From theory to practice in multiagent system design: The ... - CiteSeerX

From Theory to Practice in Multiagent System Design: The Case of Structural Co-operation Sascha Ossowski ~, A n a Garcla-Serrano . 2 and Jos6 Cuena 2 1 School of Engineering, Rey Juan Carlos University, Camino de Humanes 63, 28936 M6stoles (Madrid), Spain S.Ossowski @escet.urj c.es 2Department of Artificial Intelligence, Technical University of Madrid, Campus de Montegancedo s/n, 28660 Boadilla del Monte (Madrid), Spain {agarcia, jcuena} @dia.fi.upm.es

Abstract. In Distributed Problem-solving (DPS) systems a group of purpose-

fully designed computational agents interact and co-ordinate their activities so as to jointly achieve a global goal. Social co-ordination is a decentralised mechanism, that sets out from non-benevolent agents that interact primarily to improve the degree of attainment of their local goals. One way of ensuring the effectivity of social co-ordination with respect to global problem-solving is to rely on self-interested agents and to coerce their behaviour in a desired direction. In this paper we describe the decentralised co-ordination mechanism of structural co-operation that follows this approach, and present its formalisation within bargaining theory. We then show how this theoretical model is transferred to a practical real-world application: within the experimental TRYSA 2 system autonomous traffic control agents co-ordinate their activities by means of structural co-operation, so as to jointly perform road traffic management in an urban motorway network.

1. Introduction Distributed Problem-Solving (DPS) rely on a purposefully designed architecture of computational agents that interact in order to jointly achieve a desired global functionality. The traditional DPS design philosophy o f reductionism, that relies on a topdown decomposition of the global task, the assignment of subtasks to agents and coordination based on pre-established interaction patterns among benevolent agents [6], often turns out to be too rigid for large-scale agent systems [7]. Instead, a constructionist approach, based on the metaphor of societies o f autonomous problem-solving agents, has become popular: agents are primarily interested in their local goals and interact to increase the degree of their attainment. This decentralised interaction [5] is termed social co-ordination. In order that the DPS system copes with the global task, social co-ordination must be based on agent behaviour that lies between benevolence and self-interest [11]. A popular solution to this problem consists in building a model of purely self-interested behaviour (e.g. [16,14]) and designing a coercive external context to modify it (e.g. [15,14]).

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We have developed a social co-ordination mechanism called structural cooperation, which follows this approach [9]. Elsewhere [11] we show how this mechanism combines quantitative [14] and qualitative [16] models of self-interested action in a multiagent world within the frame of social co-ordination. The purpose of this paper, however, is not a detailed description of our abstract mechanism. We rather aim to point out how theoretical models in multiagent system research can be turned into practical results: we show how the rather abstract formalisation of structural cooperation leads to the real-world multiagent application of urban road traffic management. Section 2 presents a model of the type of domains that structural co-operation has been designed for. Section 3 describes and formalises the mechanism of structural cooperation and its operationalisation. Section 4 presents the TRYSA 2 experimental system, that uses structural co-operation to co-ordinate autonomous traffic management agents, while concluding remarks are presented in section 5.

2. The problem: reactive social co-ordination Many real-world domains are highly dynamic: perceptions are error-prone, actions fail, contingencies occur. A common way to deal with this problem is to build systems that only plan their actions for a short-time horizon, in order to assess the effects of their interventions as early as possible, and to adapt future behaviour accordingly [3]. When such systems are modelled on the basis of a multiagent architecture, two essential constraints have to be taken into account: first, agents need to cope with the fact that their plans and actions interfere because they share an environment with only limited resources; second, agents should be prepared to consider actions that attain their goals only partially due to resource limitation and environmental contingencies. In the sequel we formalise essential features of this type of problems. Let S be a set of world states and H a finite set of plans. The execution of a plan zc changes the state of the world which is modelled as a partially defined mapping

res: FI• S --->S. A plan is executable in s, if only if res is defined for a certain world state s, fact which we express formally by the predicate exec(z,s). At least one empty plan ze is required to be included in the set of plans/7; it is modelled as identity. There is a set of agents A, each of which can act in the world thereby modifying its state. An agent ~0aA is characterised by the following notions: 9 a predicate can(or, z), determining the individual plans zw_/7 that a is able to execute. An agent a is always capable of executing the empty plan zcE; 9 a predicate ideal(a,s), expressing the states se S that the agent ~ A would ideally like to bring about; 9 a metric function d,~, which maps two states to a real number, representing agent ass estimation of "how far" one state is away from another. It usually models the notion of (relative) "difficulty" to bring about changes between world states. In the scenarios that we are interested in, an agent usually cannot fully reach an ideal state. So, we will use the notion of ideal states together with the distance measure dc~ to describe an agent's preferences respecting world states. Note that the agents in A

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may have different (partially conflicting) ideal states and may even measure the distance between states in different scales. We now introduce a notion of interdependent action. The set M of multiplans comprises all multisets over the individual plans/7, i.e. M = bagof(l-1). A multiplan ft ~ M models the simultaneous execution of all its component plans, i.e. of the individual plans n~ ft that are contained in the multiset ft. The commutative operator o denotes multiset union and hence states that its operands are executed together. By identifying an individual plan with a multiplan that contains it as its only element, the partial function res is extended to multiplans: res :M x S --->S . The function res is undefined for a multiplan ft and a state s, if some of the individual plans that it contains are incompatible, i.e. in case that in a state s of a modelled domain it is impossible to execute them simultaneously. Otherwise, ft is said to be executable in s (formally: exec(ft, s)). T h e empty plan rc~ is compatible with every multiplan and does not affect its outcome. The notion of capability for executing a multiplan is also a natural extension of the single agent case. We define the set of groups F as the powerset of the set of agents, i.e. F=~o(A). A group 7 ~ F i s capable of executing a multiplan #, if there is an assignment such that every agent is to execute exactly one individual plan and this agent is capable of doing so, i.e. there is a bijective mapping V from individual plans to agents, such that can(y, ft)= Vrc ~ I t. can(ll/OZ),~z ) .

Definition 1. A co-ordination setting D is defined by the sets of individuals S,/7, A, M and F, the functions res, da and o as well as the predicates exec, can and ideal.

3. The mechanism: structural co-operation The outcome of a co-ordination process within a co-ordination setting D can be conceived as a multiplan. When it represents the result of social co-ordination, the multiplan reflects the self-interested choice of all agents, i.e. agents do not refer to a notion of joint utility and do not care for whether the multiplan contributes to the overall functionality of the DPS system or not. Structural co-operation provides a model of such self-interested action, and introduces a mechanism to bias the outcome of coordination among social DPS agents 1. The designer is supposed to use that mechanism so as to make the outcome of social co-ordination instrumental with respect to the desired functionality of the DPS system [10]. In the sequel, we will sketch both, a model of multiagent rational action as well as a biasing mechanism. Subsequently, we model these ideas within bargaining theory. Finally, we show how the outcome of social co-ordination in a co-ordination setting D can be determined and computed.

i As will be outlined below, we conceive a "social" agent to be norm-abiding.

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3.1 Social Agents In the above co-ordination setting, the need for co-ordination is expressed by the fact that, when an individual plan tr is executed in conjunction with a multiplan It, the resulting world state changes (i.e. res(Tr,s) ~ res(~ro It, s)). When an agent o~ is able to execute zc and a group ?,is able to execute/1, then the group ?'has the power to influence a: the agent depends on 7/with respect to ~z. There are different types and degrees of dependence. The strongest degree is feasibility dependence (used in section 4), in the presence of which a group ?'can turn down or enable an agent's possibility to execute its individual plan rc (in the frame of a multiplan It) [10]. We model self-interested choice within a co-ordination setting on the basis of this notion of dependence: the less an agent depends on the choices of others with respect to the outcome of its plans, the better is its position in society. And the better an agent's position in the agent society, the more weight will have its preferences in the outcome of social co-ordination; if an agreement is reached, it will be biased towards that agent. In consequence, the outcome of social co-ordination is determined by the network of social dependence relations. We now introduce the notion of normative prescription [2]: if in a situation s it is forbidden for a group ?'to enact a multiplan # we write

forbiddens( ~, It) Our social agents are norm-abiding: they do not even consider executing plans that are forbidden for them. So, we introduce the notion of preparedness as capability plus the absence of such prohibitions

prep, (?,, It) r can(?', It) ^ ~forbidden (?,, It) Reconsidering the above model of self-interested action on the basis of the notion of preparedness instead of capability, it becomes clear that by issuing prohibitions, a designer can modify the social dependence structure and, in consequence, also the outcome of social co-ordination. These ideas will be formalised in the sequel, taking into account that prescriptions are conceived to worsen the position of the involved agents, potentially improving the position of the remaining agents.

3.2 Social Co-ordination as a Bargaining Scenario In a first step, a quantitative notion of preference over agreements is introduced. Agent (x's preference for a world state s is expressed by its distance to some ideal state, which can be written as

Islo =min{d~ (s,-Y)l ideal(ot, Y)} The set X of legally enactable multiplans in a situation s comprises all plans that are executable in s and for which there is a group of agents prepared to do so:

X = {it~ Ml exec(I-t,s)^ 3?,~ F. prep,(?,,#)} On this basis we can define a quantitative preference over multiplans. Definition 2. The

utility for an agent

a of a legally enactable multiplan It~ X is

Ui(~)----Islo -[res(it, s]~,

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The utilities that each agent obtains from a multiplan can be comprised in a vector. The set of utility vectors that are realisable over X is denoted by U(X). When agents have different points of view respecting which multiplan to agree upon, they may "flip a coin" in order to choose between alternative agreements. A probability distribution over the set of legally enactable multiplans is called a mixed multiplan. Let m be the cardinality of X, then a mixed multiplan is a m-dimensional vector m

cr : (p, ..... p , , ) , O < p i < l , Z p i : l . i=t

The set of mixed multiplans is denoted by [ The expected utility of a mixed multiplan is given by the sum of each legally enactable multiplan's utility weighed by its probability: Definition 3. The utility for an agent ~ of a mixed multiplan cr~ ~ is given by

U,(cr) = ~ P,U,(I~k) 9 k=l

The set of expected utility vectors that are realisable over E is denoted by U(Z). When agents co-ordinate their strategies and agree on some mixed multiplan, the corresponding vector of utilities is what each agent expects to obtain. Still, agents are autonomous and not forced to co-operate. So, it remains to model what happens in case of conflict. In a conflict situation we define the response of the set of agents yto a single agent a ' s plan n: to be the multiplan/.t that they are capable of executing and that minimises a ' s utility from t c o p , i.e.

response, (Tc,a, , ll, 7) r

1.t = v,(~ou') min { I.t'e X I prep, (I.t', y ) } .

This models that in case of disagreement an agent must account for the unpleasant situation that all its acquaintances jointly try to harm it. As the possibility of reaching an incompatible multiplan has to be excluded, o~ can only choose from the set FEAS(ot) of plans that are feasible regardless what others do. The empty plan r~ is contained in FEAS(ot) by definition [ 11 ]. Agent a will choose the plan zc out of FEAS,(a), that maximises its individual utility value when combined with the response of its acquaintances. Definition 4. The conflict utility of the agent a is

Uia = max { U i (Tc o l.t )E 1~1~ E FEAS, (a, ) A response, (~, oti , l.t, ~ ) } . We now outline how a bargaining scenario can be defined on the basis of the above notions. For this purpose, we define the overall conflict utility as

..... < ) , and treat the conflict utility vector as an effectively reachable agreement, defining a set S to be the convex and comprehensive hull (cch) of the legally enactable multiplans plus the conflict utility vector The set S usually equals U(L-'), but may also be a (convex) superset of the latter.

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Definition 5. The bargaining scenario B associated with a social co-ordination problem is a pair B = (S, d ) S is called the bargaining set and d the disagreement point. B complies with the formal properties of bargaining models, so the whole mathematical apparatus of bargaining theory becomes applicable [17].

3.3 The Outcome of Social Co-ordination

In this section we rely on Bargaining Theory to find a solution to the associated bargaining scenario (S,d): a vector ~ e S needs to be singled out upon which a bargaining process - and the social co-ordination that it models - is supposed to converge. Strategic bargaining theory relies on a sequential setting where agents alternate in making offers to each other in a pre-specified order and eventually converge on an agreement. By contrast, the axiomatic models of bargaining that we will use in the sequel first postulate desirable properties of a bargaining solution, and then seek the solution concept that satisfies them. The five requirements of individual rationality, Pareto-optimality, symmetry, scale invariance and contraction independence that Nash bargaining models state for "fair" solutions to a bargaining scenario [18], provide an adequate model for our purposes. Theorem 1 (due to Nash [8]). A utility vector ~ , that complies with the above

axioms, maximises the function n

N(s

(xi -d,) i=1

So, a solution ~ maximises the product of gains from the disagreement point. It always exists and is unique [17]. In remains to be shown that the bargaining scenario and its solution concept capture the intention underlying normative prescriptions: a prohibition limits the agents' freedom of choice, potentially making another agent less vulnerable, i.e. less dependent on them. In consequence, the social position of the latter is strengthened and it is supposed to obtain a larger bribe in a potential compromise. In terms of the associated bargaining scenario, normative prescriptions can modify the disagreement point d by declaring the "worst responses" of an agent's acquaintances to be illegal. So, when the disagree1T \ z n ment point is moved in the direction of only one agent, the utility that it gets from the solution should increase, i.e. the bargaining outcome should "move towards" it. Still, this is precisely the property of disagreement point monotonicity of the Nash solution: if d and d ' are two arbitrary disagreement points for Figure 1. Disagreement point monotonicity the same bargaining set S, and t~

U ~

~~~ I

(Xl-dl)(x2-d~)=k

S ~

Paret~surface 2

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and 0" denote the solutions to the corresponding bargaining scenarios, then d~>-cl,, V j r ~=dj ~ r [17] Figure 1 illustrates this: the bargaining solution moves on the Pareto surface in the direction of the agent that strengthens its fallback position. By adequately designing a normative prescriptions, a designer can thus bias the solution towards an agent.

3.4 Computing the Outcome We are now endowed with a characterisation of the outcome of social co-ordination. So, there is no need to explicitly "simulate" the co-ordination process among normabiding autonomous agents. Instead, we use a distributed multistage algorithm that directly computes the solution [9]: 9 stage 1 performs an asynchronous distributed search for Pareto-optimal multiplans; this is done by a variant of the asynchronous weak commitment search algorithm [18], which we have modified to cope with distributed constraint optimisation problems; 9 stage 2 determines the mixed multiplan that constitutes the solution to the associated bargaining scenario; 9 finally, in stage 3 a specific multiplan is chosen by means of a lottery and the corresponding individual plans are assigned to the agents. Note that on the micro-level this algorithm requires agents to follow strict behaviour rules. Still, although this behaviour is rather benevolent, we can assure that its outcome corresponds to the result of social co-ordination among autonomous agents.

4. T h e application: u r b a n road traffic m a n a g e m e n t The model of structural co-operation described previously remains rather abstract. In this section we describe how it is put to use in a practical real-world case: road traffic management in the motorway network around Barcelona. 4.1 The system architecture In Barcelona, the local traffic control centre JPT is in charge of managing urban transport, so as to maintain and restore the "smooth" flow of vehicles. Traffic engineers within the JPT continuously receive information about the traffic state, identify potential problems, and act upon control devices to overcome them. It has become particularly difficult for the JPT engineers to perform this job in real time, as in the follow-up of the 1992 Olympic Games the traffic management infrastructure in Barcelona has become increasingly complex. Nowadays, information about the traffic state of the urban motorway network, consisting of one ring-road and seven adjacent motorways, is provided by over 300 telemetered sensors ("loop detectors") via fibre optics communication links. Control actions can be taken by means of 52 Variable

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Message Signals (VMS), 3 traffic lights for junction control, as well as by ramp metering on 7 ring-road drives. In the sequel, we describe the TRYSA z prototype (TRYS Autonomous Agents) 2. T R Y S A 2 is an experimental decentralised multiagent system, which proposes traffic control actions for the Barcelona motorway network in real time. In line with the traffic engineer's logical subdivision of the road network into problem areas, T R Y S A 2 relies on a set of 11 knowledge-based traffic control agents, each responsible for traffic management in one such area (Figure 2). Every few minutes, an agent receives information about the traffic state in its problem area and generates proposals of signal plans (i.e. sets of control actions) for control devices. Subsequently, potential conflicts between this signal plan and the control actions of other agents (problem area overlap!) are resolved by communication on the basis of structural co-operation. The agents' next reasoning cycle will just be based on the modified traffic state 3.

Figure 2. Autonomous traffic agents for Barcelona In the sequel we first outline the local problem-solving model approach of T R Y S A 2, by means of which the agents' local utility functions have been implemented. 4 We then show how decentralised co-ordination among the agents is achieved. Finally, we sketch the implementation and operation of the system.

4.2 Modelling Local Utility The magnitude of a traffic problem in certain part of the road network can be expressed by the amount of traffic demand that exceeds the capacity of a certain road 2 TRYSA2 is a multiagent version of the TRYS system [4], which has actually been installed and tested at the Barcelona test site. Large parts of the code and the knowledge bases of the TRYS system have been reused in TRYSA 2. 3 By not taking into account previous control action proposals, TRYSA2 agents comply with the "reactivity assumption" of section 2. a Current multiagent system research tends to take the existance of a utility function for granted. However, it is important to notice that the design of computational utility functions for real world applications is definately non-trivial.

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segment (in vehicles per hour). This is called the segment's traffic excess. The quality of a traffic management action can be measured by the reduction of traffic excess, that they are expected to produce. In consequence, TRYSA 2 traffic management agents use the overall reduction of excess in their problem areas (i.e. the sum over all road segments that belong to their area) as a local utility measure. In the sequel we show how AI techniques can be used to build such utility functions. Every couple of minutes, a TRYSA: agent receives temporal series of magnitudes such as traffic speed, flow and occupancy from the road sensors of its area. This raw data is initially pre-processed in order to filter out noisy and erroneous data. Subsequently, data abstraction is performed, calculating aggregate magnitudes such as temporal and spatial gradients for the different sections. In a second step, problem identification (and also some part of problem diagnosis) is performed by matching the abstracted traffic data against a knowledge base of frames which model problem scenarios. Figure 3 shows one such frame that matches the abstracted traffic data. Suppose that as a result of data abstraction low speed and high occupancy are identified in Ronda de Dalt en Diagonal and medium to high speed and low occupancy in Ronda en d'Eslugues. These facts match the frame shown in Figure 3, so that an incident in the central lane of Diagonal road is identified, which manifests itself as a traffic excess (with respect to the road's capacity) of 2200 veh/h between Diagonal and Llobregat in the Dalt ring-road. Traffic from Collcerola to Llobregat and, in a minor degree, from Diagonal heading towards Llobregat contributes to this excess. Diagonal

Can CaraUeu 8PIVI

Stateof Ptnel:13PlV2: l i::

::::::

::~: Section: Ronda de Dah en Diagonal

I ~ ; : [aevtaeviCes

:

speed: low . . . . p~mcy: high Section: Ronda de Dalt en d'Esplugues speed: occupancy: low :::::Critical section: between Ronda de Dalt en Diagonal and Ronda de Dalt en d'Espluges excess: 2200 veh/h paths: From Collcerola to Llobregat -> [60, 80] %

::::::: :::::

::5

:::: :

medium, lugh

I :: [[

: Regulator R1 ;

contemion level medium

:: :::

:: : ~:~

From Collcerola to Llobregat through Ro.da de Dalt-> [40,60] [~Pbtha:: : :: From Collcerola to Llobregat [ through Can Caralleu [30.40] % :::::::::::::::::::: From Colleerola to Llobregat : ::: :::: through alternative paths -> [10,20] %

[ ~

Panel8PIVI :

congestion at Diagonal congestion at Diagonal congestion at Diagonal

::i:: :: ~::::::::::::

%

;>

:::i::: State:~::: From Collcero a to Can Caralleu free From Can Caralleu to Diagonal:

::

::::: ::::::

:

with prolflero~ i

From Diagonal to Llobrcgat -> [20~40] %

Figure 3. An

example scenario

Step three, the control recommendation phase, adheres to the following line of reasoning: first, the historic traffic demand between nodes is retrieved and the contribution of each path to the problem in the critical section calculated. This is done by matching the current abstract traffic state and the state of the control devices against a knowledge base of frames, representing traffic distribution scenarios. Finally, coherent alternative signal plans are generated by using the distribution scenario frames once again: every frame applicable to the current situation is pre-

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selected. Assume that this is the case for the frame shown in Figure 3. Its short-term effects are estimated by simulating its impact on the current traffic situation. This is done by using network structure knowledge to assign traffic demand to the road network, in accordance with the distribution of traffic volume among paths that the frame specifies. In the example about one half of the traffic volume from Collcerola to Llobregat will pass through the Dalt ring-road, while a smaller amount chooses a path through Can Caralleu or other alternative paths, if the corresponding signal plan is set. If the simulation shows a reasonable decrease of excess in the critical section, the frame's signal plan constitutes one recommendation of the system. In the example, it is suggested to display congestion warnings at Diagonal for panels 17PIV1, 13PIV2 and 8PIV1, while setting the contention level of regulator R1 to medium. AS a result of this process, a set of alternative signal plan recommendations, together with their utility (i.e. their expected reduction of local traffic excess) is produced.

4.3 Modelling Social Co-ordination In order to choose a local signal plan, TRYSA 2 agents not only need to take into account their local utility, but also the effects that the control actions of their acquaintances have on it. In terms of the model presented in section 3, they need to base their decision on the utility of multiplans instead of individual plans. In the sequel we will consider feasibility relations between plans, in the presence of which an agent's acquaintances can turn down its local control plan, by threatening to take control actions that would result in an incompatible multiplan. In the domain under study, this can happen when physical conflicts between control actions are possible, i.e. when two agents have the possibility to set the same control device in different, incompatible states (e.g. by displaying different messages on the same VMS). Physical relationships between plans and the possible ways of dealing with them in terms of states of control devices are expressed in the plan interrelation knowledge base of an agent. It is represented by rules, that obey to the following format: [c d e v ~ [c d e v ~

..... .....

cdev ] ~ cdev n ] ~

[cdev ..... [nogood ]

cdevj

]

or

The operational semantics of such a rule determines that the control device states of the antecedent can be substituted by those of the consequent without any important changes in the effect of the signal plans (e.g. by merging different messages "congestion at A" and "congestion at B" to be displayed on the same VMS into one "congestion at A and B" message). If control devices are merely incompatible, the consequent is the constant nogood. In addition, TRYSA 2 agents are endowed with an agent dependence knowledge base, which hosts rules of the form [cdev~

.....

cdev

] ~

[o~

.....

of

]

They state that if all control devices cdev 1 to cdev, switch to new states, then this concerns the agents al to q . Note that these rules actually compile knowledge about the capabilities of an agent's acquaintances, upon the background of possible physical plan relations. For instance, if agent a, may set a message M~ on VMS P, and aj possibly displays a message Mj on the same panel, while both messages are incompatible, then the knowledge base will contain a rule stating that setting M on VMS P concerns

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agent %. This serves two purposes: when used with forward inference, it allows an agent to deduce which agents are "interested" in changes of its local signal plans; using backward inference, it enables an agent to determine which agents can affect the executability a certain set of control actions. On the basis of this knowledge, TRYSA 2 agents exchange messages in line with the algorithm sketched in section 3.3. It remains to be shown how normative biasing is achieved. In TRYSA 2 normative prescriptions refer to the prohibition of setting certain control device states. These are generated by the norm knowledge base, which qualifies a set of prohibitions temporally by current date and time as well as by the categories type of day (Working day, Sunday, Saturday or Holiday) and type of season (Xmas, Easter, Summer, or Normal). Different such temporal qualifications essentially reflect different traffic demand patterns, which require different sets of normative prescriptions.

4.4 The system The TRYSA 2 system has been implemented experimentally on networked workstations. The TRYSA agents constitute separate Prolog processes (with some extensions in C++), which communicate via sockets. The Barcelona test site is simulated by the AIMSUN traffic simulator [1]. AIMSUN is endowed with a precise description of the traffic management infrastructure at the test site, including detailed models of the road network, the sensors, control devices etc., and performs microscopic ("car by car") simulation of traffic flows. A special observer agent has been implemented in Tcl/Tk in order to visualise the problem-solving process and its results [9].

5.

Discussion

In this paper we have outlined the social co-ordination mechanism of structural cooperation, by means of which the outcome of autonomous agents' self interested choice is biased by normative prescriptions, so as to make it instrumental with respect to a global problem to be solved. We have shown how this theoretical model can be applied to the practical problem of decentralised multiagent traffic management in an urban motorway network. Some words on the adequacy of this mechanism appear convenient here, as the choice of classical bargaining theory as a vehicle to formalise structural co-operation entails a "price to be paid". Firstly, we assume that agents make joint binding agreements. Secondly, we do not account for the formation of coalitions. Finally, we assume agents to be perfectly rational. Still, as our aim is to build a decentralised coordination mechanism for homogeneous societies of problem-solving agents, these assumptions become less severe: law abidance can just be "build into" our artificial agents; by ignoring coalition formation, we have sacrificed some plausibility of our model in favour of efficiency, as coalition formation is a computationally complex process. The assumption of perfect rationality is justified by the fact that there exists a sound axiomatic characterisation of a solution, which allows for its direct computation without an extensive "simulation" of the bargaining process. After all, the

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T R Y S A 2 prototype indicates that the above assumptions do not necessarily limit, (but may even foster) the applicability of the mechanism to real-world problems. With respect to the adequacy of using structural co-operation for traffic management, we suggest that the decentralised co-ordination architecture of T R Y S A 2 promotes scalability in comparison to centralised architectures, which rely an a special co-ordinator agent [4]: the introduction of new agents in the system generates a shift in the outcome of structural co-operation, leading to a new baseline co-ordination. In future work we will further refine the normative knowledge within the T R Y S A 2 system. The different effects of particular types of prescriptions in real-world traffic situations will be examined by means of experimental studies. In addition, we are thinking of applying multiagent learning techniques to this task.

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