3.1 Behavior model

In this study, AV follow the behavior model outlined in Fig 3. The key component of the AV behavior model is courtesy evaluation, which is indicated by the yellow box in Fig 3. When an AV receives cut-in (e.g., lane change) requests for other vehicles, it will evaluate the current situation and decide whether to yield to others or not. More details about courtesy evaluation are given later in Section 3.2 Courtesy and Courtesy Strategies.

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Fig 3. CAV behavior flowchart.

https://doi.org/10.1371/journal.pone.0283649.g003

Fig 3 has three main types of stages: decision, process, and AV action. At every simulation step, an AV would begin with the “start” stage in Fig 3. After going through various subsequent stages, each AV will eventually arrive at least one AV action stage and execute the corresponding car-following and/or lane-changing actions. There are several important constraints on CAV acceleration. These constraints are detailed in the following four subsections.

3.1.2 Mandatory lane change (MLC).

As shown in Fig 4, an MLC involves four participants, which are the subject vehicle (SV), front vehicle (FV), target front vehicle (TFV), and target lag vehicle (TLV). Acc_CF is also used as a constraint here (i.e., the acceleration of SV should be equal or smaller than Acc_CF) so that SV would not collide with its FV. Besides on ramps and lane reduction points, MLC can also happen before off ramps when vehicles have to change lanes in order to exit a highway.

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Fig 4. An MLC scenario.

https://doi.org/10.1371/journal.pone.0283649.g004

For HDV, a vehicle’s lane-changing motivation typically increases as it approaches the merging point. In this study, AV follow “the earlier the better” principle and try to change lanes right after they enter the lane-change (LC) feasible region (e.g., acceleration lane for vehicles from the on-ramp to merge). However, successful lane changes are also subject to constraints such as sufficient TLG and TFG. Since an AV has to fully stop when reaching the merging point without being able to change lane, a deceleration constraint Acc_MP (MP stands for merging point) is introduced to make this happen. This deceleration is implemented by introducing a hypothetical stopped vehicle at the merging point in the closed lane, and the subject AV follows the CACC mode when it reacts to this “stopped vehicle”. The deceleration constraint Acc_MP is described in Eq (2) below and the only required input is the SV distance to the merging point (i.e., “stopped vehicle”). (2) where and are the acceleration and speed of the hypothetical stopped vehicle, respectively, and they are both set to 0. r(t) is the distance of the SV to the stopped vehicle. All other parameters are defined in the same way as in the original CACC formula Eq (1).

To create enough space in the target lane for the SV to merge into, the SV first executes CCM (with Acc_CCM, as indicated in Eq (1)) to generate a safe gap to the TFV. At the same time, the SV would perform a feasibility check to see if the TLV is ready for the SV to merge into its lane. This check is done by calculating the forced deceleration of the TLV assuming the SV is already in the target lane. If the calculated deceleration is larger than the maximum deceleration allowed by the TLV, the feasibility check is considered failed. The forced deceleration is calculated following the G-CACC formula (OBD = 1) in Eq (1) except that the following vehicle is the TLV and the G-lead vehicle is the SV.

The feasibility check is to make sure the intended lane change will not cause trouble to the TLV. If the feasibility check is passed, the SV would further execute a gap acceptance check just like human drivers do to ensure safety from the SV perspective. The difference is that the SV would adopt smaller gaps than human drivers. The gap acceptance check is based on a certain threshold rather than probability. A gap would be accepted if it is larger than a critical time gap threshold. Both front and lag gaps need to be larger than the threshold. The front gap can be created by the CCM strategy. However, sometimes the lag gap (because of TLV) is not enough for the SV to change lane. In this case, the SV would send a LC request to the TLV for creating a larger lag gap. Upon receiving the request, the TLV would perform a courtesy evaluation and decide what to do next. More details on the courtesy evaluation are discussed later in this paper.

To conclude, the acceleration required for the SV due to MLC is governed by three constraints, which are Acc_MP, Acc_CCM, and Acc_CF. The minimum of them will be chosen. For lane-changing maneuvers of the SV, they are based on feasibility check and gap acceptance check.

3.1.3 Discretionary lane change (DLC). The motivation of DLC is different from MLC. DLC is for pursuing higher speed or reducing travel time. In this study, AV DLC is modeled using utility. An AV would choose lanes based on their utilities. The utility of target lane i is defined as: (3) where v_t is the speed of the target vehicle, and is the average speed of target lane i. If the SV is currently in target lane i, the target vehicle is the SV’s FV. If the SV is not in target lane i, the target vehicle is the TFV. A utility difference threshold is defined so that the SV would not change lanes too often. In other words, DLC itself has an initial cost. To overcome this initial cost, the utility gain from changing lane has to be greater than a threshold of 5 m/s.

Once the utilities of each lane have been determined, the SV’s DLC decision can be made. What happens next for the SV is not much different from MLC. The SV can still send requests via vehicle-to-vehicle communications for a larger TLG. The only difference is that Acc_MP would not be considered as a constraint.

3.1.4 Courtesy acceleration. MLC and DLC are control logics from the perspective of the SV. In this subsection, courtesy acceleration (Acc_courtesy) is introduced to model the behavior of the TLV. If a TLV decides to yield to another lane-changing vehicle, Acc_courtesy is the corresponding acceleration needed. Again, Acc_courtesy is determined following the CCM framework in Eq (1), in which the following vehicle is the vehicle behaving courteously (i.e., TLV) and the G-lead vehicle is the one sending the cut-in request.

3.2 Courtesy and courtesy strategies

Some important concepts need to be introduced before going forward. Courtesy may mean a number of things in social interactions, and might be characterized as either a behavior (e.g. opening a door for another is the courteous thing to do) or a disposition (i.e. one has the character traits of being courteous). Presumably, AV have no dispositions, so we rely on courtesy in the context of MLC/DLC as cooperating with another vehicle on the road when a lane change is necessary as part of the flow of traffic. From here we can define three important terms for our model: courtesy level, courtesy proxy, and courtesy principles. Courtesy level is a pre-determined attribute of AV, and it measures AV’s level of willingness to cooperate. Courtesy proxy is an environment-dependent variable, and it is utilized by AV to decide whether to cooperate or not. Courtesy principles (or courtesy strategies) are a group of principles and/or strategies taken by AV to achieve various goals.

Fig 3 shows how AV in this study would decide whether to cooperate (i.e., show courtesy—in the case of MLC/DLC, yield) or not when receiving Lane-Changing (LC) requests. In previous studies, this decision process is implicitly considered in AV’s behavior model [8, 9] whose disadvantages are discussed in the previous section. Here, courtesy is explicitly modeled by

1. following how human behave: AV with high courtesy levels would be more likely to yield in a given scenario, but AV can have different courtesy levels that determine their cooperation.
2. pursuing certain systematic goals. In other words, courtesy can be important for its own sake (i.e., as a principle of a good road system) or can be instrumental to some other good (e.g. to minimize congestion).

This paper provides a set of courtesy principles to guide courteous interactions among AV, using speed difference as a courtesy proxy. In future work this could be replaced by other proxies such as time to crash (as a proxy for safety) or required maximum deceleration rate (for passenger experience and safety). Noninstrumental principles have been considered elsewhere, albeit not for courtesy, but we set them aside here for simplicity’s sake [21]. The proposed courtesy strategies are categorized into two groups: non-instrumental (Egoism and Altruism) and instrumental (Local Utilitarianism, Local Maximin and Local Egalitarianism), and they are detailed in the rest of this section. The strategies chosen are popular in autonomous vehicles research that focuses on ethical decisions made by these vehicles. Utilitarianism is one of if not the most commonly considered moral system for autonomous vehicle decision-making [22], while there has been recent attention to maximin as a proxy for popular social contract theories of ethics [23, 24]. Egalitarianism is less studied but is seen as a proxy for a particular kind of fairness in interactions of vehicles in which the parameter in question is equalized, or the benefit distributed, between parties [25].

3.2.1 Egoism.

Under Egoism, Target Lag Vehicle (TLV) yields only when it would be in its own interest to do so–here, when it would not require the TLV to sacrifice too much of its own velocity. In this study, we use a raw courtesy level (RCL) to describe the maximum velocity loss the TLV will incur in the name of cooperating with other cars. For example, a TLV with a RCL of 5 m/s would yield in a scenario that requires it to decelerate by 3 m/s, since 3 m/s is less than the prespecified 5 m/s. The courtesy proxy (CP) used in Egoism is thus defined as the speed difference of the TLV before and after a lane change.

(4)

Courteous behavior of TLV would be triggered if CP_Ego is less than the courtesy level of the TLV as shown in Eq (5). Otherwise, the TLV will ignore the cut-in request and choose not to cooperate.

(5)

Raw courtesy level can vary for each AV, representing its individualized willingness to cooperate. As shown in Eq (6), it is derived from a standard courtesy level which ranges from 0 to 1.

(6)

Here, 0 means AV will never yield to others, and 1 means that AV will always cooperate if there is a request. v_s is the maximum speed of the subject vehicle (which usually is the speed limit on the road).

3.2.2 Altruism.

Under Altruism, TLV makes cooperation decisions from the perspective of the vehicle requesting courtesy (i.e., cut-in requests). In this case, TLV would yield if the utility gained by the SV requesting courtesy is less than what the TLV’s courtesy level allows. For example, TLV with a RCL of 5 m/s would not yield in a scenario where the SV could speed up from 5 m/s to 11 m/s after a lane change, since the speed gain is greater than the prespecified courtesy level (11 m/s– 5 m/s > 5 m/s).

The courtesy proxy for Altruism is defined in Eq (7), which is the speed difference of SV (i.e., the one sending cut-in request) before and after a lane change. As in Egoism, courteous behavior of TLV would be triggered if the courtesy proxy is less than TLV’s RCL as in Eq (5). The courtesy proxy for each AV under Altruism is also calculated based on a standard courtesy level as in Eq (6).

(7)

3.2.3 Local Utilitarianism (LU).

Local Utilitarianism strategy accounts for the utility gain of the SV attempting to change lane and the sacrifice (i.e., utility loss) to be made by the TLV. The TLV would yield to the SV if the sum of the utility resulting from a change is positive, accounting for the change in utility in both vehicles. It is called local utilitarianism because only two vehicles are involved and the immediate impacts (speed changes in this study) are considered in the decision process. However, the local decision may also benefit the operations of the entire traffic system. While considering more vehicles and the broader impacts (e.g., missing a downstream green light) of local cooperative behavior is desirable, it is very difficult to quantify and capture such effects given the complex relationship between individual vehicle behaviors and traffic system dynamics.

(8)

One example of Local Utilitarianism (LU) is that TLV with a courtesy level of 5 m/s would yield in a scenario where the SV could accelerate from 1 m/s to 9 m/s after changing lane and the TLV would have to decelerate from 15 m/s to 9 m/s, since the sum of utility changes is positive (i.e., 9–1 + 9–15 = 2 > 0). The cooperative decision rules for TLV under LU are further defined in Eq (9).

(9)

3.2.4 Local Maximin (LM).

The idea behind Local Maximin (LM) is that the worst off vehicle (here, the one with lower speed) should be made better off. In other words, LM aims to maximize the lower bound of the interaction, and like LU only considers the two vehicles in question. Based on this strategy, if the speeds of TLV before and after changing lane are 15 m/s and 7 m/s, respectively, and the corresponding speeds of SV are 3 m/s and 8 m/s, a courteous yield would be triggered, since the minimum speed is improved from 3 m/s (i.e., Min(15,3)) to 7 m/s (i.e., Min(7,8)).

(10)

The LM decision rules for TLV are the same as those defined in Eq (9) except that CP_LM defined in Eq (10) is adopted instead of CP_LU.

3.3. Simulation setup

To evaluate various courtesy strategies, a corridor comprising 4 critical segments is designed as in Fig 5. The four segments have different levels of traffic demand and require different types of lane-changing maneuvers. Two adjacent segments are separated by a 500-meter straight roadway segment without on/off-ramps. The various types of on- and off-ramps generate many opportunities for vehicles to behave courteously and to test the proposed courtesy strategies. From left to right in Fig 5, the four segments are Type A weaving area, Type B weaving area, work zone, and Type C weaving area, respectively. The layouts of these weaving areas are taken from the Highway Capacity Manual (HCM) [26].

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Fig 5. Simulation corridor.

https://doi.org/10.1371/journal.pone.0283649.g005

To test the proposed courtesy strategies’ performance under different levels of traffic demand, three levels of traffic inputs (light, moderate, and heavy) are adopted, corresponding to different levels of service (LOS) described in the HCM [26]. Table 2 shows some sample service traffic volumes and the corresponding LOS taken from the HCM. In this study, light traffic represents LOS A, moderate traffic demand indicates LOS C, and heavy traffic input is for LOS E. LOS B and D are omitted for simplicity. If we use the traffic volumes directly from the HCM, upstream highway mainline traffic + onramp traffic–offramp traffic may not equal downstream mainline traffic, leading to imbalanced flows. To ensure flow conservation, minor adjustments (in the range of 25~125 veh/h/lane) are made to the traffic volumes corresponding to LOS A, C, and E in the HCM as in Table 2. In Table 2, numbers outside parentheses are directly from the HCM and those inside parentheses are final traffic volumes used in this study for light, moderate, and heavy traffic conditions. Note that only four volumes have been adjusted and are highlighted in bold font in Table 2. The same simulation parameters are used across different levels of traffic demand (e.g., free-flow speed: 120 km/s, volume ratio (weaving volume by non-weaving volume): 0.20, etc.)

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Table 2. HCM example service volumes for freeway weaving segments.

https://doi.org/10.1371/journal.pone.0283649.t002

The proposed AV behavior models as well as courtesy strategies are coded and simulated using SUMO [27] via the Traffic Control Interface (TraCI). Each simulation run is equivalent to one hour in the real world. The AV behaviors are updated at 2 Hz frequency, which means AV make decisions every 0.5 seconds. Such decisions include longitudinal control (accelerate or decelerate), lateral control (change lane or not), and communications with each other (sending and receiving lane-changing courtesy requests). Each combination of courtesy strategy and traffic demand (light, moderate and heavy) is simulated 10 times with different random seeds. The 10 simulation runs for each scenario allow us to calculate the means and standard deviations of performance metrics, which can be used to characterize how stable and reliable the simulation results are. As illustrated in Figs 7–11 below, the shaded areas are based on the means and standard deviations, showing the 95% confidence intervals for each strategy at each courtesy level.

For non-instrumental strategies, courtesy level can have significant impacts on the results. Therefore, the same strategy with different courtesy levels is regarded as distinctive strategies during the simulation. Table 3 summarizes the strategies simulated/evaluated in this study. For non-instrumental strategies (i.e., Egoism and Altruism), a courtesy level needs to be specified and all AV apply the same courtesy level throughout the simulation. Various courtesy levels have been tested. The test results suggest that the network performance is more sensitive to low courtesy levels. Therefore, an incremental interval of 0.02 is used when the courtesy level is between 0 and 0.2, while an interval of 0.1 is used for courtesy level between 0.2 and 1.

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Table 3. Courtesy strategies tested.

https://doi.org/10.1371/journal.pone.0283649.t003

Heterogenous courtesy is also considered. In this case, AV courtesy levels could follow certain distributions. We opt to use two distributions described based on human preferences for altruistic or egoistic AV behavior conducted at the Massachusetts Institute of Technology (MIT) [22]. In this example, an AV has to either kill its passenger for saving ten pedestrians or kill the ten pedestrians to save the passenger. The choices provided range from 0 ‘protect passenger at all costs’ to 1 “minimize pedestrian casualties on the road”. The 182 survey respondents were asked this question in two distinctive ways: (1) what will AV do? and (2) what should AV do? These two ways resulted in two distributions shown in Fig 6. Considering the connection between the MIT survey and this study (i.e., should AV be concerned more about its passenger or other people), the two distributions are also adopted in this research to model AV courtesy level: Courtesy Distribution Expected (CDE) for “what will AV do”, and Courtesy Distribution Moral (CDM) for “what should AV do?”

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Fig 6. Two distributions from an MIT survey [22].

https://doi.org/10.1371/journal.pone.0283649.g006

3.4 Evaluation

The evaluation of courtesy strategies has been conducted at both network and individual segment levels in terms of mobility, safety, and fairness. At each time step, a vehicle could be in one of three possible states: courteous, lane-changing, and other. Being in courteous state indicates the SV is yielding to a lane-changing vehicle from adjacent lane. Being in lane-changing (LC) state means that the SV is sending LC request to its TLV in the target lane and managing to find a sufficient gap to cut in (the actual lane-changing behavior is assumed to occur instantaneously). All other situations are grouped into the other state. There is also an all state covering all those three nonoverlapping states, reflecting the average performance of all possible states. The performance measures are calculated for each state and all states combined.

Mobility is measured by global average speed. For the i^th state, the global average speed is obtained by: (12) where v_i is the global average speed for the i^th kind of state. is the speed of vehicle j at time step t. indicates vehicle j is in state i at time step t and otherwise. TS is the total number of states for all vehicles, which is the sum of numbers of time steps experienced by all vehicles.

Safety is measured by Deceleration Rate to Avoid a Collision (DRAC). In this study, only the DRAC of TLV is considered when the SV is merging into the target lane. The DRAC for TLV is calculated as: (13) where v_SV and v_TLV are the speeds of the SV and TLV (when the SV is changing lane), respectively. s is the corresponding space headway between the SV and TLV. DRAC_TLV measures how risky it is when a specific lane change occurs. A global DRAC is also calculated as the average of all DRAC_TLV observed during the entire simulation.

Fairness is also an important measure when courtesy and cooperation are considered [28, 29]. This study adopts Gini coefficient as a metric to measure system fairness. Two Gini coefficients are proposed: global Gini coefficient (G_GC) and categorical Gini coefficient (C_GC). (14) where n is the total number of state speeds for all vehicles (if a vehicle stays in the network for 10 seconds, there will be 10 state speeds for it). v_i and v_j could be any state speed of all vehicles. is the average state speed. G_GC essentially measures how imbalanced the distribution of all state speeds is. The more imbalanced it is, the larger G_GC becomes. C_GC, on the other hand, measures how imbalanced the mobility of a particular state is. (15) where V_k (k = 1,2,3) is the average speed for a state (i.e., courteous state, LC state and other state). is the average speed of V₁, V₂, and V₃.

4.1 Mobility

Fig 7 shows how different courtesy strategies may affect traffic operations. The results for all states consider all vehicle states, including LC, courteous and other state. For Egoism and Altruism, courtesy level is modeled by two approaches. The first approach assumes all AV have the same courtesy level, which varies between 0 and 1 and leads to different simulation scenarios (see the left halves of each subplot in Fig 7). The second approach considers the two distributions generated by the MIT survey [22], and in each simulation run different AV can have different courtesy levels based on the CDE and CDM distributions. The results from the second approach are presented in the right halves of each subplot in Fig 7.

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Fig 7. Evaluation of the mobility performance of different courtesy strategies.

https://doi.org/10.1371/journal.pone.0283649.g007

For Egoism and Altruism, the average speeds for all states in general increase monotonically as the courtesy level goes up regardless of traffic volumes—that is, as their tendency to cooperate increases according to Eqs (4), (5), and (7). This trend is also true for two component states, LC and other, except for some minor local fluctuations.

For courteous state the impacts of courtesy level on average speed also depend on traffic. Under low traffic volume, average speed changes with the inverse of courtesy. This trend is reversed, however, with high volume. This suggests that the system benefits more from courteous behaviors when the traffic becomes more congested. When Egoism and Altruism are compared on the same courtesy level, it could be concluded that Egoism results in better overall (for all states) mobility performance under medium and heavy traffic. Although Egoism performs slightly worse than Altruism under light traffic, the differences are much smaller than those under medium and heavy traffic. After decomposing all states into three component states, the superiority of Egoism compared to Altruism primarily comes from its advantage in LC state and other state.

For non-uniform courtesy, the mean and standard deviation of courtesy distribution from the MIT survey are 0.58 and 0.35 for CDE, and 0.75 and 0.30 for CDM. The system performance considering CDE and CDM (see the right halves of each subplot in Fig 7) are compared to those with uniform courtesy levels set to 0.58 and 0.75, respectively. It is found that the global average speeds of uniform courtesy for LC and courteous states are consistently higher than or at least equal to those of non-uniform courtesy. It implies that for egoistic and altruistic courtesy strategies, a system with non-uniform courtesy may bring instability and thus cause system inefficiency. A closer look at the results of individual simulation runs for CDE and CDM suggests that some of them (about 1~2 out of 10) have surprisingly low average speeds (under 5m/s) for LC state, and there are no courteous state (means no vehicles yielded) at all. This is the same as what happens when the courtesy level is zero under uniform courtesy and no vehicles cooperate. A possible explanation is that although CDE and CDM have relatively high average courtesy levels, AV with very low courtesy level (on the left tail of the courtesy distribution) may sometimes result in system failure, where the courtesy proxy becomes very high (for both Egoism and Altruism) compared to RCL due to SV which attempt to change lane queueing up at the end of the segment. Under system failure, even AV with high courtesy levels would find it very costly or impossible to yield.

The mobility performance for CDM overall is better than CDE. This may be caused by the fact that the courtesy distribution of CDM is more skewed towards 1 compared to CDE (see Fig 6). Although under heavy traffic Egoism with CDM has smaller average speed for LC state than Egoism with CDE, this could be attributed to the randomness of simulation as more system failures occur for Egoism CDM (it is also hinted by the larger margin of standard deviation of simulation results).

Local Utilitarianism achieves the highest average mobility. This is an unsurprising result given that the courtesy strategy itself is encoded with a limited account of mobility maximization. At least in simple road networks we should expect that if individual interactions aim to maximize mobility, then the overall network will also maximize mobility.

Local Maximin and Egalitarianism perform about the same under light and moderate traffic. It is worth noting that Egalitarianism degenerates sharply under heavy traffic. This is because in this case the cooperative behavior of AV is guided by the real-time global average speed (as in Fig 8). After changing lane, the speed of SV is assumed to reach the speed of TLV, which is usually an increase during the process. When the global speed is high, the system under Egalitarianism encourages (see Eq (11)) TLV to behave courteously because the resultant speed will become closer to global speed (the speed of TLV is assumed to be unchanged after LC). However, under heavy traffic when the global speed is typically lower, egalitarian principles might discourage TLV to yield to other vehicles because a local speed increase after changing lane would increase the variation of the system’s speed. Non-cooperation would further exacerbate the congestion situation and the global speed would decrease even more, finally leading to a system failure.

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Fig 8. Different cooperative behavior under low and high global average speed in an egalitarianism system.

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4.2 Safety

DRAC is a safety measure that mandates the least deceleration a TLV needs to execute for not colliding with a lane-changing SV. The smaller the DRAC is, the safer a yielding maneuver can be. In this study, each time a TLV yields to an SV, the corresponding DRAC is recorded and the average is shown in Fig 9. For Egoism and Altruism strategies with uniform courtesy, as the courtesy level increases, the DRAC first goes up and peaks at courtesy level = 0.04, then decreases and reaches the least value (less than 0.5 m/s²) at a relatively low courtesy level (about 0.1 for moderate traffic and 0.2 for heavy traffic). This pattern is different from those seen in mobility results, where the system performance monotonically increases with courtesy level.

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Fig 9. Evaluation of the safety performance of different courtesy strategies.

https://doi.org/10.1371/journal.pone.0283649.g009

Altruism is found to be safer than Egoism when a small amount of uniform courtesy in introduced into the system, but converges with Egoism at about 0.1 courtesy level under all three traffic inputs. It is proved again that variance (i.e., standard deviation of courtesy level) added to courtesy level could negatively affect the network performance especially under high traffic input. For instrumental courtesy strategies, Local Utilitarianism achieves the most stable (very small variance) and lowest DRACs.

4.3 Fairness

An interesting pattern in the fairness evaluation results (Fig 10) is that a strategy with better mobility (for all states) often comes with better fairness. Egalitarianism under heavy traffic yields the lowest fairness performance, which is the opposite of its design intention. This probably is because it encourages courteous behavior that generates after-lane-change speed not surpassing the global average speed. When the global average speed is relatively low (usually under heavy traffic), cooperative behavior that can help to improve traffic operations and increase global speed would not be selected by the Egalitarianism strategy, although it works well under moderate and light traffic.

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Fig 10. Evaluation of the fairness performance of different courtesy strategies.

https://doi.org/10.1371/journal.pone.0283649.g010

4.4 Vehicle state distribution

To better understand how each courtesy strategy affects system performance, the percentages of courteous state and lane-changing state generated by each strategy are computed and shown in Fig 11. Such percentages can reflect how often each courtesy strategy takes effects. Also, all courtesy strategies are evaluated using the same set of traffic demand (see Table 2). For each OD matrix, the required number of lane changes (i.e., to join/leave the highway) is the same for all strategies. Therefore, comparing the percentages of courteous and lane-changing states can be useful to understand how each courtesy strategy works, for example, how long vehicles are in the lane-changing process. When driving in a very courteous environment, the lane-changing state percentage (LCSP) should be lower than driving in an uncourteous environment where nobody yields, since it takes less time for vehicles to wait for safe gaps and change lanes.

It is worth noting that high courteous state percentage (CSP) does not necessarily result in low LCSP. Given a very congested on-ramp or work zone, courteous vehicles may need to wait for a long time for lane-changing vehicles to clear the bottleneck. In this case, both CSP and LCSP could be high.

Fig 11 clearly shows that with uniform courtesy between 0 and 0.3, Egoism has lower LCSP and higher CSP than Altruism under moderate and heavy traffic. Recall that Egoism also has better mobility results than Altruism in Fig 7 under the same traffic and courtesy conditions. This suggests that more courteous behaviors contribute to reducing the LCSP and improving system mobility performance. It also suggests the importance of carefully defining courtesy proxy and courtesy level. Egoism defines courtesy proxy from the perspective of TLV, while Altruism defines it based on SV. As the magnitude of courtesy proxy (i.e., speed difference) is different for TLV and SV (the speed gained by SV is usually larger than the speed lost by TLV) during lane change, courteous behavior would be more likely to occur under Egoism than Altruism (Since the CSP for Egoism is higher than Altruism as indicated in Fig 11) under the same uniform courtesy level. This explanation is further illustrated in Fig 12 and Eqs (4)–(7). For the same courtesy level and speed loss and gain, Egoism (Fig 12A) will yield based on Eqs (4)–(6), while Altruism (Fig 12B) will not based on Eq (7).

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Fig 11. Vehicle state distributions for different courtesy strategies.

https://doi.org/10.1371/journal.pone.0283649.g011

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Fig 12. An illustration of the difference between egoism and altruism under the same uniform courtesy level.

https://doi.org/10.1371/journal.pone.0283649.g012

Another interesting finding from Figs 7 and 11 is that for a system to work well, the CSP should not be too low or too high. One example is the Egalitarianism. Low CSP indicates a lack of willingness for cooperation, which makes it difficult for SV (i.e., LC vehicles) to change lanes. While a very high CSP could be the result of a system failure.

4.5 Performance of individual segments

In addition to analyzing the performance of the entire network, the mobility results for individual segments and lanes are also collected. Table 4 shows the lane-by-lane average speed results for each of the four important segments.

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Table 4. Lane-by-lane average speed under various courtesy strategies.

(A, B, WZ, and C represent segment types; LL, ML and RL are for leftmost lane, middle lane, and rightmost lane, respectively; red and green colors are for congested and uncongested situations, respectively).

https://doi.org/10.1371/journal.pone.0283649.t004

Under light traffic, the rightmost lane of the type C weaving area’s speed performance is among the lowest under all instrumental courtesy strategies, indicating this type C weaving area is the bottleneck of this corridor. For Egoism and Altruism with low uniform courtesy, it is hard for vehicles in the closed lane (i.e., rightmost lane) to merge in the work zone area, leading to low average speeds. Overall, the results suggest that Egoism and Altruism with low level of uniform courtesy do not work well under light traffic particularly for the type A and type C weaving areas and the work zone.

Similar trends could be found for moderate and heavy traffic. For Egoism and Altruism with uniform courtesy, a higher courtesy level is critical to accommodate the increased demand from lane changes. Congestion with low average speed is mostly found in the rightmost lanes of the type A weaving area and work zone and the middle lane of the type C weaving area. Results in Table 4 are consistent with the global average speed results in Fig 7. The low speed may be caused by few slow-moving vehicles seeking lane-changing opportunities due to a lack of cooperative TLVs.

To further understand the contributions of each segment to the global mobility performance. The contribution of the i^th segment under each courtesy strategy is calculated using Eq (16). (16) where v_g is the global average speed, and v_−i is the average speed without considering vehicles in the i^th segment. The idea behind Eq (16) is to calculate the removal effect, which tells the results difference between with and without the i^th segment. A positive CT_i value means having the i^th segment does not worsen the global performance, while a negative value suggests the opposite. The distributions of segment contribution are plotted in Fig 13. It is clear that the type C segment worsens the global average speed for most of the time. The contribution ranking (from negative to positive) based on mean CT_i is: type C, work zone, type A, and type B, and the contribution stability ranking (from highest to lowest) based on the variance of CT_i is: work zone, type A, type B, and type C.

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Fig 13. Contributions of each segment to the global average speed.

https://doi.org/10.1371/journal.pone.0283649.g013