IN DEGREE PROJECT TEKNIK,FIRST CYCLE, 15 CREDITS

, STOCKHOLM SWEDEN 2018

Modellering av kommunikationsnätverk för trafikledning

JENS FAGERBERG

LUCAS BERGSTRAND

KTH ROYAL INSTITUTE OF TECHNOLOGYSKOLAN FÖR ELEKTROTEKNIK OCH DATAVETENSKAP

www.kth.se

IN DEGREE PROJECT TECHNOLOGY,FIRST CYCLE, 15 CREDITS

, STOCKHOLM SWEDEN 2018

Modelling Communication Networks for Active Traffic Management

JENS FAGERBERG

LUCAS BERGSTRAND

KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE

www.kth.se

Sammanfattning

Restider, trafikstockningar och utslapp av vaxthusgaser i stadsomraden ar ettstandigt vaxande problem med okad urbanisering. Overvakning av trafikflodetvid trafikljus mojliggor aktiv trafikledning och stora forbattringar till dessaproblem. For att trafikljus skall kunna kommunicera behovs en grundlaggandenatverksstruktur. Detta kommunikationsnatverk kan centraliserat eller decen-traliserad, dar bada har for- och nackdelar. Om befintliga natverksmodeller,sasom Barabasi-Albert och Erdos-Renyi modellerna, studeras och modifieraskan en algoritm som genererar ett robust och sakert natverk utvecklas, vilkethar varit projektets huvudsakliga mal. For att sakerstalla att en optimal modellanvandes analyserades denna ur ett robusthetsperspektiv dar parametrar sasomgenomsnittlig nodgrad, natverksdiameter, klustring och effektivitet jamfordes.Natverkets robusthet prioriterades da det starkt bidrar till natverkets driftsakerhetvilket ocksa ledde till att en decentraliserad modell anvandes.

1

D3A: SMART INFRASTRUCTURES NETWORKS

Modelling Communication Networksfor Active Traffic Management

Jens Fagerberg and Lucas Bergstrand

Abstract—Emissions, travel times and traffic congestions inurban areas have become a central issue with increasing urban-isation. By actively monitoring and managing traffic flow viatraffic lights there can be extensive improvements in these areas.To enable communication between infrastructure componentsan underlying network is needed to route information. Thesenetworks can be both centralised and decentralised which bothhave advantages and disadvantages. By studying and modifyingexisting network models, such as the Barabasi-Albert and Erdos-Renyi, an algorithm that generate a robust and safe communi-cation network can be constructed, which has been the maingoal of the project. To ensure that an optimal model is beingused, robustness was analysed by comparing parameters suchas average node degree, network diameter, clustering and effi-ciency. Network robustness was prioritised as it ensures networkreliability and resilience and this led to the conclusion that adecentralised network model was suitable for the application.

I. INTRODUCTION

With increasing urbanisation and population growth, societyface extensive environmental changes and new problems arisethat require innovative solutions. The concept of applyingInternet of Things-technology to infrastructure is a rapidlygrowing field of study and market with an estimated annualrevenue of $88.7 billion by year 2025 [1]. This technologymay be used for autonomous vehicles, smart energy man-agement, home automation, traffic management and structuralhealth monitoring to mention a few.

As the number of vehicles has been increasing since year2000 [2] and by 2030, 60% of the world’s population areestimated to live in urban areas [3], it’s clear that congestionproblems have to be resolved in order to decrease emissions,travelling times and economic loss. As of today, economicloss caused by traffic congestion, in the U.S alone, are ap-proximately $180 billion annually [4].

Changes to the road network are either extremely expensiveor not possible. It has grown over time and countless roadsegments are independent projects being connected to eachother. Therefore, solutions has to be developed with this inmind and adapt to the current infrastructure.

One solution to congestion is active traffic management. Byenabling traffic lights to connect and exchange informationwith one another, traffic flows at junctions can be monitoredand actively managed. Similar studies have initially shown thatit’s possible to achieve a 26% reduction of travel times, 40%idle time reduction and 21% reduction in emissions [5].

Communicating traffic lights provides a solution to enableincreased efficiency for existing infrastructure. Providing analternative solution, instead of large scale changes in infras-

tructure which requires large monetary investments and takestime.

Another use for this technology is for public transportationrouting and urban planning. Data collected can not only beused to reroute bus lines in case of accidents or constructionsites but also be used to evaluate future investments in infras-tructure.

This project has focused on the communication infrastruc-ture needed to connect traffic lights to each other. The networkneeded can be created and analysed with network science andmodels existing in this field of research. It has also provideda method of robustness and performance analysis.

II. NETWORK SCIENCE

Network science is the study of networks. This involvescommunication networks, computer networks, biological net-works, social networks etc. Network Science provides a largenumber of tools for modelling, analysis and optimisation of anetwork.

Networks consist of nodes, connected by links. There area number of properties to consider in a network. Theseproperties and how they correspond to parameters of a com-munication network will be introduced in this section.• Node Degree: The number of links associated with the

node.• Weight: A link can be assigned a weight which can

represent i.e. transmission distance or cost. In our networkmodel, all links are unweighed as distances are smallenough to consider transmission times as instant.

• Adjacency Matrix: Matrix representation of links andnodes in the network. Elements of the square matrixindicate if two nodes are connected. If they are, theelement is equal to the weight of the link otherwise theelement is equal to zero. The adjacency matrix for theundirected network in 1 is

A =

0 1 0 11 0 1 11 1 0 10 1 1 0

(1)

• Degree Distribution: Degree distribution of a network isdefined as the distribution of probability that a randomnode has the degree k. This is an important aspect, as thedegree distribution describes the network in an efficientmanner and also enables simple comparison betweennetworks. This aspect will be discussed further in sectionVI.

D3A: SMART INFRASTRUCTURES NETWORKS

• Undirected and Directed Networks: As shown in figure1, networks can be both directed and undirected. In com-parison to the directed network, its undirected counterpartenables two-way communication. A communication net-work is therefore in most cases undirected, as two-waycommunication is desirable. Using undirected graphs willreduce computing time as the adjacency matrix becomessymmetrical.

Fig. 1. Undirected (left) and directed network (right).

• Shortest Path: As there are not only one path betweentwo given nodes. We are interested in the shortest pathbetween the two nodes, shown in figure 2.

Fig. 2. Shortest path between node 0 and 5 in yellow.

• Network Diameter: The longest shortest path betweenany two nodes in a network is called the diameter,dmax. This parameter determines how closely connectedthe network is, increasing L will generally decrease thediameter of the network.

• Connectedness: An important parameter of a networkis connectedness. A network is connected if and only ifall paths between two nodes are finite. If a network isnot connected there are parts of the network which isinaccessible, meaning you cannot reach all nodes in anetwork from any given node. An unconnected networkis not suitable for the purpose of communication.

• Clustering Coefficient: Clustering coefficient, Ci, mea-sures the local link density around a node, i, in otherwords, how many of the nodes connected to node i areconnected to each other.

Ci =2Li

ki(ki − 1)(2)

where Li denotes the number of links between the kineighbours of node i. A clustering coefficient of 1 corre-sponds to all local nodes being connected and a clustering

coefficient of 0 corresponds to all local nodes beingdisconnected, illustrated in figure 3.

Fig. 3. Two networks with C0 = 0 and C6 = 1

III. CENTRALISED AND DECENTRALISED NETWORKS

An important aspect to consider in the design of a com-munication network is whether the network should be cen-tralised or decentralised. Two different approaches with dif-ferent strengths and weaknesses. It’s important to analyseand compare these two approaches to be able to choose theapproach most suitable for the application.

A. Decentralised Network

In comparison to its centralised counterpart, which can beseen in figure 4, decentralised networks have no hubs. Thedegree distribution is more uniform, and messages are relayedfrom node to node until it reaches its final destination. Adecentralised network is harder to maintain as there are nohubs and all nodes has to handle multiple connections and in-formation routing. The increased complexity and connectivityof these nodes result in a more robust system as informationhas multiple routes to the final destination.

Fig. 4. Decentralised network.

1) Erdos-Renyi Model: The Erdos-Renyi (ER) model wasfirst introduced in 1959 [6]. This model is used to generatedecentralised, random networks from a given number of nodes.The most important aspect of the ER models is that theprobability of connecting two nodes is uniform and hence,the degree distribution of the network is Poisson-distributed.This is an important aspect to consider and will be discussedfurther later in the article.

D3A: SMART INFRASTRUCTURES NETWORKS

The network G is defined with, G(N,p), where N is thenumber of nodes and p is the probability threshold. Thenetwork is generated by choosing two nodes and generatinga random number between 0 and 1. If the random number isgreater than p, a link is placed between the two nodes. Thisprocedure is repeated for every possible link in the network.

This model inherits some important properties [7]:• If p > (1+ε) lnN

N the network will surely be connected,and vice versa.

• If Np < 1 the network will surely not have connectedcomponents larger than O(log(N))

• If Np = 1 the network will surely have a componentwith maximum size of N

23 .

• If Np > 1 the network will surely have a giant compo-nent.

These characteristics are of importance to the ER model asit allows the user, to some extent, to control network structure.

Decentralisation is the most important factor for our com-munication network. Downtime will increase congestions andeventually expose drivers to unnecessary risks, leading topotential economic loss and larger environmental pollutionwhich is the direct opposite of what’s desired.

With these definitions in mind, it was decided that for thisapplication, a decentralised approach is most suitable. Thisapproach would provide a network with higher robustnessand connectivity but also an infrastructure where an expensivedata centre that needs maintenance and personnel is avoided,effectively reducing cost.

Choosing a decentralised network also simplifies the analy-sis of the network as they can be modelled with the ER model.

B. Centralised Network

In the centralised approach there’s a clear hierarchy. Mes-sages are communicated to a central node and then relayed toits final location. All communication passes this central node.In the mathematical models these central nodes are hubs, witha lot of links to the smaller children. This approach with acentral server will result an easier system to maintain, the hubsneeds to be very sophisticated whilst the children are simplerand only need to gather data and relay to the hub, as seen infigure 5.

The hubs are the greatest strength and the biggest weaknessof the centralised network. It provides a natural node for anal-ysis of gathered data and can be used to easily communicatewith other nodes. Although if the hub is experiencing problemsand seize to function the whole network can be crippled asthere is no way for the nodes to communicate with each other.

A centralised approach would be suitable if a data centre isneeded to perform large, real-time calculations. Something thatcould become necessary if big data analysis is implementedto prevent congestions before they occur or if public transportroutes can be effectively changed whenever problems arise.Although, these calculations can be done remotely, and controlsignals could be sent to the network of traffic lights.

1) Barabasi-Albert Model: The Barabasi-Albert (BA)model was developed by Reka Albert and Albert-LaszloBarabasi during the late 1990s. Several real networks, such as

the World Wide Web, possess scale-free properties and growthby preferential attachment, which led to the development ofthis network model [8]. Most real network have power lawdegree distributions and not Poisson-distributions. The degreedistribution of these networks can be described mathematicallyas

pk ∼ k−γ (3)

where γ denotes at which rate degree probability decrease.Networks whose degree distribution follow a power law havescale-free properties. In these networks hubs exist, which arenodes with higher than average degree. The number of hubsare small, and the number of low degree nodes are high.

The BA model will produce networks with a power lawdegree distribution, where a small number of nodes has a largenumber of links and many nodes have very few links. Thisproperty is the main difference between the ER model and theBA model and will have an effect on how the communicationnetwork will be constructed, investigated further in sectionVI-A.

Fig. 5. Centralised network.

The method of generating a network using the BA model ismore complex compared to generating a network with the ERmodel. As you start off with two nodes and connect the nodes.Then you add a third node. This node will connect to eithernode 1 or node 2 or both. This is where the random aspectis present. For every new node, the probability for the nodeto connect to another node is proportional to the number oflinks of the other node. A node with twice the number of linkswill have twice the probability to be connected. The processis repeated until the desired number of nodes is reached.

With this method of generating the network, hubs will beformed as the probability is weighed by the degree of the node.Highest degree nodes have higher probability of connecting.This method is called preferential attachment.

D3A: SMART INFRASTRUCTURES NETWORKS

IV. REQUIREMENTS

As traffic flows and the probability for congestion heavilyvaries during a 24-hour period, it is clear that situations likemorning and afternoon traffic define what requirements thenetwork has to satisfy. If information is transmitted at a toolow frequency, congestions will still occur, and desired func-tionality wouldn’t be reached. Consequently, if information istransmitted at a too high frequency, network capacity will beaffected resulting in data loss or unnecessary hardware costs.

A. Technical Specification

Every traffic light, seen as a node in the network, hasto communicate certain information at a certain frequency.During i.e. midday and at night when very little congestionoccurs, there is small or no need for active control andtherefore the system could be in standby. When the systemis actively managing traffic, we’ve estimated that each nodeshould transmit the following information every 15 seconds.

• Current state: Green or red signal.• Consumed time in current state.• Any errors detected. If the traffic light is out of order,

then other rules at that intersection (signs etc.) should beapplied.

• Current traffic flow by evaluating sensor data.

This will be a data packet. The amount of information might betrivial, but doing appropriate optimisation from the beginningensures that the network is allowed to expand, and hardwarecosts can be reduced.

B. Economic Specification

As current infrastructure has to be replaced or modified,large investments are needed and small reductions in cost foreach unit lead to large decreases in the overall project cost.

Therefore, when constructing the network, the economicalaspect should be considered. Cost can be reduced by min-imising hardware requirements. This can be done by reducingthe amount of data transmitted, minimise connections to otherunits and for wireless systems, reduce transmission range.

V. METHOD

A. Software

Algorithms have been programmed in Python in which thelibrary NetworkX has been utilized for network constructionand analysis. NetworkX provides a framework to constructgraphs. It also provides methods for calculating parameters,degree distributions and creating graphical representations ofnetworks.

NetworkX, and the authors personal preferences were themain reasons why Python was chosen as programming lan-guage over MATLAB. The documentation for NetworkX [9]has been thoroughly studied.

B. Network Models

As networks appear in technological, biological and socialapplications there is, as a result of this, various models thatquantifies different characteristics of these networks. Intu-itively, we do not expect any similarities between a socialnetwork and a communication network, but this is not the case.Networks in different applications exhibits similar behaviour.We’ll investigate if some of these models may be suitable forgenerating the network that connects traffic lights.

1) Barabasi-Albert Model: Introduced in section III-B1,this model generates a random network with scale-free proper-ties, where a preferential attachment-mechanism is used, andthe node connectivity is chosen beforehand.

Preferential attachment is a process which propose thatnodes with high degree has an increased probability to connectto new nodes in the network.

The probability for a newly added node to connect toanother node i is calculated by dividing the degree of nodei by the sum of degrees of pre-existing nodes, as shown inequation 4.

pi =ki∑j kj

(4)

which states that nodes with higher degrees achieve a higherprobability.

As the network possess the scale-free property the degreedistribution follows a power law. Average path length, l,increases proportionally to the network size

l ≈ lnN

N lnN(5)

2) Unit Disc Model (UD): Proposed in 1995 [10], thismodel aims to better model the behaviour of wirelesstransceivers. It is a popular model in which the transmissionrange of each node is taken into consideration. One flaw ofthis model is that it assumes that every transceiver has aperfectly circular broadcast range, which in reality isn’t trueand affected by antenna construction, antenna placement andphysical obstructions.

The probability for two nodes to connect in this model arebased on the Euclidean distance

pi,j = |xi − xj |< dt (6)

between the two nodes. This distance has to be lower than athreshold distance, which is defined by the transmission rangesof the nodes.

3) Adjacent Nodes Model (AN): The project group at-tempted to develop their own network model in order to gainunderstanding about the complexity of networks and theirgenerating algorithms. The base idea is to connect one node toa number of nodes in its proximity. This value can be changedtogether with a maximum distance between two nodes. Com-pared to the Unit Disc and BA model, this takes both nodeconnectivity and maximum distance in consideration.

When the algorithm generates the network, it will connect tothe adjacent nodes until it reaches either the maximum distanceor maximum connections thresholds.

D3A: SMART INFRASTRUCTURES NETWORKS

C. Geographical Data

Fig. 6. Traffic lights in Stockholm.

In order to generate a communication network for trafficlights in Stockholm, information regarding their positioningthroughout the town is needed. Data was acquired fromStockholm Municipality. GPS-position provide not only valu-able information regarding network approach but also thegeographical constraints needed if wireless communicationis being considered. In Appendix A an extraction of thegeographical data is shown, where the coordinates are in RT90and SWEREF format.

D. Network Generation

To compare and analyse networks it is needed to programalgorithms that generate these. This has been done withPython and NetworkX. The procedure to generate ER and ABnetworks has been discussed in section II.

As it has been decided to have decentralised approach,the model needs to reflect this approach, while using thegeographical data gathered. It’s theorised a traffic light willaffect nearby traffic lights more than distant ones. Therefore,the model has to be complemented to take into account thegeographical location of the traffic lights.

In order to satisfy the need for larger connectivity incloser proximity and having a decentralised approach to thenetwork, the authors propose a modification of the ER model.Instead of having a completely random network with a uniformprobability, the probability is weight with respect to distancebetween the two nodes. The probability should be proportionalto the inverse of the distance, rij. Thus, the probability can bedescribed as

pij =Cirij

(7)

Where Ci is a scale coefficient. The scale coefficient isdifferent for every node i and it defined as follows,

Ci =1∑N

j=11rij

(8)

Another version of this model has also been considered,when the probability is proportional to the inverse of thedistance squared. These models will be referred to as the Rand R2 model respectively.

VI. ANALYSIS AND OPTIMISATION

In this section we analyse network parameters in order todetermine the properties of the networks and thus determinewhich models are suitable for connecting traffic lights.

A. Degree Distribution

The degree distribution is a statistical presentation of allnode degrees in a network. It’s an intuitive representationand contains information about the network structure. Thismeasure has been mentioned in section II and in this section,histograms will be presented for each network type.

1) Erdos-Renyi Network: In the ER model, the event thatpairs of nodes connect are independent from each other,therefore, this model yields a network, that for large N,are Poisson-distributed. The structure of this network can bemodified by changing the probability for two nodes to connect,which has been explained in section II.

Fig. 7. Degree distribution for Erdos-Renyi model.

In figure 7 we can observe the typical appearance of aPoisson-distribution with a mean of approximately 30 con-nection, lowest node degree around 14 and the highest degreearound 44.

D3A: SMART INFRASTRUCTURES NETWORKS

Fig. 8. Degree distribution for Barabasi-Albert model.

2) Barabasi-Albert Network: In comparison to the ERmodel, this model captures phenomenons observed in real-world network. The degree distribution follows a power-law, indicating the existence of hubs caused by preferentialattachment.

Figure 8 represents the degree distribution of BA networkwith edge connectivity of five. We can see that the Theexponential reduction in node degrees indicate that we have afew hubs of different sizes, and that our network probably issplit into several components.

3) Unit Disc Model: The unit disc models yields a degreedistribution that share similarities with the degree distributionfor the Erdos-Renyi network.

Fig. 9. Degree distribution for Unit Disc model.

It can be observed in figure 9 that the mean node degree isaround 8. Not taking preferential attachment into considerationin our model might be one of the reasons why we don’tobserve a degree distribution following a power law.

B. Network resilience

Data transmitted across the network has to be protected inorder to ensure the integrity of the network as well as safety ofdrivers, pedestrians and vehicles. Unauthorized users gettingaccess to control signals could have catastrophic consequencessuch as traffic accidents and road blocks which obstructemergency vehicles.

The information can be protected by using data encryptionand firewalls, but also by isolating the network to communicateon a separate frequency or with a private protocol rather thanpublic options like 802.11 WLAN and 4G.

Ensuring that a network can withstand malicious attacks areof great importance but is beyond the scope of this project.Although, robustness analysis do affect network resilience,which is discussed in the next section.

C. Robustness analysis

Robustness states how well a network can ensure function-ality when nodes, link or other parts of the network breakdown which obstructs data transmission. Networks with highrobustness will avoid cascading failures when equipment failat one location by having alternative paths that data can betransmitted through.

There are several important parameters that’ll be consideredwhen analysing robustness of a network [11].

1) Average shortest path: There can be multiple pathsbetween a pair of nodes. Although, the shortest path denoteshow many nodes the information has to pass to reach itsdestination. The average shortest path distance across thenetwork indicates how dependent nodes are of each other.If the average distance is 1, then it can be concluded thatall nodes directly connected to each other. Therefore, a lowervalue indicates higher robustness.

a =1

N(N − 1)

∑i,j∈G

di,j (9)

Where di,j is the shortest distance between node i & j and nis the total number of nodes in the network G.

2) Edge connectivity: The number of edges that can beremoved prior to the networking becoming disconnected. Anetwork is robust if it stays connected even though edges arebeing removed, hence, a large edge connectivity indicates thenetwork is robust.

3) Average clustering coefficient: The local clustering coef-ficient of a node is calculated as the proportion between linksin its neighbourhood divided by the number of possible links.

〈C〉 = 1

N

N∑i=1

Ci (10)

Ci is the local clustering coefficient, defined in section II.A higher average clustering coefficient means more links

between neighbouring nodes and therefore the network is morerobust.

D3A: SMART INFRASTRUCTURES NETWORKS

4) Network efficiency: Network efficiency is based on theidea that information between two nodes travels along theshortest path. The efficiency of this communication is definedas the inverse of the shortest distance. The average efficiencyacross the network measures the mean flow-rate of information[12].

E =1

N(N − 1)

∑i 6=j∈G

1

di,j(11)

As the efficiency is proportional to the sum of inverse of thedistance, a high efficiency indicates higher robustness.

5) Algebraic connectivity: It has been proven [13] that al-gebraic connectivity is defined as the second lowest eigenvalueof the Laplacian, which has been described in previous section.The magnitude of this is a measure of how well the networkis connected and is zero only if and only if the graph isdisconnected. Considering this, a higher value result in higherrobustness.

6) Number of spanning trees: A spanning tree is defined asa graph which includes all available nodes without any cycles.In order for a spanning tree to exist in a network, it has tobe connected and therefore a higher number of spanning treesindicate a more robust network. Kirchoff’s Theorem states thatthe number of spanning trees in graph G can be calculated as:

t(G) =1

N

N∏i=2

λi (12)

Where λi are the non-zero laplacian eigenvalues.7) Effective graph resistance: By looking at the network

as an electrical circuit, all links can be considered (for anunweighed network) having resistances of 1 Ohm. The ef-fective resistance corresponds to the total resistance over thecircuit when applying a current over these series- and parallelconnections. Once again, the non-zero laplacian eigenvaluescan be used to calculate this measure [14]:

Re = N

N∑i=2

1

λi(13)

As in an electrical circuit, a lower resistance is desired andindicates higher robustness.

8) Percolation limit: Assuming that node removal occursrandomly, the percolation limit is calculated as [15]:

Pc = 1− 1〈x2〉〈x〉 − 1

(14)

where 〈x〉 and 〈x2〉 is the average node degree and thevariance respectively. The percolation limit yields the criticalthreshold of how many nodes that can be removed beforedisconnecting the network. As of this, a higher value indicateshigher robustness.

All parameters explained in this section has been collectedfor following networks:• Barabasi-Albert Network with different connectivity.• Network generated with unit-disc model.• Network generated with regard to 5 closest nodes.

These parameters for networks generated with the Barabasi-Albert model with different connectivity are presented in tableI.

TABLE IROBUSTNESS PARAMETERS BA MODEL

Network generated with BA modelEdge Connectivity 2 3 4 5 6Average Distance 3.86 3.32 3.00 2.83 2.71

Efficiency 0.29 0.32 0.35 0.37 0.39Average Clustering 0.040 0.040 0.044 0.054 0.061

Algebraic Connectivity 0.53 1.18 2.11 2.93 3.79No. of Spanning Trees 3.99 5.97 7.95 9.92 11.88Eff. Graph Resistance 170e3 98e3 69e3 53e3 43e3

Percolation limit 0.89 0.91 0.93 0.94 0.95

It can be observed from the data in table I, that theBarabasi-Albert network model, in which desired connectivityis selectable, robustness increases as we increase the connec-tivity. All parameters increase in magnitude except for averagedistance and graph resistance which decrease with increasingrobustness.

TABLE IIROBUSTNESS PARAMETERS RANDOM AND UNIT-DISC MODEL

R model R2 model AN modelEdge Connectivity 1 1 1Average Distance 3.10 3.95 11.55

Efficiency 0.346 0.277 0.126Average Clustering 0.03 0.11 0.13

Algebraic Connectivity 0.551 0.301 0.004No. of Spanning Trees 9.61 6.70 4.40Eff. Graph Resistance 49e3 84e3 375e3

Percolation limit 0.90 0.85 0.74

In table II robustness parameters are presented for the R,R2 and unit-disc model. All three networks have an edgeconnectivity of 1, which is caused by that two clusters areconnected through 1 link. This can be altered with to increaserobustness. But as mentioned earlier if the distance is largebetween nodes the effect is decreased. Thus this might not bean issue, but analysing this is beyond the scope of this project.

Comparing the AN model to the R and R2 models, it canbe concluded that the 5 closest model is inferior. Seen in tableII the effective graph resistance is a factor 10 larger than theR and R2 models. The average distance is four times largerfor the 5 closest model and algebraic connectivity is a factor100 smaller. With respect to these aspects we discard the ANmodel in favour of the R and R2 models.

The R and R2 models, provides a good alternative tothe the Barabasi-Albert model with the exception for edgeconnectivity. When the probability of a node establishing alink is reduced in the R2 model, average clustering increase,increasing robustness, but remaining parameters indicate thatthe network generated with the R2 model is less robustcompared to the R model.

As a modern communication network can handle largeinformation of data with low hardware requirements and

D3A: SMART INFRASTRUCTURES NETWORKS

transmission speeds being very high. We conclude that amodified ER model with a probability proportional to theinverse of the distance between the nodes is suitable fora decentralised network approach. The R model is froma robustness perspective better compared to the R2 model,although both models can be used.

VII. RESULTS

The network study performed and presented in this re-port verifies that random models, even after modification,is suitable for the application of connecting traffic lights.By developing a new model and comparing to known ones,such as Erdos-Renyi and Barabasi-Albert, characteristics andperformance was able to be estimated.

Three models were developed and tested, being mentionedas ”Adjacent Nodes (AN)”, ”R” and ”R2”, where R and R2 arethe same model but with probability of connecting reducingwith linearly and quadratically. The AN-model were discardedas it didn’t provide satisfactory results in either performanceor robustness. The other two were based on the Erdos-Renyiand Unit Disc models.

This proved to be a well functioning model in regard torobustness with e.g. low resistance and high percolation limit.As a decentralised approach were chosen, it was decided tomodify the ER model as the random model doesn’t createany hubs. Consequently, the network do not follow a power-law degree distribution which is common for real networksand provides an almost constant average path length when thenetwork is growing.

The model needs improvement as edge connectivity, asseen in table II, is only 1. This is related to nodes having amaximum number of connections and the order in which nodesare connected to the network. If all adjacent nodes within thetransmission range of a node i has reached this limit, it willnot be able to connect to something. Also, if network growthis of importance, it might be a good idea to do modificationsto the BA model instead of the ER, which was done here.

Fig. 10. Network generated with ”R”-model.

VIII. FUTURE WORK

As network structure is the foundation to enable communi-cation between traffic lights, further work is required beforeimplementation. In terms of network analysis, the algorithmcan be further developed in regard to network growth and bymodifying the Barbasi-albert model instead of Erdos-Renyimodel. One important improvement to the chosen algorithmis to increase edge connectivity.

A communication protocol suitable for this application hasto be chosen and evaluated through simulation, which is alsoneeded to analyse network performance. The project groupresearched and planned to perform simulation in OmNet++,but this test was discarded as it is beyond the scope of thisproject. When simulation has been conducted one might lookinto hardware solutions and investigate the economic cost ofthis project.

IX. CONCLUSION

The goal of this project was to model and analyse a networkmodel for traffic lights in an urban environment with the long-term goal of active traffic management. This has been doneby researching network models and implementing appropriatemodels with gathered geographical data of traffic lights inStockholm, Sweden.

The authors decided, after having evaluated both a cen-tralised and decentralised approach, that a decentralised ap-proach is better with the main argument of higher networkrobustness even though economical costs will be larger. Inorder to compare results a centralised model was analysed.

The models used was the Barabasi-Albert model, Erdos-Renyi model and models based on the Erdos-Renyi model, R and R2 models and a model connecting the 5 closesttraffic lights. The R, R2 and AN models was introduced totake into consideration the geographical location of the trafficlights. As the authors theorised that nodes in close proximitywill communicate more frequently and the effect of trafficmanagement diminish as distance between nodes increases.

Analysis of the different models yielded results resultingin the AN being discarded as the performance and robustnesswas inferior to the R and R2 models. Comparing the R and R2models, with data from II, the performance and robustness aresimilar but as average distance and effective graph resistanceis larger and algebraic connectivity and efficiency is lower.The R model is superior.

The Barabasi-Albert model produced similar results to the Rmodel. Acting as a confirmation that the R model is applicablefor the application. As the Barabasi-Albert model models acentralised network, the R model provides an alternative for adecentralised approach.

It is concluded that using a random model which takesgeographical data into consideration is suitable for use intraffic light communication with a decentralised approach.Further research is required to implement such a network.

ACKNOWLEDGMENT

The authors would like to thank their supervisor LamiaVarawala for her guidance, support and swift answers toquestions during the project.

D3A: SMART INFRASTRUCTURES NETWORKS

APPENDIXEXTRACT OF TRAFFIC LIGHT GEOGRAPHICAL DATA

NTS_ID Namn RT90_X RT90_Y Extra_In Sweref_N Sweref_E160038 Lidingovagen - Fortifikationsforvaltningen6582968 1629888 RT90 6582815 675602160039 Karlbergsvagen - Dalagatan6582374 1627409 RT90 6582191 673131160040 Odengatan - Sveavagen6582525 1628031 RT90 6582349 673751160041 Karlbergsvagen - Vastmannagatan6582386 1627522 RT90 6582204 673244160042 Karlbergsvagen - Upplandsgatan6582400 1627619 RT90 6582219 673341160043 Odengatan - Upplandsgatan6582320 1627660 RT90 6582140 673383160044 Norrtullsgatan - Vanadisvagen6582827 1627541 RT90 6582645 673257160045 Tegnergatan - Dalagatan6581732 1627766 RT90 6581553 673496160046 Dalagatan - Radmansgatan6581841 1627704 RT90 6581661 673432160047 Odengatan - Dobelnsgatan6582595 1628166 RT90 6582421 673885160048 Odengatan - Roslagsgatan6582688 1628343 RT90 6582516 674061160049 Roslagsgatan - Surbrunnsgatan6582771 1628293 RT90 6582598 674010160050 Odengatan - Birger Jarlsgatan6582735 1628430 RT90 6582564 674147160051 Birger Jarlsgatan - Surbrunnsgatan6582817 1628385 RT90 6582645 674101160052 Odengatan - Tulegatan6582642 1628258 RT90 6582469 673977160053 Sveavagen - Surbrunnsgatan6582605 1627996 RT90 6582429 673715160054 Sveavagen - Frejgatan6582783 1627899 RT90 6582605 673616160055 Frejgatan vid Tulegatan6582904 1628117 RT90 6582729 673832160056 Valhallavagen - Roslagstull6583342 1628022 RT90 6583166 673732160057 Valhallavag - Ingemarsgatan - Birger Jarlsgatan6583147 1628201 RT90 6582973 673913160058 Sveaplan 6583187 1627685 RT90 6583007 673397160059 Sveavagen - Vanadisvagen6582963 1627798 RT90 6582784 673513160060 Norrtull 6583186 1627383 RT90 6583002 673095160061 Norra Lanken - Uppsalavagen6583318 1627302 RT90 6583133 673013160062 Norra Stationsgatan - S:t Eriksgatan6583045 1627213 RT90 6582859 672927160063 Valhallavagen - Lidingovagen6582537 1629374 RT90 6582377 675093160064 Valhallavagen - Engelbrektsgatan6582674 1629049 RT90 6582510 674767160065 Valhallavag - Danderydsg. - Dr Kristinas Vag6582745 1628951 RT90 6582580 674668160066 Valhallavagen - Uggelviksgatan6582730 1628842 RT90 6582564 674559160067 Valhallavagen - Odengatan6582868 1628676 RT90 6582700 674392160068 Valhallavagen - Frejgatan6583057 1628406 RT90 6582886 674119160069 Birger Jarlsgatan - Frejgatan6582993 1628281 RT90 6582820 673995160070 Frejgatan - Roslagsgatan6582948 1628200 RT90 6582774 673915160071 Valhallavagen vid Surbrunnsgatan6582940 1628585 RT90 6582771 674300160072 Valhallavagen - Sibyllegatan6582343 1629705 RT90 6582187 675427160073 Valhallavagen - Artillerigatan6582323 1629832 RT90 6582169 675554160074 Valhallavagen - Vartavagen6582137 1630254 RT90 6581988 675978160075 Valhallavagen - Banérgatan6582089 1630391 RT90 6581942 676116160076 Valhallavagen vid Gyllenstiernsgatan N & S6581976 1630675 RT90 6581832 676401160077 Karlavagen - Oxenstiernsgatan6581663 1630641 RT90 6581519 676371160078 Valhallavagen - Erik Dahlbergsgatan6582240 1630034 RT90 6582089 675757160079 Sveavagen - Kungsgatan - Apelbergsgatan6581652 1628490 RT90 6581482 674220160080 Sveavagen - Olof Palmes Gata6581692 1628472 RT90 6581522 674202160081 Sveavagen - Adolf Fredriks Kyrkogata6581821 1628404 RT90 6581650 674132160082 Sveavagen - Tegnergatan6582025 1628297 RT90 6581853 674023

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