*3.2.2 Slot based method*

velocities and paths to be followed. The control zone encompasses both the main road and the on-ramp. Vehicles are allowed to merge from the on-ramp onto the main road in the merge zone, which is located at the end of the control zone.

*Models and Technologies for Smart, Sustainable and Safe Transportation Systems*

given by,

where *pi*

which the vehicle enters the control zone.

*the vehicle speed inside the merging zone is constant*.

defined as,

process.

**3.2 Various methods**

*3.2.1 Optimal control method*

merging zone at any time.

**132**

The vehicles involved are modelled based on simplistic second order dynamics

*p*\_ *<sup>i</sup>* ¼ *vi*ð Þ*t v*\_*<sup>i</sup>* ¼ *ui*ð Þ*t*

ð Þ*t* , *vi*ð Þ*t* , *ui*ð Þ*t* denotes the position, velocity and acceleration/ deceleration (control input) respectively for each vehicle. The vehicle state is then

> ð Þ*t vi*ð Þ*t*

> > 0 *i* <sup>¼</sup> *<sup>x</sup>*<sup>0</sup>

*xi*ðÞ¼ *<sup>t</sup> pi*

Furthermore, assuming that lateral control keeping the vehicle in lane is managed elsewhere, the vehicle can be modelled as a point mass moving along the center of the lane with the following state equation, where time 0 is the point at

*x*\_ *<sup>i</sup>* ¼ *f t*, *xi* ð Þ , *ui* , *xi t*

Additionally, all the methods discussed have the shared assumption that,

To compare these algorithms, the two main performance indicators are *throughput* (maximum number of vehicles that can merge onto the highway in an hour) and *delay* (average delay experienced by vehicles compared to the ideal travel time). In addition to these parameters, some research in this area also takes into consideration the savings in fuel consumption due to improvements in the highway merging

So, let's now explore some of the methods used in handling the highway merging problem in greater detail. Here, multiple approaches and methodologies to address this problem are discussed. Most of the work done in finding an optimal solution to automated freeway merging is based on posing the problem in the form of an optimization problem [34] with centralized control [35], virtual slot-based dynamics [36] problem or as broadcast communication [37] problem.

This problem is posed as an unconstrained optimization problem [34] and then further extended to also consider the impact of fuel consumption [35]. The output was the ability to derive online an optimal closed-form solution for vehicle coordination at a merge intersection. The importance of safety constraints is also stressed here. Constraints in positioning, maximum velocity and maximum accelerations are imposed. Additionally, the algorithm only allows one vehicle to enter into the

The algorithm calculates the time at which each vehicle would enter the merge zone and requires that this time does not conflict with any of the other vehicles.

(32)

(33)

*<sup>i</sup>* (34)

This method [36] primarily relies on creating virtual slots for each vehicle that moves along the freeway at a constant velocity. Then all changes to this behaviour such as switching lanes, on-ramp merging and exiting the highway on an off ramp are modelled as a switch from one virtual slot to another. A virtual slot *S* is defined with five properties as is denoted by *S* ¼ f g *z*, *p*, *t*, *b*, *o* , where *z* is the size of the slot, *p* is the position, *t* is the time, *b* is the behaviour of the slot and *o* is the density status of the slot.

Slots are created by a central slot controller and vehicles can request to change from one slot to another. This change will then be approved by the slot controller as long as the slot is not already occupied or there is no other vehicle requesting to switch to that same slot. This approach was also shown to work in the absence of infrastructure at the merge junction since vehicles can use V2V communication to find an unoccupied virtual slot and perform the merging task.

An additional benefit of this slot based system is the ease by which the method can be extended to allow the entire bandwidth of the freeway to be used in order to further improve efficiency. For example, if the slot controller realizes that there are a lot of empty slots in the central lanes of the freeway, the controller can request that vehicles in the outer lane prior to the merge point to move into the empty inner lane slots. This creates more empty slots in the outer lane and provides more opportunities for vehicles on the on-ramp to merge successfully. This type of cooperative behaviour has been proven to drastically improve the throughput of vehicles through these freeway merge zones.

Using simulations, it has been shown that throughput at merge intersections can be increased and delay can be decreased drastically (throughput: 230% increase and delay: 452% decrease) vs. human driven vehicles under heavy traffic conditions.

Disadvantages: Many limitations brought about by having slot based systems include, difficulty in robustly handling emergency/breakdown situations, lack of flexibility in catering to different needs such as different vehicles requesting different speeds, inefficiency in heavy traffic density situations where not enough free slots are available to facilitate lane changes etc. Moreover, the slot based method places a lot of restrictions on the way vehicles can move about and position themselves on the freeway. Communication between vehicles and infrastructure also needs to be extremely good for this system to work and this type of perfect communication is rarely available in practice.

### *3.2.3 Broadcast communication based method*

Some of the major issues in coordinating automated vehicles at merge intersections are the problems caused by imperfect communication. In these type of applications, delays of even a few seconds can have devastating results. Work on using Pseudo-perturbation based broadcast communication (PBC) [37] instead of unicast communication focuses on reducing the overhead on the V2I communication systems and leveraging the capabilities of V2V communication to handle any short term changes. In this method, a global controller (infrastructure) broadcasts an identical message to all vehicles in its vicinity. Each of these vehicles uses this information along with V2V data from other vehicles to select a suitable control strategy to safely perform the coordinated merging task. Vehicles send updates back to the central controller and the controller uses this feedback to decide its next broadcast message.

disadvantages. Therefore, it falls on the highway regulatory agencies to decide which of these are most suitable to the conditions of each individual highway

*Models and Methods for Intelligent Highway Routing of Human-Driven and Connected…*

*DOI: http://dx.doi.org/10.5772/intechopen.94332*

**4. The overtaking behavior with the combination of HDVs and CAVs**

The final section of this chapter focuses on providing an in-depth analysis of a complex scenario in which the autonomous vehicle (AV) has to perform maneuvers in the presence of HDVs. Upon a cursory glance at the current state of AV research [39], it becomes obvious that not a lot of emphasis is being placed on explicitly modelling the varying behavior patterns of HDVs on the road. One such instance that highlights the need to model the varying HDV driving patterns is the car overtaking problem in a bidirectional traffic flow setting. In this problem, a scenario with three vehicles is considered; two HDVs and one AV (ego vehicle), as shown in **Figure 3**. The HDVs are travelling in opposite directions in adjacent lanes and the ego vehicle is following one of the HDVs. The objective of the AV is to safely overtake the vehicle travelling ahead while maintaining safety distances to the HDV in the adjacent lane, the HDV travelling ahead and the boundaries of the road. This is a particularly hard problem to solve because it involves a scenario composed of both human-driven and autonomous vehicles. The first major complication is the lack of global information because the V2X communication protocols cannot be leveraged in this scenario due to the presence of HDV. Then, there is the problem of uncertainty that arises due to the varying driving patterns so the algorithm needs to be robust enough to handle the different driving patterns of human drivers. Moreover, the traditional Supervised Learning based approaches cannot be applied directly to this problem due to a lack of labeled training data. Finally, the model-free Reinforcement Learning (RL) based techniques [40] cannot be employed due to a lack of safety guarantees while the model-based RL or Control techniques [41] cannot be employed since they require an accurate representation of system model and cannot capture uncertainties that arise due to varying driving

In this chapter, a simplified stochastic control based formulation taken from [42] is laid out to provide a mathematical description of the problem. The formulation is followed by a brief discussion of a couple of algorithms to give the readers a glimpse of the possible avenues that could be taken to reach a solution. The references to detailed resources are also provided for the interested readers to explore

system.

patterns well.

further.

**Figure 3.**

**135**

*Overview of the car overtaking problem.*

The key focus of this research was to extend available PBC capabilities to handle the multi-state vehicle dynamics and the multi-objective optimization required to solve a freeway merging coordination problem. The capability of this system to handle both CAVs as well as a mix of CAVs and human driven vehicles was also showcased. Here, the CAVs are controlled by the coordination system and are shown to be able to function even in the presence of human driven vehicles. The smoothness of the actual merging process was also evaluated through simulation. The main output of this research was to show that complex coordination problems such as freeway merging can be successfully solved with the use of minimal communication bandwidth.

Disadvantages: Lack of focus on the actual merging algorithm. Based on the broadcast signals, the decisions individual vehicles make may be sub-optimal and cause an unnecessary delay in the system. Also, very little work has been done on seeing whether this system actually has a effect on throughput.

### *3.2.4 Temporal logic based method*

This method involves formalizing traffic rules using temporal logic [38] in order to ensure safety and robustness of automated highway vehicle control. This method helps with formulating existing traffic rules in a mathematical way in order to be easily applied in CAVs. While this method does not solely focus on the merging problem, the merge window is addressed in the metric temporal logic (MTL) formulas included. When the merge operation is formulated as a MTL formula, it leads the way to specifying safety guarantees in autonomous vehicles. Furthermore, the legality of trajectories generated by a motion planner can be easily checked using these MTL formulae. It also allows the use of standard verification and validation methods in order to ensure that there are no loopholes or issues in the generated logic.

#### **3.3 Summary**

While there are many methods to improve intelligent merging behavior, the core fundamentals of these algorithms are quite similar. They look into minimizing gaps or under-utilized space on the road while minimizing the control inputs (acceleration and braking) needed to achieve this. All algorithms also prioritize safety and fairness in the merging process. Additionally, there are extensions that focus on maximum capacity utilization by moving vehicles already on the highway to less congested lanes, which further improves the efficiency of the merging process. Each of the algorithms discussed in the section has its own advantages and *Models and Methods for Intelligent Highway Routing of Human-Driven and Connected… DOI: http://dx.doi.org/10.5772/intechopen.94332*

disadvantages. Therefore, it falls on the highway regulatory agencies to decide which of these are most suitable to the conditions of each individual highway system.
