8 Highway Road Traffic Modeling for ITS Simulation – Networking Simulation for Intelligent Transportation Systems

Highway Road Traffic Modeling for ITS Simulation

8.1. Introduction

Future Intelligent Transportation Systems (ITS) will rely heavily on new data transmission technologies, which will transform vehicles into actual communication hubs. Among such ITS-enabling technologies, those realizing direct vehicle-to-vehicle (V2V) communication are the most disruptive. They are expected to interconnect vehicles into self-organized networks whose functions are fully distributed, and provide an important complement to the current mobile communication architecture, which is instead based on a radio access infrastructure that centralizes all data exchanges. Matter-of-factly, upcoming 5G networks will integrate traditional cellular and vehicle-to-vehicle (V2V) direct communication into a unifying framework that will allow users to benefit from the best of the two worlds. Specifically, V2V communication is expected to support services that require rapid, stateless, multicast transmissions, including, for example, collision avoidance, cooperative awareness or localized data dissemination.

After years of research and development, the deployment of V2V communication is now close: standards such as IEEE 802.11-20121, IEEE 16092, OSI CALM-M53 and ETSI ITS-G54 have been finalized, and regulators in the USA plan to enforce V2V radio interfaces on all new vehicles by 2017 [MAS 14]. Extensive field tests are also in progress: representative examples are the German simTD project in Europe and the Ann Arbor Safety Pilot in Michigan, USA.

However, the cost and complexity of large-scale experiments still make computer simulations the method of choice for the performance evaluation of networking solutions based on V2V communication. Dependable simulations are therefore paramount to a proper evaluation of network protocols and algorithms intended for vehicular environments. In this context, the correct modeling of road traffic has been repeatedly proven to be a crucial aspect [FIO 08, BAI 09, UPP 14]. In addition, as well as being dependable, simulations need to be reproducible: this makes the public availability of road traffic datasets as important as their realism [JOE 12].

In this chapter, we focus on the representation of road traffic for the simulation of highway vehicular networks based on V2V communication technologies. In section 8.2, we review different open-access approaches to highway road traffic modeling for network simulation. In section 8.3, we include in our review an original fine-tuned measurement-based mobility model. In section 8.4, we compare the diverse approaches in terms of the instantaneous vehicular network connectivity they induce in a practical case study, i.e. highway segments in the conurbation of Madrid, Spain. The results shed light on the fact that a fine-tuned measurement-based model yields a level of detail in the mobility representation that is necessary for a reliable simulation under generic network settings. In section 8.5, we then leverage such a model to derive fundamental properties of the highway vehicular network connectivity, which are shown to hold across heterogeneous road traffic scenarios. In section 8.6, we conclude the chapter by discussing the networking implications of our investigation.

8.2. Road traffic models

The recognized impact of road traffic modeling on the simulation of vehicular networks has led to a significant effort in increasing the realism of road traffic traces used by network simulators.

A first approach consists of recording real-world movements of vehicles, typically by logging their position via GPS. These mobility traces can then be replayed in simulation to reproduce the actual road traffic. However, datasets of this type are limited to specific vehicles, e.g. fleets of taxis [HUA 07] or buses [DOE 10]; this clearly limits the scope of the networking studies they can support, both in terms of scale and penetration of the V2V communication technologies. In addition, there is currently no real-world dataset of vehicular mobility that is specific to the highway environment we consider in this chapter.

The generation of synthetic vehicular traces is the de facto standard approach to road traffic modeling. Here, special attention has been paid to urban road traffic: in this case, the generation process relies on microscopic road traffic simulators, such as SUMO [KRA 12] or VanetMobiSim [HÄR 11]. These are fed with (i) real-world road topologies that describe the layout and features (e.g. direction, number of lanes, speed limit, signalization) of all streets in the considered scenario and (ii) origin–destination matrices collected from user surveys [UPP 14, RAN 03] or from roadside detectors [COD 15] that describe the macroscopic flows followed by the vehicles within the urban environment. Several datasets were generated using such an approach, e.g. Zurich [RAN 03], Cologne [UPP 14] or Luxembourg [COD 15].

However, the dynamics of traffic over urban regions are not comparable to those of highways: the former are characterized by vehicles traveling at low or medium speed and often crossing intersections regulated by traffic lights or roundabouts; the latter feature instead high speeds and frequent overtaking. In the case of highway road traffic, three basic components are required for the generation of synthetic vehicular mobility:

  1. – the highway scenario is a description of the highway road segment to be simulated; it includes the segment span, number of lanes, and speed limits on each lane, and the presence of inflow or outflow ramps;
  2. – the traffic input feed is the characterization of the inflow of vehicles at the beginning of the considered highway segment; it models the inter-arrivals of vehicles on each lane, as well as their initial speed;
  3. – the mobility model is the mathematical representation of the driving behavior of vehicles that travel on the simulated segment; the model is typically microscopic, i.e. it determines the acceleration or deceleration of each vehicle separately, based on the surrounding conditions.

The vehicular networking literature is very heterogeneous when it comes to the implementation of the three components mentioned above. Some works propose to use aggregate statistics to describe vehicle inflows, while others employ fine-grained, per-vehicle traffic count data. Some works employ stochastic models of drivers’ behavior, whereas others leverage complex microscopic models. Many works neglect the presence of entry and exit ramps, whereas others consider them. Next, we propose a limited set of prototypal models that capture the vast majority of those employed in the literature. Specifically, we focus on the traffic input feed and on the mobility model, since they are independent of a specific context and can be employed across different highway scenarios. We will instead detail the specific highway scenario we consider in our discussion later on in section 8.4.1.

8.2.1. Traffic input feeds

All traffic input feeds fall in between two extreme approaches. The first is that of real traffic input feeds, and it imposes that vehicles enter the simulated highway segment according to some real-world traffic counts. Such traffic counts shall provide information on the actual transit of each vehicle, and include data such as the lane, the precise (e.g. order of millisecond) timestamp, the speed and possibly the length or type of the vehicle. Such high-precision data is challenging to collect: usually, real-world counts are obtained via induction loops, infrared counters or cameras, which are programmed to provide coarse-grained data. This is because the public transportation authorities that gather such information are generally interested in aggregate measures on, e.g. the number of vehicles transiting on a road, their average speed or the percentage of heavy vehicles, so as to detect major alterations of traffic conditions. Collecting fine-grained real-world counts implies changing the setup of the devices, so that they store data on each transiting vehicle separately.

The second extreme approach is that of synthetic traffic input feeds, where probability distributions are used to model the inter-arrival or inter-spacing of subsequent vehicles. Such distributions can be then used to generate the inflow into the simulated highway segment. Many varied distributions have been employed in the literature, which include deterministic [AKH 15, FEL 14], exponential [KHA 08] and lognormal [WIS 07] arrivals, up to generative models for mixture distributions [GRA 14].

Intermediate situations between these two approaches are also possible. Specifically, synthetic traffic input feeds can be trained on real-world traffic counts. In this case, traffic counts are leveraged to infer experimental distributions of the inter-arrival times; then, theoretical distributions are fitted on the experimental ones. Since inter-arrivals are not constant over time (consider, e.g. rush hours and overnight traffic conditions), such a process is repeated over disjointed time windows of duration w [BAI 09, MON 12]. Clearly, the shorter the time window w, the more accurate the input feed but the larger the number of theoretical distributions needed to model the feed.

Drawing from the classification above, we consider a set of five input feeds. In the following, real indicates a real traffic input feed, where vehicles are inserted into the simulation using their actual lane, timestamp and speed. By synthetic-w, we denote instead four different versions of synthetic input feeds. There, w is the time window over which the traffic count data is aggregated: 5 minutes, 10 minutes, 30 minutes or one hour. The inter-arrival times for the feed synthetic-w are exponentially distributed as follows:

where is the average number of vehicles per unit of time. The starting lanes are randomly selected in the synthetic-w case, and vehicles enter them with a uniformly random speed extracted from a distribution:

Specifically, is the average inflow speed observed during time window w. For the sake of consistency with common practices in the literature [BAI 09], we train the λw and Sw parameters of synthetic-w models from measurement data.

8.2.2. Mobility models

The mobility models employed in the literature on highway vehicular simulation are many and varied. They range from simplistic constant-speed representations [YOU 08, BAI 09] to complex dedicated implementations [AKH 15, FEL 14]. We tested the following representative methodologies.

The unstructured approach simply assigns a speed to each vehicle entering the simulated highway segment, and allows each vehicle to travel at that constant velocity along the whole segment. The speed is typically extracted from a uniform probability distribution [YOU 08], which may be calibrated using real-world measurements [BAI 09]. The second option, closer to reality, is the one we adopt in our discussion. In any case, this model clearly neglects all interactions among vehicles, and possibly allows them to overlap during movement. It is, however, a computationally inexpensive approach that has been largely adopted in vehicular networking research.

The SUMO approach leverages the SUMO tool, i.e. the de facto standard open-source software for the simulation of vehicular mobility [KRA 12]. SUMO implements microscopic car-following and lane-changing models. The former is Krauss’ model [KRA 97], which regulates each vehicle’s acceleration as a function of the distance to the leading one, the current speed, the safety distance or the acceleration and deceleration profiles. The latter is Krajzewicz’s model [KRA 09], which allows vehicles to make overtaking and lane-change decisions, considering the position and speed of nearby vehicles on different lanes. These models provide a much more complex and realistic representation of the movement of each vehicle within the traffic flow. An important remark is that Krauss’ and Krajzewicz’s models are employed with their standard parameterization, as done in virtually all works that rely on SUMO for their simulations.

8.3. Fine-tuned measurement-based model

In addition to the mobility models outlined in section 8.2.2, we also consider an original fine-tuned mobility model that builds on measurement data. The model, first presented in [GRA 16], leverages the IDM [TRE 00] and MOBIL [TRE 02] microscopic representations of the car-following and lane-changing behaviors, respectively. Although widely adopted in the vehicular networking literature, the IDM and MOBIL are invariably used with their default settings. Instead, the mobility model we introduce here performs an accurate tuning of IDM and MOBIL parameters, so as to better mimic real-world driving behaviors on highways.

Table 8.1. IDM and MOBIL parameter settings

Model Parameter Meaning Value
IDM a Maximum acceleration 1 m/s2
IDM b Maximum (absolute) deceleration 2.5 m/s2
IDM vimax Maximum desired speed ˜ fv(v)
IDM xsafe Minimum distance 1 m
IDM tisafe Minimum safe time headway ˜ fT(∆t)
MOBIL p Politeness factor 0.5
MOBIL aL Bias acceleration (left) 0 m/s2
MOBIL aR Bias acceleration (right) 0.2 m/s2
MOBIL k Hysteresis threshold factor 0.3

Table 8.1 summarizes the calibration adopted by the model. Specifically, the default values indicated in the original works [TRE 00, TRE 02] are found to work well for the acceleration a, deceleration b, politeness factor p and minimum bumper-to-bumper distance Δxsafe. The other parameters instead have to be tuned so as to avoid instability in the synthetic road traffic [GRA 16], as detailed below.

Maximum desired speed. Vehicles can be introduced in the simulation at the time and with the speed defined by the real-world traffic count dataset. However, we also need to configure their maximum desired speed , i.e. the velocity that vehicle i would keep if alone on the highway.

To that end, we recall that speeds measured from real-world traffic in free flow traffic conditions are representative of desired speeds. Indeed, free flow indicates complete lack of road traffic congestion: vehicles in free flow state have very little interaction, and travel at velocities around their maximum desired speed. Free flow speed distributions can thus be extracted for each lane of the target highway scenario: exemplary Probability Density Functions (PDF) are shown in Figure 8.1(a), 1.1(b) and 1.1(c), for the reference highway scenarios introduced in section 8.4.1. The PDFs are separated by lane, as drivers traveling on different lanes tend to have dissimilar maximum desired speeds. Interestingly, the distributions are different across lanes of the same highway, as faster drivers tend to stay on the leftmost lanes5. Moreover, all PDFs have Gaussian shapes, with fitted theoretical distributions indicated by solid lines in Figure 8.1.

Figure 8.1. Calculation of the maximum desired speed . (a,b,c) Empirical and fitted distributions of the free flow speed on each lane of M30, M40 and A6, respectively. (d) Example of per-vehicle truncation and normalization of the fitted distribution, so that only values larger than the initial speed are considered for Figure from [GRA 16]. For a color version of this figure, see www.iste.co.uk/hilt/transportation.zip

The PDFs mentioned above allow us to model the maximum desired speeds as Gaussian-distributed random variables, whose mean μh,l and standard deviation σh,l vary depending on the highway h and lane l considered. In fact, this is not sufficient: as drivers traveling on a same lane are not all equal, we adapt the final distribution on a per-vehicle basis as follows:

The expression in [8.1] truncates the Gaussian distribution at the speed recorded in the real-world traffic count data for vehicle i and ren ormalizes it. Figure 8.1 (d) provides a graphical example. The initial velocity of i, i.e. , becomes a lower bound to this ensures that the maximum desired speed of a vehicle i is never lower than its initial , which would conflict with the real-world measurements.

Minimum safe time. The minimum safe time headway is known to vary across real-world scenarios, in the range from 0.9 s [NHT 01] to 3 s [WHI 14]. In the proposed mobility model, we infer its value, on a per-vehicle basis, from road traffic measurements.

Specifically, the inter-arrival times between vehicles recorded in real-world traffic can be directly related to the values. However, this only holds when the road traffic is very dense, and inter-vehicle spacing actually maps to safety distances. More formally, according to traffic flow theory, the traffic density ρ on lane l of highway h can be expressed as follows:


where L is the average length of the vehicles, vh,l is the average speed and is the average safe time headway [CHO 14]. From density ρh,l, we can compute the vehicular flow qh,l = ρh,l vh,l, which results in:


Expression [8.3] directly relates to the maximum value of the flow qh,l and average speed vh,l. The maximum flow qh,l can be inferred from a real-world traffic count dataset by identifying the time interval during which a speed breakdown occurs on all lanes. The average speed vh,l is extracted from the same data as the average velocity of vehicles in free flow conditions, and L is the average vehicle length.

Figure 8.2. Calculation of the minimum safe time headway (a) Reference distributions of the typical safe time headway on each lane of M30, as inferred by the experimental flow, speed and inter-arrival information contained in the traffic count dataset. (b) Example of per-vehicle truncation and normalization of the reference distribution, so that only values smaller than the initial inter-arrival time are considered for Figure from [GRA 16]

The reference Gaussian distribution of safe time headway is then assigned the computed mean . The standard deviation σh,l can be set such that the minimum inter-arrival time recorded in the real-world traffic count dataset represents the 0.99 quantile of the distribution, i.e. three standard deviations. An example of the resulting per-lane distributions is provided in Figure 8.2 (a) for one of the reference highway scenarios detailed in section 8.4.1: we remark that the values of obtained for all lanes (2.11, 1.93, 1.66 and 1.52 s from the rightmost to the leftmost lane, respectively) are well aligned with those found in the literature [TRE 00, WHI 14, NHT 01].

As a final step, similar to what done for the maximum desired speed, a per-vehicle distribution is to be determined from the lane-dependent reference ones. In this case, the final distribution is given by:

where is the initial inter-arrival time of vehicle i recorded in the traffic count dataset. As shown in Figure 8.2 (b), [8.4] allows to become the upper bound to This ensures that no vehicle enters the simulation with an inter-arrival time that is lower than its minimum safe time headway.

Lane change bias and hysteresis threshold. In our highway scenarios, the default MOBIL settings result in a traffic that is highly skewed towards the left lane, which thus suffers from unrealistic congestion. We ran a comprehensive campaign to identify the combination of right (aR) and left (aL) lane change bias, and lane change hysteresis threshold factor (k) that grants quasi-stationary traffic over the different lanes. Such consistent ingress and egress per-lane properties were obtained for aR = 0.2 m/s2, aL = 0 m/s2 and k = 0.3. Interestingly, the lane change bias favors movements to the right in absence of a clear preference among lanes, which is in compliance with road regulation in Spain.

The mobility model arising from all the fine-tuning above is indicated as IDM in the following. A software implementation and sample datasets of synthetic highway road traffic generated with this model are open to the research community6.

8.4. Comparative analysis of road traffic models

In this section, we provide a comparative evaluation of the different strategies for synthetic highway traffic generation presented before. We thus test combinations of real and synthetic-w traffic input feeds with unstructured, SUMO and IDM mobility models. More precisely, we consider a reference highway scenario, detailed in section 8.4.1, and study the effect of the diverse approaches on the connectivity of the vehicular network built on V2V communication, according to the metrics presented in section 8.4.2. The results of this approach are summarized in section 8.4.3.

8.4.1. Case study scenarios

The highway scenario considered in our comparative evaluation is that of highways around the conurbation of Madrid, Spain. Fine-grained real-world traffic counts were collected by the Madrid City Council on M30, M40 and A6 for the purpose of our study. The data describes individual vehicle transits (including vehicle speed and type) with a 100 ms time accuracy, and covers heterogeneous traffic conditions from very sparse overnight traffic to rush hour congestion.

The different traffic input feed and mobility models presented in sections 8.2 and 8.3 are fed with this real-world measurement data. The real feed matches the data, whereas in the unstructured feed the initial speed is derived from a probability distribution fitted on the data. In IDM mobility model, the target speed and minimum gap between subsequent vehicles are calculated as described in section 8.3.

In addition to the highway settings, a reliable study of vehicular networks also requires a proper representation of the RF signal propagation model. Indeed, such a model determines whether vehicles are capable of communicating via V2V technologies. We thus extract V2V communication distance from a state-of-the-art propagation model [ABB 15], considering the transmission power is set to 20 dBm, a received signal strength threshold of −91 dBm and a reliability of .99. Shadowing effects due to nearby vehicles are considered as well, via an additional path loss when the latter obstruct the line-of-sight.

8.4.2. Connectivity metrics

Our investigation is based on a protocol-independent approach that focuses on instantaneous connectivity metrics of vehicular networks. The metrics describe the global structure of the vehicular network and measure its level of connectivity or fragmentation. They are formalized as follows.

At each time instant t, we represent the network as an undirected graph . Each vertex in the set maps to the vehicles i in the network at time t, and each edge in the set connects vi(t) and vj(t) if a V2V communication link exists between vehicles i and j at time t. We also denote as the number of vertices in the graph, i.e. the number of vehicles in the scenario, at time t.

Let us define a component as a subgraph of , where includes all and only the vertices corresponding to vehicles that can reach each other via direct or multi-hop communication at time t. Equivalently, . We denote as the size of the component Cm(t). Since components are disjointed by definition, is the number of components appearing in the network at time t. The number and size of components in the network at each time instant will be our network connectivity metrics.

The component availability and component stability metrics study large connected components emerging in the network, which are especially interesting as they allow for significant multi-hop communication opportunities. In particular, the two metrics focus on (i) the presence and (ii) the temporal fluctuations of such large components. Formally, we refer to the largest component appearing in the network at time t as . Then, is the size of the largest component at the same time instant. The normalized value of at each instant will be our reference metric for the study of the component availability, whereas its temporal variations will be leveraged to analyze the component stability. More precisely, the component stability is assessed through the correlograms of Smax(t): correlograms are derived by dividing Smax(t) time series into time windows, and computing the temporal autocorrelation at different lags, for each window.

In the remainder of the chapter, we will drop the time notation for the sake of brevity and refer all metrics to a generic time instant. We will thus use N to indicate the number of vertices in the network, C for the number of components and Smax the largest component size.

8.4.3. Results

We first assess the impact of mobility modeling on the global network connectivity, expressed as the component availability, i.e. the ratio between Smax and N. Figure 8.3 portrays smoothed scatter plots that refer to different combinations of traffic input feed and mobility models. All plots show the metrics as functions of the road traffic density, in vehicles per km. We highlight remarkable differences across plots, as follows.

Figure 8.3. The relative availability Smax/N versus the vehicular density N. The red line denotes the average. Figure from [GRA 15]. For a color version of this figure, see www.iste.co.uk/hilt/transportation.zip

First, the parameter w (in minutes) strongly influences the connectivity and availability metrics. While Figure 8.3 (a), 8.3 (b) and 8.3 (c) show a comparable and realistic behavior; using synthetic traffic with w = 60, in Figure 8.3 (d), yields an abrupt transition between the disconnected (∼20% percent availability) and fully connected (∼100% percent availability) phases. Equivalent considerations hold when synthetic traffic is combined with microscopic mobility, see, for example, the striking difference between Figure 8.3 (g) and 8.3(j). We conclude that an exceedingly coarse inflow granularity risks completely losing the state transitions that occur in real-world traffic, as well as the associated connectivity and availability states. Unfortunately, w is often a non-configurable parameter decided by the data providers, who are typically only interested in rough aggregates of the inflow traffic for statistical purposes.

Second, the use of SUMO appears to cause issues with the observed metrics. All plots where SUMO is used to model the vehicular mobility show that the mobility generator is just unable to insert all the vehicles in the simulation. This is clear when looking at Figure 8.3 (f) and 8.3(g)–8.3(j). While unstructured and IDM attain a peak traffic density of about 70 vehicles per km, SUMO never exceeds 40 vehicles per km. This is a parameterization issue: the default settings of Krauss’ model do not allow accommodating high inflows observed in the real world, which forces SUMO to delay the insertion of a vehicle until Krauss’ model safety requirements are fulfilled. In turn, this affects network connectivity and availability.

These results prove that using a validated microscopic model of vehicular mobility is not sufficient to obtain a realistic representation of road traffic: the parameterization of the model is extremely important, and a careless setting can lead to biased simulation outcomes. Clearly, this is not a problem of Krauss’ model per se. In order to prove it, we also show the connectivity and availability metrics obtained using the mobility dataset described in [AKH 15], which was generated using SUMO with customized (but undisclosed) parameterization. Figure 8.3(l) shows similar trends to those obtained with unstructured and IDM.

Third, an interesting observation is that a very simple constant-speed simulator using synthetic (but sufficiently detailed) traffic input feed results in a network connectivity and availability comparable to those attained by much more complex models. Figure 8.3(a), 8.3(e) and 8.3(k) shows precisely this effect.

Fourth, we stress that the highway road traffic dataset in [AKH 15] describes traffic in a different scenario, i.e. Interstate highway 5 (I5) in CA, USA. Still, the connectivity and availability scatter plots and mean curves are identical to those of our reference scenarios in Spain. This result allows us to speculate on the general validity of our findings, which could apply to different highway environments.

The correlograms of Smax in Figure 8.4 display the temporal variation of the largest connected component in the network: they map to the component stability metric. Here, we only display a subset of the results, for the sake of brevity and since w did not appear to influence the component stability. Again, SUMO, in Figure 8.4(b) and 8.4(d), shows a very different trend due to the maximum density issue we already discussed. However, the important result here is that the unstructured mobility model exhibits clear limitations. Figure 8.4(a) and 8.4(c) proves how the lack of interaction among vehicles in these models results in correlograms that differ from that obtained with IDM, in Figure 8.4(e). In the latter model, drivers are forced to adjust their speed according to the surrounding road traffic conditions, which leads to well-known phenomena, such as synchronized traffic: in turn, the global reduction of speed and queuing of vehicles noticeably improve connected component lifetime. We conclude that a simplistic representation of microscopic mobility does not impact network-wide metrics, but leads to connected components that may be significantly less stable in time than what would occur in the real world.

Figure 8.4. Smax/N correlograms. Figure from [GRA 15]

8.5. Fundamental properties of highway vehicular networks

In this section, we leverage the most realistic highway traffic representation among those evaluated in section 8.4, i.e. the IDM mobility model tuned on a real data feed to derive key properties of vehicular connectivity in highway environments. Specifically, we investigate the existence of general laws explaining the fluctuations of vehicular network connectivity as a function of two system parameters: the V2V communication range, denoted as R, and the road traffic density N.

Figure 8.5 portrays the evolution of C and Smax versus N. Each plot refers to a different R and shows the average behavior recorded in the M30 highway scenario (black solid line), as well as the dispersion around that mean (0.05–0.95 quantile range, as a light gray region). The vertical dashed lines roughly separate N ranges corresponding to sparse overnight traffic, typical free flow traffic and synchronized congested traffic.

The dynamics of both C and Smax are related to N. The largest component size, in the bottom plots, features a clear positive correlation with N. The number of components, in the top plots, instead displays a skewed bell shape. A clear three-phase connectivity in N emerges, under any R, from Figure 8.5. The three phases, or behavioral regions, are as follows:

  1. I) For low N, Smax 1 and C grow linearly with N: the network is very sparse and increasing the number of vehicles just means adding more isolated nodes, i.e. singleton components;
  2. II) Once a first critical N threshold is reached (denoted by the leftmost red dotted vertical line “A” in the plots), a second behavior ensues. Namely, Smax grows superlinearly with N and C decreases sub-linearly with N. The reason is that, beyond a critical vehicular density, new cars tend to join existing components or even bridge them into larger ones;
  3. III) The third region is attained after a second N threshold (the rightmost red dotted vertical line “B” in the plots) is passed. There, Smax ∼ N and C ∼ 1, i.e. the vehicular network is fully connected into a single component whose size matches the number of vehicles on the highway segment.

The behavior mentioned above is invariant over different values of the communication range R. Yet, the value of R greatly affects the critical N thresholds that trigger phase changes, which are anticipated for larger values of R.

The fact that the M30 curves show a moderate 0.05–0.95 quantile interval around the mean allows us to theorize that considering one single road traffic parameter, i.e. N, is enough to properly characterize the vehicular connectivity in all situations encountered during a typical working day. An interesting corollary to this observation is that other features, such as the daytime, day of the week, number of lanes, speed limits or presence of ramps are only responsible for minor variability in the connectivity. Such an observation also holds for the actual road traffic conditions (i.e. free flow to synchronized or jammed traffic, which are known to induce, for example, major speed variations), which are not decisive to connectivity region transitions.

Figure 8.5. C and Smax versus the number of nodes N for the M30, M40, A6, I5 and I880 datasets, for different R values. For a color version of this figure, see www.iste.co.uk/hilt/transportation.zip

Figure 8.5 also includes the C and Smax recorded in the M40 and A6 highway scenarios (represented as filled circles in the graphics), as well as in additional I5 and I880 highway scenarios (empty squares). The latter correspond to the highway environments considered in [AKH 15], where measurement data from the US Freeway Performance Measurement System (PeMS) is fed to a properly calibrated SUMO simulator to generate synthetic road traffic. For the M40, A6, I5 and I880 scenarios, dots represent the mean C and Smax values and error bars denote 0.05 and 0.95 quantiles. We remark that the majority of M40, A6, I5 and I880 dots fall very close7 to the mean behavior observed in the M30 case, and their 0.05–0.95 quantile ranges tend to correspond to those of M30. Therefore, we conclude that the same three-phase connectivity dynamics in N hold for all of the highway scenarios we consider. Moreover, the impact of R on the network connectivity is equivalent in all such scenarios. Once more, these observations allow us to speculate that the three-phase connectivity law may have general validity for vehicular networks in highway environments.

8.6. Discussion and conclusions

The results presented in section 8.4 demonstrate that a specialized highway mobility model like IDM, fine-tuned on a real data feed, is necessary for a faithful representation of road traffic in network simulations. If such a requirement is not met, significant errors emerge in the V2V communication-based connectivity, which can then propagate to the performance of network solutions.

Surprisingly, even a state-of-the-art mobility simulator such as SUMO cannot be used straight away, due to an inappropriate parameterization of its mobility model default settings. Instead, an unstructured simulator where vehicles travel at constant speed may be sufficient, but only for simulating network solutions that only rely on the availability of large connected components (e.g. best-effort data dissemination or collection); when more precise dynamics of the vehicular network must be properly modeled in simulation (e.g. for cooperative awareness or collision avoidance) such an approach can bias the results. We also observe that synthetic data can be used to feed simulators, if not aggregated over too large temporal windows w that lose state transitions in real-world traffic.

The following discussion in section 8.5 allows us to conclude that the topology of highway vehicular networks is driven by two major factors, i.e. the V2V communication range and the road traffic density. More precisely, such an interdependence occurs through an invariant three-phase relationship that connects connectivity and road traffic density (not to be confused with the road traffic state).

Overall, these results shed light on the fundamental dynamics of vehicular network topologies, and have clear implications in the design and performance evaluation of adaptive networking solutions intended for vehicular environments.

8.7. Bibliography

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Chapter written by Marco GRAMAGLIA, Marco FIORE, Maria CALDERON, Oscar TRULLOLS-CRUCES, Diala NABOULSI.