Autonomic Systems Design for ITS Applications - IEEE Xplore

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Autonomic Systems Design for ITS Applications. Apostolos Kotsialos, Member IEEE, and Adam Poole. School of Engineering and Computing Sciences. Durham ...
Proceedings of the 16th International IEEE Annual Conference on Intelligent Transportation Systems (ITSC 2013), The Hague, The Netherlands, October 6-9, 2013

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Autonomic Systems Design for ITS Applications Apostolos Kotsialos, Member IEEE, and Adam Poole School of Engineering and Computing Sciences Durham University Durham, South Road, DH1 3LE, United Kingdom {apostolos.kotsialos, adam.poole}@durham.ac.uk

Abstract— This paper discusses a systems design approach inspired from the autonomic nervous system for ITS applications. This is done not with reference to the employed computing system, but to the requirements of traffic engineering applications. It is argued that the design and development of autonomic traffic management systems must identify the control loop that needs to be endowed with autonomic properties and subsequently use this framework for defining a desired set of self-∗ properties. A macroscopic network modelling application is considered for showing how autonomic systems design can be used for defining and obtaining self-∗ properties, with particular emphasis given in self-optimisation.

I. INTRODUCTION Biological systems are highly robust, fault tolerant and able to sustain successful operation through a wide range of environmental conditions. By studying the properties of biological structures it is possible to design systems with similar properties. One such idea has been the development of autonomic computational systems. In the Autonomic Computing Manifesto [1], the vision of autonomic computing was outlined, aiming at the development of highly complex computational systems that are hiding the complexity of managing them from the system administrator allowing for high level policy to change and modify the whole system automatically. This is achieved by embedding, by design, a number of self-∗ properties to the system, such as selfconfiguration, self-healing, self-management, self-protection, self-optimisation and so forth. Autonomic computing’s biological inspiration comes from the Autonomic Nervous System (ANS), a subsystem of the peripheral nervous system. The ANS acts below the level of consciousness controlling visceral functions, such as the heart rate, digestion, respiratory rate, salivation, perspiration and sexual arousal. This system operates within a wide range of environmental as well as own states without a conscious effort. This is the important property. The autonomic coordination effort and marshaling of resources allows the conscious part to focus on more important, high level issues. In this sense, autonomic technological systems that are highly complex, heterogeneous and spatially distributed are designed to hide the complexity of the low level “involuntary” operations from their users. The users’ input comes in the form of high-level policy statements and goals, expressed in intuitive terms, which disaggregate into sets of subgoals further down the hierarchy. The building elements in this case are not cells or other biological material, but rather 978-1-4799-2914-613/$31.00 ©2013 IEEE

technological artifacts that form at some level of abstraction autonomic elements. Designing such elements requires the definition of a set of self-∗ properties. The meaning assigned to them is domain and application specific. The notion of autonomics for system design purposes has been used in many domains, including energy management systems [2], communication networks [3], financial markets [4] and spacecraft operations [5]. This paper takes a look towards defining autonomic systems for Intelligent Transport Systems (ITS). Similar lines of research have been proposed by the organic computing initiative [6]. An architecture for real-time traffic management is proposed in [7]. Optimisation of decentralised autonomic systems for traffic control is reported in [8]. The rest of this paper is structured as follows. Section II describes the autonomic control loop and section III how it is adapted for ITS applications. Section IV proposes the structure of an autonomic network traffic flow modelling application. Section V concludes this paper. II. THE AUTONOMIC CONTROL LOOP The first step when trying to design or embed systems with autonomic properties, is to identify the level at which subsystems are going to show self-∗ behavior. The design effort depends on the range and depth of this behavior. Bearing in mind it is hierarchical and highly complex systems that require such treatment, the successful development of systems with “visceral” functions requires the identification of the control loops that should possess self-∗ features. The criterion for describing a system as autonomic remains that of the unconscious and sustained operation over the full range of environmental and own-state conditions. Technological competencies and system integration approaches define the decoupling point between the conscious and the unconscious regimes of a functioning system. It is the feedback control loop of the uncoscious part that should possess self-∗ properties. The general autonomic control loop can be seen in Figure 1. It depicts the basic architecture of an autonomic element consisting of a managed resource and an autonomic manager. For the whole system to exhibit self-∗ behavior, the autonomic manager goes through the Monitor-Analyse-PlanExecute (MAPE) process with knowledge management in the background. Sensors are used to collect information about the resource and effectors for interactions. This architecture

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Fig. 1.

The autonomic element control loop adopted from [1].

is common in one form or another in control engineering, where sensors attached to the process under control are used to observe the system’s state and the system is driven to a desired state by a controller. The self-∗ requirement dictates the shape and form of methods to be used. It is the whole system that needs to be autonomic and be at liberty of organising responses for every conceivable combination of environmental conditions and be aware of the tools (controllers, optimisers, filters, estimators, predictors etc.) at its disposal. This is one of the points of convergence between control theory and artificial intelligence, necessary for designing autonomic systems [9].

system state tends to be maintained at a stable band in view of changing environmental conditions. This is achieved by multiple dynamic equilibrium adjustments using a variety of regulation mechanisms. Hence, an autonomic system must maintain a model of itself and a model of its environment; using both, it should coordinate its resources and regulation mechanisms to achieve a homeostatic condition. This can be a low level one or a high level spatial and temporal condition desired and customised by the operator and other users or applications. An interesting discussion on the role of homeostasis for self-healing software may be found in [10]. For ITS applications, such conditions can be expressed as high level statements made by the network operator, e.g. maintain capacity flow at link x and 80% flow at link y or maintain mean travel time equal to x minutes for route R from A to B, or as low level application requirements, e.g. send to application ‘‘control traffic light’’ vehicle counts every 10 seconds. The scope of autonomic systems design goes beyond the single application but aims at integrating diverse systems. The next sections are describing a limited interpretation of a modelling application within this context. IV. AUTONOMIC ROAD NETWORK MODELLING APPLICATION A. The Autonomic Element

III. AUTONOMIC ITS APPLICATIONS There are two types of autonomic applications for ITS. The autonomic manager is a construct that resides in the virtual computing world, while the managed resource can be a computing resource, e.g. a processor in a parallel computing system, or an application domain specific resource, e.g. the capacity of a controlled on-ramp. Autonomics can be applied for the computing systems supporting ITS applications. This is one of the possible ways of autonomics influencing ITS, especially in view of ad hoc wireless vehicle-to-vehicle networks, global positioning systems, trackers and cloud computing. Here, emphasis is on the ITS applications themselves as operating systems, rather than on the supporting computational resources. It is useful to imitate the structure of the ANS, which consists of two partially but mostly complementary components, i.e. the sympathetic and the parasympathetic system. The sympathetic system is responsible for actions requiring fast responses (“fight or flight”) whilst the parasympathetic is responsible for actions not requiring immediate reaction (“test and digest”). In this setting, automatic control methods designed for real-time traffic management tend to be more relevant for the sympathetic system and computing science methods, such as automatic planning and machine learning, tend to be more relevant for the parasympathetic system, without necessary exclusions, though. In a living organism, the sympathetic and parasympathetic systems are used by the ANS to achieve homeostasis. Homeostasis is a living systems property whereby the internal 978-1-4799-2914-613/$31.00 ©2013 IEEE

Following the general architecture of autonomic elements shown in Figure 1, the first step is to provide the details of the autonomic manager and the managed resource. Here, the managed resource is the application network model, which in our case is the second order macroscopic traffic flow model METANET [11]. This modelling approach describes a road network as a set of links and nodes. Links are used for representing uniform motorway sections with the same number of lanes and no changes in curvature or gradient; vehicles travel along motorway links. The demand originating from the surrounding environment is channeled into the network through the origin links; on-ramps and the boundaries of motorways are modelled as origin links. The flow is moved outside the network via destination links; off-ramps and exit motorway boundaries are modelled as destination links. Nodes are used for modelling junctions and changes in geometry. A number of incoming and outgoing links are attached to each node, modelling this way the networked structure of a motorway system. The traffic conditions in a motorway link are described by the traffic volume (veh/h), the vehicular density (veh/km/lane) and the space mean speed (km/h) at discrete road segments belonging to the link. The traffic conditions in an origin link are described by a queue of vehicles waiting to enter the network (veh.), the demand originating from the environment (veh/h) and the discharge into the motorway (veh/h). Traffic conditions in a destination link are modelled through the exit flows (veh/h) from that link.

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The drivers’ routing behavior is modelled through the turning rates at each bifurcation node. A more detailed description of traffic composition emerges when Origin-Destination (OD) information is used, see [11] for more details. In effect, the model, which is the managed resource, is a dynamic system in the form x(k + 1) = f [x(k), d(k); p] , x(0) = x0

(1)

where k is the index over the model’s discrete time steps of duration T , x is the state vector consisting of the density ρm,i and space mean speed vm,i of every segment i of link m and the queue length wj of every origin j; x0 is the network’s initial state at time k = 0; d(k) is the vector of system disturbances consisting of the demand dj originating in origin link j and the turning rates βnµ ∈ [0, 1], which is the percentage of the incoming traffic to bifurcation node n that chooses to take leaving link µ; p is a vector of parameters modelling particular features of the specific network and is the outcome of a model validation effort, which will be examined closely later. All the above constitute the managed resource network model. As a resource this model receives as input the initial state x0 , and a forecast of the disturbance trajectories d(k), k = 0, 1, . . . , K − 1, where K is a pre-specified time horizon, and delivers the density ρm,i (k), speed vm,i (k) and queue wj (k) profiles over K time periods in the future for the entire network. The autonomic manager manages this resource responding to requests from other applications, e.g. a control strategy trying to assess the possible outcome of a course of control actions, or from system users, e.g. the traffic manager requesting a forecast of traffic conditions. The manager also handles the requests to other applications for necessary information. B. Definition of Self-∗ Properties The self-∗ properties of the autonomic element can be defined with respect to different aspects. The MAPE process should be designed and the autonomic manager be equipped with those tools that will enable the whole system to display autonomic behavior. With respect to the traffic engineering perspective, several self-∗ properties can be defined. 1) self-healing; the ITS self-healing related property of network model is defined with respect to the application’s need to provide the required output in view of possible disruptions to its operation. Possible disruptions can be caused by incomplete input data and by gaps at the outputs, i.e. by missing data in disturbance vector d(k), or by gaps in the state profile x(k). Hence, a network model application possess a self-healing property if it is able to heal the input data required for delivering its output and if it is able to heal gaps and omissions of its output. The autonomic manager’s MAPE process should monitor the disturbance and state trajectories for their integrity; analyse those trajectories and identify gaps and inconsistencies; plan a response to this analysis 978-1-4799-2914-613/$31.00 ©2013 IEEE

according to the available means; e.g. use data fusion methods to heal data or use probabilistic reasoning for filling out missing output data; invoke the corresponding applications of data healing or data fusion and update the disturbance trajectories. Such a MAPE process guarantees the self-healing property of the modelling application. 2) self-configuring; the self-configuring of the modelling application has to do with: The simulation setup, e.g. incident simulation. The network configuration; the application must possess the capability of understanding and updating the network topology and geometric characteristics, e.g. by being capable to import and translate data from GIS; this information should be further translated to the configuration of the state and disturbance trajectories of the discrete dynamic system (1); for example, the inclusion of new motorway in the network would result to the automatic discretisation of the link and the corresponding extension to the system’s state and disturbance vectors. The simulation’s stated purpose; depending on this, different functionalities may be needed, e.g. a demand prediction application may be needed to be called in case a future state forecast is needed, which is not necessary when used for evaluating off-line the possible impact of control actions, where archived data may be necessary to be retrieved. 3) self-optimising; the meaning of this property may be defined by considering the model’s accuracy; this accuracy depends on the input data (x0 and d(k)), and the validity of the model parameters p. The MAPE process of the autonomic manager should be able to deliver good data (in conjunction with the selfhealing property) and good sets of parameters for different simulation setups (in conjunction with the self-configuring property). In effect, the model must be aware of its accuracy and automatically calibrate itself selecting the best parameter vector p∗ . Hence, the road towards autonomicity requires the development of a MAPE able to deliver automatic self-calibration. This way, the modelling application possessing the self-configuration and selfoptimisation properties can deliver a model output that is relevant to the user needs and accurate to the degree possible. Subsections IV-C and IV-D elaborate more on that. In order to embed self-optimisation into network model, the sympathetic and parasympathetic subsystems approach is taken. C. Parasympathetic System Functions for Self-Optimising As mentioned in section III the parasympathetic subsystem function is oriented towards the “rest and digest” type of operation. The interpretation of this description for a selfoptimising macroscopic traffic flow modelling application takes the form of a system that can learn over time the most suitable plans and responses. This calls for the development

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of a long term appreciation and understanding of the decision making model employed by the autonomic manager for finding the optimal set of model parameters p∗ . Another important function of the parasympathetic subsystem is the evaluation and configuration of the optimisation method (or solver) used for identifying p∗ . A number of solvers may be available. Each of them has a number of tuning parameters influencing the method’s performance. For example, if a GA is used, the population size, the probabilities of mutation and other parameters need to be assigned values. The optimal values can emerge from the continuous assessment of the results obtained. Hence, there is a MAPE loop related to the solver’s performance in the autonomic manager that automatically sets up the optimisation solvers. The pattern behind those functions is that of a learning mechanism. In other words, the parasympathetic system can be designed by using tools based on artificial intelligence and machine learning methods. There is medium to long term time scale in this operation as it requires the collection, aggregation and abstraction of knowledge based on repeated experiments. Automatic planning platforms [12] are particularly suitable for the development of this kind of systems. D. Sympathetic System Functions for Self-Optimising The sympathetic system function aims at delivering the optimal model parameter vector p∗ for a particular network with specific and constant topology. Hence, a rigorous validation effort needs to be organised automatically by the autonomic manager along the following lines: Collecting the data for performing model calibration; the manager must make sure the traffic data used, cover the entire spectrum of traffic conditions (free, critical and congested flow). Setup and formulate the optimisation problem based on data with different time stamps. Select a set of data that is going to be used as input to the optimisation and another set of data to be used for verification only. Be aware of journalistic information for every set of data used for calibration. Run verification tests for a candidate p∗ using data that were not used for obtaining it. Set up the requirements for p’s components; default values may be used for some members of p and only a selected few may be allowed to change. In the case of motorway traffic flow model validation, two issues require special attention. The first one is the relationship between the model motorway link discretisation and its relationship to the sensors’ location. For example, let us assume that loop detectors are used delivering flow and speed measurements. The loop’s location will belong to one motorway link segment, for which the model (1) calculates the flow and speed. However, the model calculated speed is the space mean speed, estimated by the harmonic mean of the loop’s speed measurements for an area around the loop detector. Hence, ideally the road discrete element, i.e. the segment, should be delimited so that the loop detector is somewhere near its middle. But the flow calculated by the model refers to the number of vehicles per hour exiting the segment, hence the loop detector should be at the segment’s end. Typically, it is the expert opinion that assigns loops 978-1-4799-2914-613/$31.00 ©2013 IEEE

to segments and decides which of the produced data to be used for comparison. This problem is eliminated altogether with the use of an alternative sensing technology, e.g. with a sensing system that measures directly the space mean speed over a discrete segment’s area and the flow at its exit boundary. The method used for calculating p∗ should deal with this issue without having to resort to human intervention. The second issue where expert opinion is required, is the spatial extension of the validity of the same fundamental diagram. This is one of the most important relationships in the whole model (1) determining the equilibrium relationship between density and speed. In METANET it takes the form  α   ρm,i (k) m 1 (2) V [ρm,i (k)] = vf,m · exp − αm ρcr,m where vf,m is the free speed of link m, ρcr,m denotes the critical density of link m and αm is a parameter. Assigning a different fundamental diagram to each discrete segment or even to each link, would be a mistake since it leads to over-parametrisation. To avoid this, the engineer setting up the validation process splits the network in parts where a single fundamental diagram applies. The parameters of those fundamental diagrams are included in p. The spatial extension of each of the fundamental diagrams used, however, is defined by the expert. Hence, the autonomic manager should be able to undertake this task without human intervention. The MAPE process that is able to address those two issues for a motorway network equipped only with loop detectors leads to a problem formulation and solution algorithms that lifts the need for human intervention. This is done by using a black box approach with a population based optimisation algorithm minimising an appropriately defined objective function and constraints. Let us assume that there are M loop detectors available each at point j on the motorway providing flow and speed measurements for segment i of link m with sample time Ts = 60 seconds. Given flow and mean speed measurements yj,k,q and yj,k,v , respectively, from loop detector at point j during the minute the model time period k occurs, the model validation problem consists of minimising the total flow and mean speed square error between measurements and model output. This is to be done by selecting an optimal set of the parameters included in eqn. (1), which are summarised as follows (see [11] for details): • • • • • •

the critical density ρcr,m of every motorway link m; the maximum density ρmax ; the fundamental diagram parameter αm of every motorway link m; the free speed in every link m, vf,m ; the minimum speed vmin ; the mean speed equation parameters τ , ν, φ, δ and κ.

All these parameters are organised into p. The objective function needs to be able to compare the model outputs to measurements. Flow and mean speed were

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L3 L5 L6 L8 L9 L10 L2 L4 L7 L1 0.9km 7.1km 1.9km 0.8km 3.4km 2.4km 1.6km 2.3km 0.7km 0.8km

utilised. The contribution to the objective function of the flow square error for a point j is given by

Leeds Leicester

(3) J30

k=1

where fj,k,q is the flow calculated by the model at time interval k for point j. The same is applied for the mean speed K X 2 J(p)j,v = (yj,k,v − fj,k,v ) . (4)

Fig. 2.

SOLUTIONS OF

The total weighted square error J(p) is calculated by summing over all points j, with weightings Aq and Av M X

Schematic of Sheffield site

TABLE I C OUNTS OF FUNDAMENTAL DIAGRAMS (FD) FOUND IN OPTIMAL

k=1

J(p) =

[Aq J(p)j,q + Av J(p)j,v ]

Starting link of FD 10 1 1 1 7 6

(5)

j=1

s

+wρ

XX

+wα

XX

r

r

(ρrcr − ρscr )2

s

(αr − αs )2

(6)

s

where r and s are indices of the different fundamental diagrams and wv , wρ , wα are weightings accounting for variable magnitude. Subsequently, in the overall objective function is J 0 (p) = J(p) + wp Jp (p). (7) This process directly increases the complexity of the problem and adds an extra variable for each fundamental diagram. This variable is used to define the region where the fundamental diagram is applicable. The model validation optimisation problem aims at minimising J 0 (p) of eqn. (7) subject to the model constraints (1) by changing vector p. Let us consider as an example a medium sized motorway network in Sheffield (Northbound M1), which is 21.9km long, Figure 2. The congestion is typically a short wave in the centre and difficult to capture. This congestion typically occurs at the end of the link 6 where the off ramp is short and unable to cope with the demand of traffic which then backs up onto the main carriageway. Data was used from the 1st , 8th and 15th of June 2009. For this model site, automatic fundamental diagram assignment takes place. Out of 18 runs, 7 different permutations for the arrangement of the fundamental diagrams were observed amongst the optimum solutions found. The modal case (8 occurrences) was to have two with the split being at the end of link 9. This then allowed for the 978-1-4799-2914-613/$31.00 ©2013 IEEE

End link of FD 10 9 6 5 9 9

Frequency 17 8 4 3 3 2

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Middle of congestion: Link 6

Flow (veh/h)

r

S HEFFIELD MODEL

second fundamental diagram to cover link 10, which has slower flowing traffic as it is approaching a flyover with a reduction in the number of lanes. All the remaining solutions allowed for three fundamental diagrams. The frequency of fundamental diagrams found by the optimal solution from each algorithm (a genetic algorithm and a particle swarm optimisation) is shown in Table I. It can be seen that although there were variations in the overall configuration all except one run found that a new fundamental diagram was required for link 10. An example of calibration results is given in Figure 3. More detailed results can be found in [15]. The whole effort regarding the selection of the optimisation algorithms, their tuning, particularly with the proper selection of weights, and the analysis of the obtained results

7000 6000 5000 4000 3000 2000 1000 0 0

Flow (veh/h)

In order to achieve the automatic assignment of fundamental diagrams in an intelligent way, penalty terms are used. This removes the need for bottleneck identification as used in [13], [14] or choosing an arbitrary (based on educated opinion) point for a change in parameter set [11]. The penalty term aims to minimise the squared difference between the fundamental diagrams’ components, i.e. XX Jp (p) = wv (vfr − vfs )2

J34

J33

M18

J31

60

Model flow Model velocity Fig. 3.

140 120 100 80 60 40 20 0

60 120 180 Downstream of congestion: Link 7

7000 6000 5000 4000 3000 2000 1000 0 0

140 120 100 80 60 40 20 0

Velocity (km/h)

2

(yj,k,q − fj,k,q )

Velocity (km/h)

J(p)j,q =

K X

Nottingham

120 Time (mins)

180

Meas. flow Meas. velocity

Sample time profiles for calibrated Sheffield 1st model

can be automated as it is based entirely on the data obtained. This way it is possible to introduce into the application network model a sympathetic system, which in conjunction with the parasympathetic can result to self-optimising behavior. V. CONCLUSIONS This paper described a systems design approach inspired from the functioning of the autonomic nervous system for ITS applications. The autonomic approach towards system design was discussed not with reference to the employed computing system, but with reference to the requirements of traffic engineering applications. It has argued that the design and development of autonomic traffic management systems must identify the control loop that needs to be endowed with autonomic properties and subsequently use this framework for defining a desired set of self-∗ properties. Once these definitions are in place, the resulting design objectives need to be articulated, which may result to the use of existing tools but also new problem formulations. Following the split of the autonomic nervous system into the sympathetic and parasympathetic subsystem, is a useful tactic as it tends to separate the kind of functionalities needed to be introduced. Furthermore, the parasympathetic system is more associated with learning algorithms based on computer science methods, whilst the sympathetic tends to use control engineering methods for achieving its goals. The fusion of these approaches within MAPE processes in an autonomic manager can deliver autonomic elements in hierarchical systems. The paper also presented an interpretation of an automatic macroscopic modelling application within the context of autonomics. Particular attention has been given to the self-optimising property, which is based on an automatic calibration system. It is argued that the ensuing analysis can be automated, removing this way the need for repeated human expert interventions in the use of such applications. The discussion of the modelling application also reveals the scope and challenge of autonomic traffic management systems. It goes beyond the simple application of a stand alone application based on a single methodological approach, but it encompasses computer science and traffic engineering knowledge to deliver solutions that perform a host of sophisticated, complicated and challenging activities without the final user noticing them. Future work on this area is focused on the fusion of learning and automated planning algorithms with traffic control methods and on understanding the way high level user requirements disaggregate and translate into the unconscious low level autonomic system behavior requirements.

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ACKNOWLEDGMENTS The authors would like to thank the support of EPSRC for funding part of this work, the Highways Agency for providing traffic data and the COST ARTS Action (TUD1102 – Towards Autonomic Road Transport Support Systems) for supporting this research effort. R EFERENCES [1] J. Kephart and D. Chess, “The Vision of Autonomic Computing,” IEEE Computer, vol. 36, no. 1, pp. 41–50, January 2003. [2] M. Warnier, M. van Sinderen, and M. Brazier, “Adaptive knowledge representation for a self-managing home energy usage system,” in Proceedings of the Fourth International Workshop on Enterprise Systems and Technology (I-WEST), Athens, Greece, 24-25 July 2010, pp. 132–141. [3] R. Sterritt, “Autonomic networks: engineering the self-healing property,” Engineering Applications of Artificial Intelligence, vol. 17, pp. 727–739, 2004. [4] G. Cheliotis and C. Kenyon, “Autonomic economics,” in Proceedings of the IEEE International Conference on E-Commerce, 2003. [5] W. Truszkowski, H. Hallock, C. Rouff, J. Karlin, J. Rash, and R. Sterritt, Autonomous and Autonomic Systems: With Applications to NASA Intelligent Spacecraft Operations and Exploration Systems, ser. NASA Monographs in Systems and Software Engineering. Springer, 2009. [6] U. Richter, M. Mnif, J. Branke, C. M¨uller-Schloer, and H. Schmeck, “Towards a generic observer/controller architecture for organic computing,” in GI Jahrestagung (1)’06, 2006, pp. 112–119. [7] H. Etemadnia, K. Abdelghany, and S. Hariri, “Toward an autonomic architecture for real-time traffic network management,” Journal of Intelligent Transportation Systems: Technology, Planning and Operations, vol. 16, pp. 45–59, 2012. [8] I. Dusparic and V. Cahill, “Multi-policy optimization in decentralized autonomic systems,” in Proc. of 8th Int. Conf. on Autonomous Agents and Multiagent Systems, 2009. [9] Y. Diao, J. Hellerstein, S. Parekh, R. Griffith, G. Kaiser, and D. Phung, “A control theory foundation for self-managing computing systems,” IEEE Journal on Selected Areas in Communications, vol. 23, no. 12, pp. 2213–2222, 2005. [10] M. Shaw, ““Self-Healing”: softening precision to avoid brittleness,” in Proc of ACM SIGSOFT WOSS ’02, 2002, pp. 111–114. [11] A. Kotsialos, M. Papageorgiou, C. Diakaki, Y. Pavlis, and F. Middelham, “Traffic flow modeling of large-scale motorway networks using the macroscopic modelling tool METANET,” IEEE Transactions on Intelligent Transportation Systems, vol. 3, pp. 282–292, December 2002. [12] C. Guzman, V. Alcazar, D. Prior, E. Onaindia, D. Borrajo, J. FdezOlivarez, and E. Quintero, “PELEA: a domain independent architecture for planning, execution and learning,” in Proc. of ICAPS’12, 2012, pp. 38–45. [13] L. Munoz, X. Sun, D. Sun, G. Gomes, and R. Horowitz, “Methodological calibration of the cell transmission model,” in Proceeding of the 2004 American Control Conference, Boston, MA, USA, 2004, pp. 798–803. [14] L. Munoz, X. Sun, R. Horowitz, and L. Alvarez, “A piecewiselinearized cell transmission model and parameter calibration methodology,” in Proceeding of the 85th Transportation Research Board (TRB) Annual Meeting, Washington D.C., USA, 2006, pp. 183–191. [15] A. Poole and A. Kotsialos, “METANET model validation using a genetic algorithm,” in Proc. of the 13th IFAC Symp. on Control in Transportation Systems, Sofia, Bulgaria, 2012, pp. 7–12.

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