Alleviating Congestion in Restricted Urban Areas with Cooperative Intersection Management

Abstract

Congested urban traffic frequently deviates toward residential areas, where due to local conditions congestion builds up quickly. The increasing traffic flow there causes health, environmental and safety problems. A pragmatic solution is to make these areas infeasible as escape routes. In the following, an area wide cooperative intelligent intersection management system is proposed, aiming at suppressing the number of passing-through vehicles if their density increases too much. The solution is based on communicating traffic light controllers using the analogy of the Explicit Congestion Notification (ECN) protocol and organized as a hierarchical Multiagent System. The system was implemented by extending an open-source traffic simulation tool, so called Eclipse SUMO. Simulations were performed on a simplified model of a residential area. The efficacy of the proposal was evaluated with Macroscopic Fundamental Diagrams of the investigated traffic. The results are promising opening way to further research.

Appendix

1.1 A. Searching for a Set of Strongly Coupled Intersections

In road networks, defining intersection dependence is not trivial. In e.g. American-like, rectangular road networks at least two independent routes between any points of the network may exist, while European-like, irregular networks may contain bottlenecks, i.e. sections which are used by the whole traffic flow between two points of the network. These points or intersections are coupled somehow together, and the whole road between such coupled intersections behaves similarly to the conflict zone of a single intersection. Vehicles are competing for the usage of this road surface. For this reason, it might be beneficial to avoid congestion and therefore to limit the amount of conflicts along these road segments.

The goal is thus to identify the maximal group of coupled intersections. The algorithm accepts as input road network (topology) (N), every possible route through this network, given by an ordered list of the visited junctions (R), the highest distance bound between the coupled intersections (Lmax) and a given intersection (a), which coupled intersections are to be found. The algorithm runs like follows:

1st step::

X := {a}

2nd step::

x : = an intersection in N, which has an out going route to an intersection y, already in X and the distance d(x,y) < Lmax.

3rd step::

K : = {every route from R, containing road segment x → y}

4th step::

If there is no element in K, containing both x and y, and any other intersection from N in-between, then $\mathrm{X} :\, = \mathrm{X} \cup \{\mathrm{x}\}$

5th step::

If there is another applicable intersection in N, then go to 2nd step Otherwise: Return X

The returned X set contains intersections coupled with the originally selected (a) intersection. Whole sections of the road network between such intersections behave similarly to the conflict zones of the traditional intersections. In order to reduce the number of possible conflicts, coupled intersections should share the congestion notification between each other.

As an example consider Fig. 1. Left turns are prohibited at two junctions. At B, moving from A C is prohibited. Similarly, at G, moving from F towards E is also prohibited. The question is which junctions are coupled to junction H?

Fig. 1.

Collecting coupled intersections.

Fig. 2.

General setup of the congestion alleviating MAS system (lower cartoon by www.freepik.com, last accessed 2020/02/27.)

Fig. 3.

Schematic view of the intersection cooperation based on the ECN warning.

Fig. 4.

Test environments representing residential areas: (a) a single attractive escape route with a web of blind alleys, (b) a web of passable residential streets. The traffic flow is bidirectional, but only the single direction flow is shown for simplicity. ECN-judges are shown with circles.

Fig. 5.

Flow vs. Density Macroscopic Fundamental Diagram (MDF). Left side belongs to the (stable) non-congested free flow, with the maximal (permissible) speed of driving, until the critical density is reached (the top of the diagram). Right side shows the formation of an unstable congested flow, with an ever increasing density and drop in velocity, until the traffic stops entirely at the jam density. In our measurements the % occupancy of the area loop detectors was taken as the (equivalent) measure of the traffic density.

Fig. 6.

MFD diagram showing the effect of ECN-based traffic limitations in the test environments. Test (a) left column, test (b) right column (* - ECN, o - traditional solution).

Fig. 7.

Congestion alleviating effect of the ECN-messages in the test environment (a). Traditional signal control (blue), ECN-based control (red).

With the proposed algorithm we found that G is a part of the coupling set of H, since due to the prohibition of the left turn, every route, containing G → H, will contain H directly after G. Let us see now the case of E, a neighbor of G. Because there are two possible routes from E to G (one direct route, and one via intersection F), E is not a part of the coupling set of H. The same also holds for F, therefore it does not belong to the set either. As the example network is symmetric, we can accept also B as a part of the coupling set of H, but not C and A.

The last intersection to be investigated is D. Due to the many possible routes between them (e.g., DH, DC(A)B, DE(F)G), D have to be left out from the set.

1.2 B. Signal Phase Generation as an Integer Programming

Our simulation platform receives a two-dimensional matrix, the so-called conflict-matrix C as a configuration input. This matrix describes which directions may not pass through the intersections simultaneously. (If allowed, it would cause a risk of a collision.) [C]_i,j element is 1 if the ith and jth directions are prohibited to move simultaneously, and is 0 otherwise.

The principal goal of signal phase generation is to provide green lights for as many vehicles as safely possible. Some other constraints also have to be taken into consideration, like the scheduling decision, or the traffic reduction indicating by the incoming ECN-message, proposed in this paper.

This problem can be formalized as an integer programming problem (IP). Let us define vector x as the vector of directions. The x_i coordinates of x will be numerically constraint to be 0 or 1, indicating that the ith direction can or may not receive a green light in the current phase. Naturally our goal function is to maximize the L₁-norm of x, i.e. max Σ |x_i|.

The constraint matrix of the IP problem can be formed as follows. Let us iterate through the conflict matrix C. If a specific [C]_i,j element equals 1, we add a new constraint: x_i + x_j ≤ 1. These constraints (and their integer solution) ensure that at most one of the conflicting directions will receive a green light. Moreover, we shall add an x_i ≤ 1 for every ith coordinate. This two types of constraints warrant that every x_i coordinate will fall in the range [0,1], but the integer solution will warrant that every x_i will equal either 0 or 1.

For the kth direction which must receive a green light, due to the scheduling decision, an x_k = 1 constraint will be added. Similarly, when an l direction must not receive green light, in effect of an ECN-signal, x_l = 0 constraint will also be added.

The solution of this problem (2) will provide an optimal configuration of the traffic lights. The constraints also prevent conflicting directions to receive green lights simultaneously.

$$ max\sum\nolimits_{i} {\left| {x_{i} } \right|} $$

(2)

subject to:

$$ x_{{i_{1} }} + x_{{j_{1} }} \le 1, x_{{i_{2} }} + x_{{j_{2} }} \le 1, \ldots , x_{{i_{m} }} + x_{{j_{m} }} \le 1 $$

(constraints)

$$ x_{k} = 1 $$

(scheduling)

$$ x_{{l_{1} }} = 0, x_{{l_{2} }} = 0, \ldots , x_{{l_{n} }} = 0 $$

(ECN-notification)