomena.

[0013] The scale free topology of the real traffic network has very important consequences on the functioning of traffic signals.

[0014] To explore whether the networks are scale free, we should look into the statistical profile of the degree distribution. For creating the statistical profile of the degree distribution, we consider nodes to be any sites, at which a vehicle stops or parks. Links are the pathways that allow one or more vehicles to travel between them. Traffic lights are nodes. [3,7 For example, a parked vehicle within the physical boundary of a house is treated as node with degree 1.

[0015] The number of vehicles that have stopped at the red signal of a traffic intersection is also its node degree.

[0016] We also select nodes based on fitness of the actions they have chosen [4a].

[0017] The fitness of the node can be measured by its proximity to other nodes, the site car park capacity, the time constraints and its betweeness measurement.

[0018] In the case in which the nodes are entangled in such a way that one cannot count their individual degrees, we select their nodes based on their fitness equation.

[0019] The neighborhood nodes can share their fitness in order to be in a better position to compete. An example of this type of fitness sharing is when a car is waiting its turn to park within a street parking site subject to a time restriction.

This may cause the traffic queue beyond the car. The fitness sharing allows the degree of these cars to be added to the node of the parked vehicle.

[0020] Super nodes are the ones that belong to the tail of the degree distribution.

[0021] If the fitness sharing results in creating a supernode, then it would be a critical point for traffic planning. The supernodes created in this way are called Entangled Supernodes.

[0022] Those skilled in the art will appreciate that once the statistical profile of the degree distribution is known, then we generally plot the degree probability distribution on a logarithmic scale. [1] [0023] The slope of the logarithm graph is the exponent y of the power function.

[0024] The exponent power of y is a fine-tuning parameter. The smaller the value of y, the more appearance of supernodes, and therefore the increase in value of the clustering coefficient of the traffic network. Our algorithm exploits the local clustering knowledge to find the optimal routing strategy for the traffic assignment.

[0025] With the fitness of the supernode, the traffic light would be synchronized to change the fitness at a local level.

[0026] Clustering coefficient is a measure of how many clustered subgraphs of three nodes (triangles) in the corresponding map generalization is present. It is a measure of the local structural order within the network. [0027] We can measure the clustering coefficient by the following algorithm: [0028] Find the car park capacity of each node i (ci).

[0029] Find the parking occupancy within each green signal phase for each node I (pi).

[0030] Calculate pi/ci for each node i.

[0031] Count the number of vehicles around the intersection with a red signal.

[0032] Calculate the maximum mean traffic queue at peak time for each intersection.

[0033] Calculate the local clustering coefficient for the intersection.

[0034] Calculate the average global clustering for the entire network.

[0035] Scale free networks provide an extremely efficient transport system, as vehicles can easily navigate within the network, through directing their flow toward the supernode or away from it.

[0036] The charactering properties of the scale free network create the boundary conditions in which one can optimise the minimum green time interval or the cycle length.

[0037] Optimisation Problem [0038] The achievement of small-world behavior is related to average path length L and the global clustering coefficient C. The average path length measures the efficiency of the network. It is defined as being the average number of links in the shortest path between any pair of nodes within a network [0039] The real traffic network has a limited number of main roads with longrange connections. The network should be designed in a way that it has the smallest possible average path length. [0040]. A sample distribution of the nodes will combine to form the basis of a basic network that then joins to create local clusters with a selective choice of links. In statistical mechanics, this corresponds to the selection of the particles within the energy levels.

[0041] Our optimization strategy is to group the nodes within the network into basic structures called Network Atomic Spectra. The network atomic spectra contains a given number of nodes with a distinct pattern with regard to their fitness distribution and their degrees distribution when centered around supernodes. Within each seed is also at least a traffic signal. An example of such configuration is the Marion Shopping Center in Adelaide, South Australia. It is a supernode attracting a significant number of vehicles. The neighborhood around the center provides a connected subnet of shortcuts in which L is smallest as the minimum value.

[0042] The atomic spectra unit classification then serve as a basis of our generalisation method.

[0043] The key idea of our solution is to increase the number of triangles for each node, while keeping the degree of each node unchanged for the given target y.

That may include reducing the maximum green time interval around the super nodes. This affects the route and short path selection.

[0044] This causes an increase in the clustering of the whole graph and a decrease in the fitness of the supernodes. The supernodes became unsatisfied. Increasing council parking lots around the vicinity of large shopping centers can compensate for this.

[0045] The algorithm is as follows: [0046] Generalise the urban traffic data based on the network atomic spectra classification strategy.

[0047] Select the optimal clustering coefficient based on the target scaling coefficient.

[0048] Calculate the clustering coefficient for each node i.

[0049] Calculate the average clustering for all nodes within the atomic spectra unit.

[0050] If the average clustering of the generating seed unit is less than optimal; [0051] Then choose another node j within the vinicity of the atomic spectra unit.

[0052] Apply the fitness sharing algorithm to the node j.

[0053] If the fitness of the node j is decreased and the node j is unsatisfied then [0054] Increase the parking lot or decrease the maximum green light interval for that node.

[0055] Continue the procedure for all other nodes in the generalized map.

[0056] calculate the global clustering coefficient.

[0057] The cycle length and phase duration is related to the average optimal global clustering coefficient obtained from the above algorithm.

[0058] The number of traffic lights is directly proportional to the global clustering coefficients. This will ensure the global connection of the network.

[0059] The minimum green time interval may only be extended until the maximally efficient strategy for the target scalability coefficient y, is achieved.

[0060] When adding new roads to an existing transport network, the planned scale free structure must be followed.

[0061] Those knowledgeable in the art will appreciate the embodiments of the present invention, and will lend themselves to new integrated computer management system based on the properties of scale free networks.

[0062] The programming would be based on the object technology. Both object technology and scale free networks exhibit Scalability and evolutionary transitions as their characteristics As a result, it is often easier to create the faster algorithm for the scale free network than the corresponding random traffic network.

EXAMPLE

[0063] A running example of the evolving network can be found around the vicinity of a large shopping centre in Adelaide. The shopping centre would services customers from the southern and southwestern regions of Adelaide Metropolitan area. The supernode attracts about 2500 vehicles within each traffic phase.

[0064] From our measurements, the scaling exponent y However, we also observed an unexpected sign of a characteristic dip at degree 2).

REFERENCES

Albert, R. and Barabasi, A. L. (2002) Statistical Mechanics of Complex Networks, Review of Modern Physics, Vol. 74, No. 1, 47-97.

Alexanddrov, N. (2004) Transportation Network Topologies, Langley Research Center, National Aeronautics and space Administration,

NASA.

Ikeda, Vogiatzis, Wibisono, Mojarrabi, B. and Woolley, J. E.

(2004b) Three Layer Object Model for Integrated Transportation System, Proceedings 1st International Workshop on Object Systems and Systems Architecture,Victor Harbor, Australia,11-14 January 2004.

[4a] Mojarrabi, Vogiatzis, N. (2004) Using Bose-Einstein Statistics to Minimise End-to-End delay in Dynamic Traffic Networks, Journal of Eastern asian Society for Transporation studies, EASTS, Vol 6, page 1398 [4b] Mojarrabi, B. and Mojarrabi, B. (2005) Scale Free Network of Urban Traffic, Malaysian Jurnal of Fizik, vol 27, No 1 or in IMFP 2005 Journal accepted papers.

Nishikawa, Motter, Lai, Y.C. and Hoppensteadt, F.C. (2002) Smallest Small World Network, Physical Review E, Vol. 66.

Toroczkai, Z. and Bassleri, K. E. (2004) Jamming is Limited in Scale Free Networks,Nature,Vol. 428, No., 716.

Vogiatzis, Ikeda, H. and Wibisono, W. (2004) On the Locality-Scope Model for Improving the Performance of Transportation Management Systems, Proceedings 27th Australasian Transportation Research Forum, Adelaide, South Australia.

Claims (4)

1. A method of improving a traffic network by: inferring, within the traffic network, a scale free network having a power law distribution; identifying properties of the scale free network, including the exponent of the power law; characterising the scale free network; and selecting one or more modifications to the traffic network, based on the characterisation, to more closely conform the traffic network to the identified properties of the scale free network.

2. A method according to claim 1, wherein includes employing a model of nodal fitness.

3. A method according to claim 1 or 2, wherein includes measuring the scaling coefficient and the clustering coefficient of the scale free network.

4. A method according to any of claims 1 to 3, wherein the one or more modifications include one or more modifications to the sequence of traffic light signals within the traffic network. A method according to any of claims 1 to 4, wherein the one or more modifications include one or more modifications to the positioning of roads or traffic signals within the traffic network. Dated this 5f day of September 2006 Bahram Mojarrabi By his Patent Attorneys MADDERNS