A MULTI-AGENT APPROACH
TO DYNAMIC TRAFFIC MANAGEMENT
Ben Immers
Chris Tampère
James Stada
Bart Janssens
University of Leuven (KUL)
Department of Civil Engineering
Traffic Planning and Highway Engineering
Kasteelpark Arenberg 40
3001 Heverlee
Belgium
tel. +32.16.321669
email: [email protected]
KEY WORDS: Dynamic Traffic Management, Multi-agent control, Environment
Theme Area: Network Dynamics, Environmental and safety aspects of transport
1
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. It is also possible that this higher-level agent
intervenes when there are conflicts between the underlying agents. The above approach can be
extended by adding additional layers, establishing a pyramidal control structure. Each control
layer represents a level that requires co-ordinated control including measures to realise the
goals formulated on this specific level.
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 co-ordinated control pyramid (CCP) 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 CCP
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.
2
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].
Central control
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.
Ramp metering
Route information
Output criterion
Traffic flows
Variable speed limitations
etc.
Perturbations
Reality
Controller
Analysis
Control
strategy
Estimate situation
Real-time
measurements
Prediction
Overall objective
Figure 1: Principle of central control
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.
3
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, that safeguards the performance of the street as a whole.
Figure 2 a) Example of a network with a hierarchy of agents. b) Delegation of responsibilities
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 can intervene to try to
attain the objectives on a 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].
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].
4
Figure 3: Agents in a non-hierarchical structure.
“Self-organising” systems
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.
Mixed systems
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.
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:
5
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.
Robustness
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 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.
6
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
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 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.
Design of the individual agents
Agents
The network consists of links and nodes. Both network components are represented by means
of agents.
7
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 4a shows the characteristics of a link.
[i] = link number
Li = link length
qi1 = inflow of traffic from upstream node
qi 2 = outflow of traffic to downstream node
X i = number of vehicles on the link
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.
wi = priority of the link
For every link we can write an equation expressing the conservation of vehicles:
t + ∆t
∫q
t
t + ∆t
i1
(t )dt =
∫q
i2
(t )dt + ∆X i
(3.1)
t
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.
C kr ,i = intersection capacity of node i
The node capacity is also bounded by the state of the downstream links. If maximum density
has been 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.
8
Figure 4: a) Graphical representation of a link
b) Graphical representation of a node
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.
The Belief-Desire-Intention model
The belief-desire-intention model (BDI-model) [14,20] is used to design the reasoning of the
individual agents. Figure 5 depicts the behavior of such an agent.
Figure 5: The BDI-model for agents.
For each agent in the model 3 separate layers are distinguished:
•
•
•
Beliefs: representing the real world as observed by the agent. The picture of the real
world actually is a composition of various pictures: the environment, the self-image of
the agent and the image of other interacting agents.
Desires: representing the objectives the agent would like to realise
Intentions: representing the plans/measures/actions applied by the agent to realise the
desires.
We will apply this conceptual model for the representation of an agent to describe the link and
node agents in our network. We furthermore will distinguish 2 different link agents
(throughput and buffering) and 2 node agents (active and passive).
9
Link agents
Situation
The Link agents will check whether a specific link will provide a dedicated (desired) quality
(e.g. max. flow or min. travel time) to the traveler. If the desired quality is not offered the link
agent will come into action.
Beliefs
In order to be able to control the situation each link-agent should encompass all variables
describing the link state. Some of them are fixed or considered to be fixed e.g. the length Li of
a link, the fundamental diagram (e.g. speed-density relationship) and the link priority wi .
Furthermore the link-agent will ask neighboring node agents (upstream and downstream) for
incoming and outgoing flows ( qi1 and qi 2 ). As links operate pro-active they will also ask
upstream nodes for a prediction of the incoming flow qi1 .
The number of vehicles on the link, Xi is continuously checked using the conservation
equation. Given Xi and Li the density ki can be calculated using the simple equation:
X
(3.2)
ki = i
Li
Applying the fundamental diagram also yields values for the average speed U i .
In this way the link agent has a complete picture of the link state. The beliefs are identical for
all link-agents.
Desires
The desires need to be formulated for each link type.
Throughput agent:
For some links it is very important that they generate a large throughput (e.g motorway
sections). A large throughput is more or less equivalent to a high average speed.
Figure 6: Assessing speed and density using the fundamental diagram.
10
The minimum speed (Umin) can be guaranteed if the density doesn’t exceed k g . The desire of
the agent thus is to keep the density smaller than k g . The throughput on the link
equals X i , g = k i , g Li .
Buffer Agent:
Some road sections (e.g. on and of-ramps) are used to buffer the traffic thus avoiding
congestion on other sections (where throughput is important).
The traffic in the buffer will be metered thus avoiding peaks on the downstream road section.
∆X i ,max is the metering rate per time period. Thus the maximum number of vehicles in the
buffer in the next time period ∆t will be:
X i , g (t + ∆t ) = X i (t ) + ∆X i ,max
(3.3)
Intentions
The link agents cannot directly intervene in the traffic flow; they will realize their intentions
by ‘asking’ neighboring node-agent to perform some actions.
Asking for capacity downstream
To be able to unload the traffic freely, it is important for the agent that the downstream node
offers enough capacity. The link-agent knows (from the upstream node-agent) how much
incoming traffic will load the link in the next time period (left part of conservation equation).
t + ∆t
∫q
t + ∆t
i1
(t )dt =
t
∫q
i2
(t )dt + X i (t + ∆t ) − X i (t ) (3.4)
t
He also knows the amount of traffic on the link at time t. And for t + ∆t he assumes that the
number of vehicles equals the desired throughput
(3.5)
X (t + ∆t ) = X i , g
Thus the only unknown parameter is the integral of the outflowing traffic. We assume that this
capacity is adjusted in a downstream active node per time period ∆t and remains constant
during the time period, than
t + ∆t
∫q
i2
(t )dt = qi 2 ∆t
(3.6)
t
In this way the threshold value of the desired outflow can be calculated:
t + ∆t
∫q
qi 2 =
i1
(t )dt
t
∆t
−
(X
i, g
− X i (t ) )
∆t
(3.7)
11
qi 2 , g = max(qi 2 ,0)
(3.8)
This value is passed on to the downstream node-agent (to be realised in the next time period
∆t . The node-agent will try to realise this goal, but there are more constraints!
If the downstream node is a passive node, active intervention is not possible. However,
problems can be detected comparing desired and actual flow values.
Asking for less inflow from upstream
In this case the integral of the outflow is known. Applying simular assumptions as in the
downstream case, the integral of the income flow can be represented by:.
t + ∆t
∫q
i1
(t )dt = qi1∆t
(3.9)
t
The desired inflow value for the link-agent will be:
t + ∆t
∫q
qi1 =
i2
(t )dt
t
+
∆t
(X
i,g
− X i (t ) )
∆t
qi1, g = max( qi1 ,0)
(3.10)
(3.11)
If we are dealing with a fixed outflow, there will also be an upper limit o the inflow. As soon
as the density on a link equals the maximum density k max , no additional vehicles can be added.
The upper limit of the inflow can be calculated by substituting the maximum density in
equation (3.10). The maximum inflow qi1,max will be;
t + ∆t
∫q
qi1,max =
i2
(t )dt
t
∆t
+
(X
i , max
− X i (t ) )
∆t
(3.12)
Again these values will be passed on to the neighboring upstream node agent. An active nodeagent will try to comply with the values under prevailing constraints. A passive node-agent
can only assess possible problems by comparing desired and actual values.
Node-agents
Situation
Node-agents represent nodes in the network. They connect links and transfer traffic from one
link to the other. Nodes also have a specific capacity C kr ,i .
12
Beliefs
Neighboring link-agents will approach the node-agent with requests for a specific outflow
qi 2, g from an upstream link-agent or (downstream) a desired inflow qi1, g , with a maximum
value of qi1, max . The weight factor wi is an indication of the priority of such a desire. Finally
the node-agent is familiar with the intersection capacity C kr ,i of the node itself.
Desires
To some extent passive and active nodes will share the same desires. On top of that active
node-agents will exhibit some additional desires.
Active and passive nodes: shared desires
Each node will predict the future situation (e.g. traffic flows) and will pas on this information
to neighboring link-agents.
If a node–agent is dealing with a problem that is beyond the scope of available solutions it will
attempt to trace the source of the problem in the neighboring link-agents. If such a source can
be detected the node-agent will contact the relevant link-agent asking for a solution.
Active nodes
An active-node can actively intervene in the traffic situation by applying an control
mechanism e.g. traffic lights.
The desire of the node agent is to match the available capacity with the various requests. If
demand exceeds capacity the node agent will start contacting the neighboring link-agents.
Intentions
Predictions for downstream links
All links upstream of a node will pass on their demand qi 2, g for the next period ∆t to the
downstream node. In this way the node automatically will be informed about the future
demand.
The node will pass on the predicted demand to the downstream link-agents. Furthermore, the
node-agent knows that the maximum flow is restricted by the maximum node capacity C kr ,i .
The same principle is applied throughout the network
Assignment of the downstream capacity to the upstream demands for capacity (only relevant
for active nodes)
Figure 7 represents the situation where an active node Ckr,i receives requests from upstream
link-agents for capacity and from downstream link(s) for flow.
13
Figure 7: Assignment of the various capacities by an active node-agent
The node-agent will try to comply with the various demands of the link-agents. The maximum
flow that the node-agent can handle will be:
C i , max = min(C kr ,i , qb , max )
(3.13)
Furthermore the flow requests upstream and downstream need to be harmonized. This applies
e.g. to situations where the downstream flow request qb, g is smaller than C i , max . Differences
between requests for capacity and the available capacity will be settled according to the
priority of the various link-agents. The assignment of capacity will be done in the following
way:
case 1: flow request downstream is larger than capacity request upstream
QH , g = ∑ q hi , g ≤ min(C i , max , qb , g )
(3.14)
i
Each upstream link-agent will assign a traffic load of q hi , g to the downstream node. There will
be no problem if the sum of all these requests is smaller than qb , g and also smaller than C i , max .
The harmonization of the requests for flow q hi , g of the downstream link-agent and the actual
flow q hi will be done as follows:
Q H , g < min(C i ,max , qb , g ) =>
q hi = q hi , g +
whi
(min(C i ,max , qb, g ) − QH , g ) (3.15)
∑ whi
i
case 2: Flow request downstream is smaller than capacity request upstream
QH , g = ∑ q hi , g > min(C i ,max , qb , g )
(3.16)
i
14
If demand exceeds capacity, we need to determine a capacity Ci for the node-agent that will
be assigned to the upstream link-agents. The flow request of the upstream link-agent will be
q hi . The flow request of the downstream link-agent might also change and, as a consequence
this link-agent might have to handle more traffic.
The harmonization of the various requests will be done based on the link priorities wi.
wh1 * max(q h1, g − q h1 ,0) = ... = whn * max(q h 2, g − q h 2 ,0) = wb * (qb − qb , g )
Furthermore
∑q
hi
= qb
(3.17)
(3.18)
i
This results in (n) linear independent equations that can be used to calculate the unknown (n1) variables q hi and qb .
If there is no request for flow from a specific link-agent ( q hi , g = 0 ), no capacity will be
assigned to this link.
If qb > C i ,max , equilibrium is not feasable. In such cases the value of qb will be made equal to
C i ,max and this value will assigned to the upstream links using the link priorities (as indicated
above).
Case 3: no capacity request upstream
If there is no capacity request upstream, capacity qb , g will be assigned proportionally to the
links:
q
(3.19)
q hi = b
n
The approach described above can be seen as a harmonization of flow requests on the one
hand between links upstream and downstream of the node-agent and on the other hand among
the upstream links themselves. Incorporation of the link priorities allows for a further
finetuning taking into account the the objective functions of the individual link-agents but also
the overall relationship between the agents.
Application
Introduction
In 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 [21,22]
15
established the priority order of traffic operations on the road network around Antwerp (see
figure 8)
Figure 8: Main road network of Antwerp and link priorities.
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. Figure 9 shows a simplified subnetwork that respects the hierarchy between the
different road types.
Exit
road
Figure 9: a) Selected test network. b) Choice of link and node agents for the 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 the 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. This is because the
priority rating of the Singel is higher than that of the exit road. It 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
16
tailbacks on the exit road. If the tailback keeps on growing, then blocking back may occur
onto 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.
Application to the test network
The test network is an example of two parallel roads with a buffer in between (see figure 9b).
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.
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.
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
•
keeping 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.
17
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
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.
# vehicles
Flow (veh/h
Simulating traffic for a period of 300 minutes gave the results shown in figure 10:
Time (minutes)
Time (minutes)
Figure 10: a) Number of vehicles on the links b) Capacity allocation node 5
18
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 an ‘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.
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.
Computation of the option ‘keep the problems localised to where they occur’
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.
# vehicles
Flow (veh/h
Simulating traffic for a period of 300 minutes gave the results shown in figures 11:
Time (minutes)
Time (minutes)
Figure 11: a) Number of vehicles on the links b) Capacity allocation in node 5
Like in the preceding simulation an ‘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.
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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.
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 lost equals the time period that a vehicle spends on the network
summed over all vehicles that pass through the network.
The following table shows the number of vehicle hours lost per system and per link:
Table 1: Comparison of the vehicle hours lost.
Link
1
2
3
4
5
Priority
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
The total number of vehicle hours lost is almost the same, 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 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.
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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 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 that
may be compared with each other.
Table 2: Comparison of deviation from policy objectives.
Link
1
2
4
5
Priority
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.
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
21
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.
Conclusion
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. As an
example, economically important traffic on high priority links can be spared at the cost of less
important traffic
The agent system can be seen as a traffic management tool that is capable of distributing
congestion problems and the associated time losses through the network according to pre-set
(policy) objectives. If these objectives have been carefully defined, application of an agent
system may well lead to a network-wide improvement of traffic operations.
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