**3.1 Standard problem formulation**

Most approaches to solving the highway merging problem use a similar structure to model the physical highway on-ramp. **Figure 2** shows an abstracted model of a highway on-ramp. A control zone is defined, where all vehicles in this zone communicate with a central controller and each other to decide individual optimum

**Figure 2.** *On-ramp merging regions and infrastructure model.*

network. The objective was to avoid congestion on the main road and to balance the traffic flow on the alternate routes. The obtained results showed that the proposed algorithms could establish user equilibrium between two alternate routes even

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

In 2019, Martin Gregurić et al. [33] proposed the approach of coordination between controlling on-ramp flows with ramp metering (RM) and dynamic route guidance information systems (DRGIS), which reroute vehicles from congested parts of the motorway. DRGIS is used to inform drivers about current or expected travel times and queue lengths so that they may reconsider their choice for a certain route. It can be seen that DRGIS can directly impact on traffic demand at the urban traffic system by informing the drivers about travel times on its crucial segments. Reduced traffic demand on congested urban motorway section or at congested on-ramp in coordination with the adequate ramp metering control strategies can prevent "spill-back effect" and increase overall throughput of the

To conclude, in this section, a review on the integration of RM and RG controllers was presented. The section started by describing the two most commonly used discrete first-order and second-order traffic flow models. Then, it continued with an overview of the popular RM and RG control strategies and it finished by

discussing most of the important studies on the integration of RM and RG. Most of them considered TTS as the performance metric and applied an MPC optimization framework since it reduces the computation efforts required to solve the optimization problem specially if the traffic evolution model used was the METANET model since it makes the formulation non-linear and non-convex. Overall, all the studies reviewed here have shown improvements in the network performance in compari-

The discussion so far has centered around the macro-level control of intelligent highways. However, an integral component of the transportation system of a smart city is the micro-level control of autonomous vehicles. It is, therefore, imperative that we cover some micro-level details pertaining to the CAVs. The following sections address problems related to the micro-level vehicle coordination. Commonly found interactions include highway merging, off-ramp exit, vehicle overtaking and lane changing. Focus is placed on on-ramp merging and overtaking in presence of incoming traffic, as these two tasks combined encompass most of the

The selection of the on-ramp merging task (see Section 3) as a key area to be explored is due to both the extent of variables involved in coordinating this process and the dynamic nature of the process itself. In fact this is one of the tasks that today's autonomous vehicles find difficult to carry out due to the need of reactive control and precise planning. The role of inter-vehicle coordination in efficient merging is also discussed in detail. While coordination of human-driven vehicles is mostly reactive, CAVs can be assigned goals proactively so as to optimize the merging process. Similarly, a detailed discussion is provided on the car overtake problem (see Section 4) to emphasize the need for explicit modelling of human behavior when designing algorithms for CAVs. This seemingly simple problem is specifically chosen to draw attention to the complexities that could arise due to the presence of human drivers on the road. A naive data-driven algorithm can fail catastrophically in scenarios where humans may behave unpredictably so an overview of algorithms that explicitly take human behavior into consideration is

son with the case of having either of these controllers alone.

complexities involved in inter-vehicle interactions.

provided later on in this chapter.

**130**

when the on-ramps have different traffic demands.

urban motorways.

**2.5 Summary**

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.

The vehicles involved are modelled based on simplistic second order dynamics given by,

$$\begin{aligned} \dot{p}\_i &= \nu\_i(t) \\ \dot{\nu}\_i &= \mu\_i(t) \end{aligned} \tag{32}$$

This ensures that a lateral collision can never happen. Additionally, the algorithm also directs that vehicles maintain at least a specified gap between each other which ensures that rear-end collisions do not occur. Hamiltonian analysis is then used to convert the optimization problem into a system of four equations that can be solved

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

Simulation of this system was then carried out to show that the algorithm performs as desired. It was found that compared to a baseline situation where onramp vehicles always give way to vehicles on the freeway this algorithm performs significantly better. An improvement of 52% in fuel consumption when compared

Disadvantages: Only one lane of the freeway is in use and the benefits obtained from allowing/forcing vehicles to switch lanes in the freeway are ignored (i.e. full capacity of the freeway is not used). Additionally, vehicles are given merging rights based on a simplistic FIFO (First In First Out) queue which can cause additional

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

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

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

Using simulations, it has been shown that throughput at merge intersections can be increased and delay can be decreased drastically (throughput: 230% increase

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

and delay: 452% decrease) vs. human driven vehicles under heavy traffic

find an unoccupied virtual slot and perform the merging task.

vehicles through these freeway merge zones.

communication is rarely available in practice.

in real time to output the optimal control for each vehicle.

to the baseline situation was also reported.

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

delays and is definitely sub-optimal.

*3.2.2 Slot based method*

of the slot.

conditions.

**133**

where *pi* 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 defined as,

$$\mathbf{x}\_{i}(t) = \begin{bmatrix} p\_{i}(t) \\ v\_{i}(t) \end{bmatrix} \tag{33}$$

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 which the vehicle enters the control zone.

$$
\dot{\boldsymbol{x}}\_i = \boldsymbol{f}(t, \boldsymbol{x}\_i, \boldsymbol{u}\_i), \qquad \boldsymbol{\varkappa}\_i(t\_i^0) = \boldsymbol{\varkappa}\_i^0 \tag{34}
$$

Additionally, all the methods discussed have the shared assumption that, *the vehicle speed inside the merging zone is constant*.

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 process.

#### **3.2 Various methods**

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.
