A MULTI-AGENT CONTROL IN ROAD TRAFFIC MANAGEMENT

ENVIRONMENTAL ENGINEERING May 22-23, 2008 The 7th International Conference Faculty of Environmental Engineering, Vilnius Gediminas Technical University Saulėtekio al. 11, 10223 Vilnius-40, Lithuania Tel.: +370 5 2744719; e-mail: [email protected] A MULTI-AGENT CONTROL IN ROAD TRAFFIC MANAGEMENT Chris Tampère, Ben Immers, James Stada, Bart Janssens University of Leuven (KUL), Department of Mechanical Engineering, CIB/Traffic and Infrstructure Celestijnenlaan 300A, B-3001 Heverlee, Belgi email: [email protected], tel. +32.16.321669 Abstract: Current traffic management measures increasingly exhibit dynamic features by taking into account the dynamics in traffic demand and transportation system supply. Demand actuated traffic signal settings or variable message signs are examples of traffic management devices driven by the dynamic characteristics of the traffic. In most cases however, these traffic management devices are implemented as stand-alone systems, meaning that there is no, or hardly any, co-ordination between the various traffic management measures taken. The lack of co-ordination carries within it the risk of reduced effectiveness. The various measures could, for example, serve opposing objectives or even generate a negative impact on traffic flows that or not in any way related to the problem that the traffic management device was meant to solve in the first place. The uncoordinated application of dynamic traffic management measures thus could possibly be counter-productive. The setbacks of uncoordinated control can be avoided by carrying out the control task in two different ways: in a detailed way by focusing on the problem(s) that need(s) to be solved (distributed control), and in a more generic way by controlling the overall traffic performance in the network (generic control). In this paper we analyse the possibility of combining both distributed and generic control in one control strategy using hierarchic agents. In effect the approach tries to match local and global impacts by using autonomous agents interacting with each other in a horizontal and in a vertical (hierarchical) way. The local agents (defined in terms of network links or network nodes) control the traffic in their specific area according to predefined performance goals. One layer higher in the hierarchy another agent controls the traffic performance in a part of the network, checking the results of individual control strategies against the overall performance goal of that specific part of the network. We present the results of a modelling experiment featuring a control system with two layers. The first layer consists of link agents directly serving the traveller by guaranteeing reliable travel times and/or maximal throughput. The second layer consists of node agents that try to harmonize conflicting goals of the various link agents. An important characteristic of our approach is that the higher level agent is dominant in the negotiation process (i.e. a higher weight is attached to the decision of the higher level agent). The multi-agent control strategy described above is applied to a test network consisting of a part of the road network around the city of Antwerp. The results show that it can easily deal with the goals of the various agents. In the case of conflicts, the attached control priority determines how differences will be settled. An interesting feature of the above approach is the lack of a central mechanism controlling the various agents. The global optimum that is established in the system is the result of selfish behaviour on the part of the various agents combined with some co-ordination based on pre-set priorities. Actually the system is finding this optimum in a self-organising way. This is a very interesting feature as it allows us to apply a large range of control strategies. Keywords: Dynamic Traffic Management, Multi-agent control, Environment, 1.1. Central control 1. Dynamic traffic management and control Overview of different control systems In this section we present an overview of several different principles by which systems can be controlled. The main distinguishing characteristic is the degree of decentralisation of the control process [1,2,3,4,5]. A system with central control has one central component that receives data from all sensors and directly sends control signals [6,7]. The central control component analyses the received signals, translates these to a possible traffic situation and subsequently determines the optimal set of control signals on the basis of a global objective function [8]. This process is shown in the diagram of figure 1. 1052 Ramp metering Route information Output criterion Traffic flows Variable speed limitations etc. Perturbations Reality Controller Analysis Control strategy Estimate situation Prediction Real-time measurements Overall objective function Fig 1. Principle of central control 1.2. Hierarchical system with agents This system is based on the idea that local control devices, referred to as ‘agents’, are best suited to deal with local problems. To ensure that the system as a whole also functions in a satisfactory way a hierarchy of control layers is established based on the same idea, but at a higher level [8]. An agent may be taken to be piece of software or a robot that observes its environment and responds to it, its behaviour being mainly autonomous and partly dependent on its own experience. The example in figure 2 illustrates a hierarchical system based on agents. The figure shows a simple network consisting of a few streets [8]. Every intersection is governed by a local control unit, an intersection agent. In addition these local control units are supervised by a control unit, call it a street agent, which safeguards the performance of the street as a whole. The problems are tackled on the level where they arise. The intersection agents are concerned with smooth traffic operations on their own intersection. Although an intersection agent might take the right decisions from a local point of view, these decisions might in some cases have a detrimental effect for the street as a whole. In such cases the street agent street-wide basis. The interaction takes the form of some sort of negotiation [9,10] between intersection and street agents trying to reach a consensus between the objectives of both agents [8,11,12]. This system can be extended to higher levels: neighbourhood agents, district agents, network agents. It is also possible to mobilise special agents for important routes etc. Clearly using agents is not limited to the control of traffic lights. Agents could also be developed to control ramp metering installations, dynamic speed indication signs, dynamic route information panels and other dynamic traffic management measures, such as devices directed at a flexible use of the infrastructure [9]. 1053 Fig. 2 a) Example of a network with a hierarchy of agents. b) Delegation of responsibilities 1.5. Mixed systems 1.3. Non-hierarchical agent systems In a non-hierarchical system we also use local, independent and autonomous control agents. Every agent in such a system is responsible for its own area and communicates with nearby agents to assess the situation in its immediate neighbourhood [11,13] (see figure 3). The nearby agents consult and negotiate on the basis of their own priorities [11,14,15]. Because this happens through the whole system all agents undergo some direct or indirect influence of all the other agents. This form of communication still enables the system as a whole to attain a global optimum [13]. Clearly the principles of the control systems discussed in the preceding sections can be combined. In certain situations the advantages of one system over the other might be retained while in other situations we might want to eliminate some of the weak points of a system. Certain parts of the system, for example, could be controlled by agents, while other parts would be under some central control. Another possibility would be to apply a non-hierarchical agent structure in normal situations, while imposing a strict hierarchical control if something unexpected happens, for example if the network suddenly needs to be used for an evacuation in the case of an emergency. For the sake of clarity we will not consider these mixed systems any further. 2. Selection of a system We compared the systems presented in the previous section on the basis of a number of criteria. The following criteria were used: Alertness The term alertness is used to indicate the quickness of response of a system to a new situation. The more distributed the control, the faster the system is able to react, because the problem is split up into smaller and simpler subproblems. Fig. 3. Agents in a non-hierarchical structure. 1.4. “Self-organising” systems Robustness By increasing the decentralisation of control we ultimately arrive at systems where there is no consultation at all between individual agents. These agents decide on their actions in a completely autonomous way [16,17,18,19]. It appears contradictory to refer to these independent, very local control entities as a ‘system’, because at first sight there seems to be no relation whatsoever between different control actions. One tends to overlook, however, that information is still being exchanged between agents. In fact the traffic flows themselves are the carrier of the information. A centrally controlled system is more sensitive to disruptions than a distributed system. A breakdown in a distributed system only leads to local repercussions, while if a central control unit fails global traffic control breaks down. Flexibility This is the ability of the system to adapt to new and unknown situations. Because distributed systems only rely on the local performance of agents they lack 1054 flexibility. Introducing hierarchy improves the situation because more global problems may be addressed by the higher level agents. Transferability Transferability refers to the practical reusability of the system in an environment different from the one it was designed for. The dedicated nature of a centrally organised system hampers tranferability. Pro-activity Instead of reacting only to actual traffic conditions we might want to anticipate on possible future traffic conditions. It reaquires that traffic situations can be forecasted over a certain time horizon. A centralised system is perfectly suited for such pro-active control. The ‘model-based control’ method ca be applied [6]. A hierarchical, distributed system also lends itself to proactive control, but the implementation of such a system is more demanding. Extendability The adding of additional control devices is easier in a distributed system than in a centrally organised system. Learning capability Learning is the process by which the system learns to recognise situations it has encountered before and also the gaining of knowledge about the likely reaction of the traffic to control measures. Non-hierarchical systems only have local feedback, while centrally controlled systems have global feedback. A hierarchical system contains local and global elements, meaning that learning takes place on a local as well as a global scale. availability of alternative routes, travel times, and the blocking back of congestion to upstream road sections. The more distributed a system is, the more skill it requires to recognise these network-wide relationships. Closely related to network orientation is the issue of closely monitoring traffic operations between (economically) important OD (origin-destination) relations. In a hierarchical system one can assign a special agent responsible for these relations. A centrally organised system also allows these relations to be explicitly included into the controller. In completely distributed systems it is difficult to introduce this quality into the system. Data availability To be able to extract statistical information the ready availability of data from the system is of some importance. Obviously, if the data are distributed throughout the system, this hampers the easy extraction of data. The systems discussed in the previous section were compared to each other by awarding them a score (on a scale of 1 to 4) on each of the above-mentioned criteria. It appeared that the hierarchical system with agents obtained the best score, closely followed by a centrally organised system. In the following sections of this paper we proceed to a closer examinination of such a hierarchical system. 3. Application Implementation This refers to the ease of practical implementation. A self-organising system is the easiest to implement. Distributed systems, with agents consulting each other, require the implementation of a large amount of communication protocols. Transparency Fig. 4 Main road network of Antwerp and link priorities. The structure of a hierarchical system may closely correspond to a certain policy structure. A centrally organised system also reflects the policy objectives in a clear way. Completely distributed systems lack this quality. Network orientation Especially in a centralised system the existing relationships within the whole network are easily discernible. Examples of such relationships are the In the third step of our investigation we examined the possibility of using the selected system (a hierarchical system with agents) to control traffic on the road network of Antwerp. A former study [20,21] established the priority order of traffic operations on the road network around Antwerp (see figure 4) In the road network of Antwerp an important part is played by the interaction and co-operation between the Ring Road (in red) and the Singel (in blue). The Singel, an important thoroughfare, is a kind of inner ring road, running mostly parallel to the main Ring Road motorway. 1055 ̇ Figure 5 shows a simplified subnetwork that respects the hierarchy between the different road types. ̇ Not all links in a network are of equal importance. For that reason every link has a priority assigned to it in the form of a weighting factor. Exit road ̇ Fig. 5 Selected test network. The exit road of the Ring motorway leads towards an intersection of the Singel Road. It allows traffic coming from the Ring Road to take the Singel. The intersection allows traffic to pass through, either the traffic travelling on the Singel or traffic arriving from the Ring Road. A limited capacity is available for the two traffic flows taken together. There may arise an important conflict in interests between both roads. Traffic on the Singel should not be hampered too much by traffic coming from the exit road. After all the priority rating of the Singel is higher than that of the exit road. This means that traffic on the exit road will experience a longer delay than traffic coming from the Singel. If the traffic flow on the exit road starts to increase, more vehicles will have to wait at the intersection causing long tailbacks on the exit road. If the tailback keeps on growing, then blocking back may occur on the Ring Road. This means that the waiting line extends all the way to the motorway obstructing other traffic on the motorway that has no intention whatsoever to leave the motorway. This situation should be avoided, if at all possible. 3.1. Agents 3.1.1. Links A link is the connection between two nodes. From a traffic perspective, a link is a road that connects two traffic nodes. A link has a certain length and carries a certain number of vehicles at a certain moment in time. Figure 6 shows the characteristics of a link. [i ] = link number ̇ Li = link length qi1 = inflow of traffic from upstream node wi = priority of the link For every link we can write an equation expressing the conservation of vehicles: ∫q t + ∆t t i1 (t )dt = ∫q t + ∆t i2 (t )dt + ∆X i t 3.1.2. Nodes Different links are joined by means of nodes. One or more links may converge at a certain node and also one or more links may depart from a certain node. A node agent is confronted by a certain traffic demand arriving from the upstream nodes and a supply of capacity of the downstream links. The node agent can deal with this situation in a number of ways. There are two different types of node. On the one hand we have active nodes that can intervene in the connection between different links, in the way that intersections use traffic lights. This type of node plays an active role in distributing the demand from the upstream links over the available capacities of the downstream links. The available capacity is first and foremost restricted by the capacity of the node itself, because the number of vehicles that can pass the intersection is bounded. ̇ The network consists of links and nodes. Both network components are represented by means of agents. ̇ qi 2 = outflow of traffic to downstream node X i = number of vehicles on the link C kr ,i = intersection capacity of node i The node capacity is also bounded by the state of the downstream links. If maximum density is reached in one of the downstream links no further traffic can be taken care of. The actual distribution of traffic depends on the situation in which the node agent has been deployed. A node agent controlling a ramp metering installation at the entrance to a motorway will behave differently from a node agent overseeing an intersection. Fig. 6 Graphical representation of a link. ̇ Fig. 7 Graphical representation of a node. 1056 On the other hand there are many passive nodes in a network. Their only duty is to connect different links and there is no way of controlling capacity. But these nodes, like active nodes, also have a bound to their capacity. 3.2. Application to the test network The test network is an example of two parallel roads with a buffer in between (see figure 8). The links on the Ring Road and the Singel, indicated respectively by [1] and [2] and by [4] and [5], should guarantee free circulation of traffic. These links will be assigned an agent responsible for this task. The exit road, link [3], functions as a buffer between the Ring Road and the Singel. Traffic leaving the Ring Road should not intervene in a serious way with the traffic on the Singel. Because the exit road is relatively short in comparison to the other links, free circulation is of minor importance. By buffering the traffic leaving the Ring Road on the exit road and by carefully feeding traffic onto the Singel we can try to guarantee smooth traffic operations on both major roads. Fig. 8 Choice of link and node agents for the test network. To take care of buffering it is necessary to make node 5 an active node. Node 5 will ask link 3 and 4 for information about their respective traffic states and on the basis of this information will distribute capacity. The other nodes in the test network are passive nodes. Node 2 is the branching point on the Ring Road leading to the Singel. Nodes 1 and 4 symbolise the input to the system; they represent upstream boundary conditions. At nodes 3 and 6 traffic leaves the system. If there is congestion downwards of these nodes they represent a downstream boundary condition. 3.3. Testing the behaviour of the agents and the system for different parameters We now examine the behaviour of the system. Two different policy options to deal with congestion in the network will be investigated. We shall also compare the quantitative results of this system to a system operating without agents. The two policy options are: ̇ fairly sharing the congestion misery ̇ keep the problems localised to where they occur Fair share of the misery A possible option could be to spread out congestion problems over the network. Seen from the viewpoint of the users of the network this means that one prefers some slight disruption for a lot of road users to heavy discomfort for a limited group of users. The reliability of travel times could benefit from such an approach, making a network less vulnerable. A network will appear more reliable to most users if a problem on one of the links only causes a light increase in travel time on all of the other links. Assume that one wants to apply this principle to the test network. This would mean that if the intersection at node 5 gets overloaded (implying an overload for the buffer at link [3] also), the congestion misery would be spread out over link [1] and the links [4] and [5]. Keep the problems localised to where they occur The other way of managing the network starts from an opposite concept. The idea is that it is best to keep a problem in the network localised, thus keeping interference with other flows that have no relation to the problem at a minimum. In the test network this means that a problem occurring on a local intersection, such as node 5, should have no consequences for the flow on the motorway. In a reservoir model the number of cars that are present on the link can also be interpreted as the number of cars waiting at the downstream node. Waiting vehicles on the motorway have to be avoided at all costs. The problems occurring on the network thus should be spread out over the buffer of link [3] and over links [4] and [5]. This can be attained by drastically decreasing the value of the desired number of vehicles on link [1] and by increasing these values for link [4] and [5]. For both policy options traffic flow on the network has been simulated. The following priorities have been assigned to the links: w1 = w2 = 2 ; w4 = w5 = 1 and w3 = 0.5 3.3.1. Computation of the option ‘fair share of misery’ For each link ‘qualities’ have been defined which one would preferably realise. For the option ‘fair share of misery’ the agents will attempt to safeguard the following qualities: ̇ Links [1] and [2]: a minimal average speed of 80 km/h ̇ Links [4] and [5]: a minimal average speed of 50 km/h ̇ Link [3]: a maximal rise in the number of buffered vehicles of 10 vehicles per time step of 1 minute. Simulating traffic for a period of 300 minutes gave the results shown in figures 9 and 10: 1057 3.3.2 Computation of the option problems localised to where they occur’ ‘keep the # vehicles In this option we want to prevent that a problem on a local intersection, such as node 5, will interfere with the traffic on the motorway (links [1] and [2]). Furthermore the waiting of vehicles on the motorway should be avoided at all costs. The problems that occur in the network should therefore be distributed as much as possible over the buffer of link [3] and over links [4] and [5]. For this option the agents will attempt to safeguard the following qualities ̇ Links [1] and [2]: minimal blocking back of traffic from link [3] ̇ Links [4] and [5]: a desired average speed of 30 km/h ̇ Link [3]: a maximal rise in the number of buffered vehicles of 10 vehicles per time step of 1 minute. Time (minutes) Flow (veh/h Fig. 9 Number of vehicles on the links # vehicles Simulating traffic for a period of 300 minutes gave the results shown in figures 11 and 12: Time (minutes) Fig. 10 Capacity allocation node 5 In addition, it appears that during this period of excess, links [4] and [5] show nearly exactly the same deviation of the objective over time. Thus the system shows behaviour in accordance with the desired policy, namely spreading the hindrance. Time (minutes) Fig. 11 Number of vehicles on the links Flow (veh/h The figures clearly show that the hindrance caused by an inflow into the network that exceeds the maximum outflow is spread out over the different network components over time. This leads to ‘equilibrium of hindrance’, all links will suffer from a loss in quality in proportion to the assigned link priority. In the figure it can be seen that from t = 20 min to t = 45 min links [1], [4] and [5] have to make a concession as to the desired quality. The exceeding of the maximum desired number of vehicles shows the same progression for all links. The maximum deviation of links [4] and [5], however, is double that of link [1], about 20 (60-40) compared to 10 (85-75). This perfectly agrees with the priorities assigned to the links. Time (minutes) Fig. 12 Capacity allocation in node 5 1058 Like in the preceding simulation ‘equilibrium of hindrance’ arises. All links will suffer in performance, according to the assigned link priority. But clearly, because of a different choice of parameters, this equilibrium differs considerably from the preceding example. Links [4] and [5] will have to handle much more vehicles, while link [1] is relatively spared. The progress in the excess of the desired number of vehicles on links [4] and [5] is not exactly the same in this situation. The equilibrium assignment of traffic at node 5 during the first 30 minutes results in total flow on the node exceeding the capacity of the intersection. Therefore the downstream link receives an inflow equal to the intersection capacity. Upstream, between link [1] and [4], equilibrium is indeed found. As from t = 35 min a global equilibrium is achieved lying within the capability of the intersection. This causes a limitation on the inflow of link [5] leading to an equilibrium in the behaviour of links [4] and [5] after t = 40 min. The behaviour also shows the same progress after t = 40 min. This shows that the system always tries to comply with the policy as much as possible within practical boundaries. 3.4. Comparison of the number of vehicle hours lost In a first quantitative analysis we compared the number of vehicle hours lost (VHL). The number of vehicle hours loss equals the time period that a vehicle spends on the network summed over all vehicles that pass through the network. difference could have many causes. The difference however is too small to make any judgements. A reduction in the absolute number of lost vehicle hours cannot be obtained by agent based control. But it is true that the network as a whole behaves better in accordance with the policy options drawn up for the individual links. This improvement in performance should be measured by another criterion, namely in terms of deviation from the policy objectives. 3.5. Deviation from the objectives In this quantitative analysis we examine to what extent the system complies with the policy objectives for the different links. The qualitative analysis showed that the ‘misery’ gets well spread out in the system employing agents. In a system without agents especially link [5] has a hard time while the rest of the system is spared. By calculating the total deviation from the policy objectives we can find which of the two situations presents the best perspectives and to what degree. The total deviation from the policy objectives may be computed by determining the deviation per time step of each link with respect to the policy objective and aggregating over all links and the total time period of the simulation. The deviation of a link from its policy objective at time t equals the number of vehicles on the link minus the desired number of vehicles according to the objective. deviationi = max(X i (t ) − X i ,g ,0 ) The following table shows the number of vehicle hours lost per system and per link: The deviation is expressed in number of vehicles and, moreover, a negative deviation, meaning compliance with the objectives, is not counted. In this way we get values, indicating non-compliance with the policy objective ( X i > X i , g ), for the whole simulation period Table 1: Comparison of the vehicle hours lost. Link Priority 1 2 3 4 5 2 2 0.5 1 1 Total Weighted With agents 10.67 5.63 156.30 146.83 188.98 508.40 446.55 Without agents 40.75 5.63 89.81 0 366.67 502.85 504.32 that may be compared with each other. Table 2. Comparison of deviation from policy objectives. The total number of vehicle hours lost is almost constant, regardless of using a system with or without agents. The reason is that inflow and maximum outflow in both systems is the same and the capacity of node 5 is bound to a maximum. There is not much space to escape from these boundary conditions. The lost vehicle hours in the system with agents exceed those in the system without agents by 1.1%. So, in absolute numbers, a system without agents is even slightly better than a system with agents. This small Link Priority 1 2 4 5 2 2 1 1 Total Weighted With agents 394.49 242.50 678.45 529.02 1853.50 2490.50 Without agents 2261.70 242.50 0 11095.00 13599.00 16104.00 Link [3] has not been included in this analysis because this link only serves as a buffer, and does not offer any quality to the user in terms of free circulation of traffic. 1059 This analysis does show the big difference between the two systems. The system involving agents reduces the exceeding of policy objectives by about 87 % as compared to the system without agents. Even if we correct the results by taking into account the link priorities the reduction still amounts to about 85%. This reduction could be expected. The system with agents is designed in such a way as to comply as well as possible with the policy objectives, while the system without agents only exercises local control. Notable are the deviations per link in the agent system. We find that the deviations are, as much as possible, distributed among the links according to their priorities. In the system without agents, by contrast, there is a large excess of vehicles on link [5], while link [4] has no excess at all. Although the other links are operating much less underneath their objective, the comparison shows that from a global point of view this downstream accumulation does not represent a desirable situation. 4. Conclusions From the qualitative analyses it appears that the system will perform according to its design specifications. The quantitative analysis furthermore confirmed that by choosing a distributed system we achieve the goal of conciliating local and global performance. Our investigations showed that the distribution of deviations with respect to the policy objectives that corresponds to the link priorities also leads to a reduction of the total deviation. The fact that every agent pursues its own interest also brings about a global improvement for the whole system, a result that is not self-evident. The agent system is designed to be able to translate policy objectives into actual practice. These policy objectives are usually formulated in terms of desired qualities, such as maximum travel time, minimum speed or reliability of travel time or speed. The agent system does not lead to a reduction of lost vehicle hours, but it allows for a spreading of these lost vehicle hours over different components of the network in a way that is judged expedient. 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