Realtime urban traffic amount prediction models for dynamic route guidance systems
 Zilu Liang^{1}Email author and
 Yasushi Wakahara^{1, 2}
https://doi.org/10.1186/16871499201485
© Liang and Wakahara; licensee Springer. 2014
Received: 31 January 2014
Accepted: 30 April 2014
Published: 22 May 2014
Abstract
The route guidance system (RGS) has been considered an important technology to mitigate urban traffic congestion. However, existing RGSs provide only route guidance after congestion happens. This reactive strategy imposes a strong limitation on the potential contribution of current RGS to the performance improvement of a traffic network. Thus, a proactive RGS based on congestion prediction is considered essential to improve the effectiveness of RGS. The problem of congestion prediction is translated into traffic amount (i.e. the number of vehicles on the individual roads) prediction, as the latter is a straightforward indicator of the former. We thereby propose two urban traffic prediction models using different modeling approaches. Model1 is based on the traffic flow propagation in the network, while Model2 is based on the timevaried spare flow capacity on the concerned road links. These two models are then applied to construct a centralized proactive RGS. Evaluation results show that (1) both of the proposed models reduce the prediction error up to 52% and 30% in the best cases compared to the existing Shift Model, (2) providing proactive route guidance helps reduce average travel time by up to 70% compared to providing reactive one and (3) nonrerouted vehicles could benefit more from route guidance than rerouted vehicles do.
Keywords
1 Introduction
Urban road traffic congestion has been a global issue for many years due to rapid urbanization. Residents in cities are suffering from the most annoying sideproduct of urbanization every day. According to data from IBM [1], there are more than one billion cars running on all the roads around the world, and the number will double by 2020. Traffic congestion not only causes mental stress in drivers, but also leads to more severe pollution, higher gasoline consumption and huge economic loss [2, 3]. There are three levels of solutions to urban road traffic congestion: reducing road traffic demand, shifting road traffic to other travel mode, and spatially distributing traffic to maximize the usage of traffic network capacity. Since it is not always possible to reduce the number of trips or persuade drivers to change their travel mode, distributing traffic through route guidance is considered a most feasible, effective and economic solution to urban road traffic congestion. Consequently, the route guidance system (RGS) has attracted great research interest from the government [4], companies [1, 5, 6] and research institutes [7] for many years. In our daily life, RGS has been widely used to facilitate driving either in unfamiliar or familiar environment through providing turnbyturn route navigation or recommending realtime optimal route information.
The route guidance provided by RGS can be based either on prevailing realtime traffic condition (prevailing route guidance) or predicted traffic condition (predictive route guidance), and it has been widely recognized in the transportation engineering community [8] that when predictions are accurate, predictive information is generally expected to be more effective than prevailing information because predictive information accounts for the rapid change of traffic conditions spatially and temporally. Although a couple of anticipatory RGSs have been proposed in academia [9, 10], these systems are fundamentally reactive solutions. In other words, current route guidance systems are no more than alert systems, as they provide drivers traffic information after congestion happens instead of proactively guiding drivers to prevent congestion from happening. Due to this strategic limitation of current RGS, the traffic prediction module in existing RGS has been mainly focusing on travel time prediction and the consistency of predicted travel time.
We argue that an RGS has the potential to bring more benefit to a transportation system if it gives proactive route guidance to related vehicles, which helps drivers detour to reduce the degree of congestion and even prevent congestion from happening. The mechanism of this kind of proactive RGS is to provide route guidance to drivers when traffic congestion is predicted. In this paper, the problem of congestion prediction is translated to the prediction of traffic amount (i.e. the number of vehicles) on a road link, as high traffic amount is a straightforward indicator of congestion. We propose traffic amount prediction models tailored for urban road links adopting two distinct modeling approaches, with the intension of laying a foundation for proactive RGS. The first model is based on the propagation of traffic flow along the successive road links on a route, while the second model is based on timevaried occupied link capacity on the concerned links. In order to evaluate the prediction accuracy of the proposed models, we run simulations in a microscopic simulator SUMO [11], conduct prediction using the proposed models, and analyze the prediction errors under the effect of varied prediction interval. The results demonstrate advantages of the proposed prediction models compared to an existing one. We then apply the prediction models to an RGS to investigate how the proactive route guidance affects the performance of a traffic network (i.e. average travel time, average travel length) and the impact of rerouting on drivers (e.g. the number of rerouted vehicles, average travel time of rerouted/nonrerouted vehicles, etc.).
The main contributions of this paper are listed below:

We propose two novel traffic amount prediction models tailored for urban traffic networks based on two distinct microscopic modeling approaches.

We construct a proactive RGS based on the proposed prediction models to improve the performance of RGS.

We evaluate the prediction accuracy of our models using realistic traffic traces on real city maps, and compare their performance with a good baseline model. We demonstrate the advantage of the proposed models with respect to varied prediction interval.

We investigated the effectiveness of proactive route guidance with respect to the performance of a traffic network on the system level and the impact of the guidance on rerouted and nonrerouted drivers.
The rest of the paper is organized as follows: In section 2, we discuss related works on RGS and traffic prediction; the proposed urban traffic amount prediction models are presented in section 3; in section 4, we construct a centralized proactive RGS based on the prediction models; in section 5, we evaluate the prediction accuracy of the proposed models, and investigate the impact of proactive route guidance on a traffic network; in the last section, we draw the conclusions.
2 Related work
2.1 Route guidance systems (RGS)
Route guidance systems [12] were originally invented to facilitate drivers to arrive at their destinations when traveling in unfamiliar environment. Early route guidance service was limited to invehicle car navigation [13], which was initially used only by a small proportion of people because these systems were expensive and mainly installed in highend cars. Moreover, first generation route guidance systems primarily compute the shortest routes on the basis of static map and do not respond to realtime traffic condition.
With the development of traffic surveillance infrastructure and communication technologies, it is possible to generate dynamic route guidance based on realtime traffic conditions [14, 15]. The benefit of route guidance system has thereby been extended far beyond the traditional turnbyturn navigation function. Even when drivers are traveling in familiar environment, they feel the need to use route guidance service to acquire the information on not only realtime traffic conditions and suggestions on alternative routes that avoid ongoing congestion, but also road pricing, parking availability, and even entertainment facilities. Although the efficiency of route guidance is closely related to the quality of realtime traffic data, simulation study has confirmed the potential of RGS in reducing average travel time and congestion severity even with imperfect traffic information [16].
In academia, besides the research effort on the mechanism of route guidance generation, many researchers have also devoted to the study on individual drivers’ responses or compliance to route guidance [17–21]. It is worth noticing that, in [21], the authors conclude from questionnaire surveys that ‘it would be naive to assume that... a guidance system could cause equipped drivers in a familiar network to take routes very different from those they would wish to take’ and ‘those drivers who are congestion avoiders would be more malleable than those who are time minimisers’. At the same time, most drivers have high expectations of the potential savings in time that might be gained by following route guidance for travels made in congested conditions even in familiar environment. The above fact confirmed the necessity to improve the function of RGS in terms of combating road traffic congestion, which will not only bring more benefit to drivers but serve as enforcement to drivers’ compliance. In recognition of this need, we intend to design a dynamic RGS that helps reduce the degree of traffic congestion or even prevent congestion from happening. Specifically, our goal is to reduce average travel time in the traffic network by providing proactive route guidance that is based on shortterm traffic amount (and thus congestion) prediction.
2.2 Traffic prediction
Intensive research effort has been made on traffic prediction in traffic engineering, with a dominant amount of work done on travel time prediction. According to the type of data a prediction model is based on, we can classify existing models into two categories: models based on historical traffic data and models based on realtime traffic data.
Most of the traditional prediction models belong to the first category, including historical average and smoothing techniques, parametric and nonparametric regression [22–24], autoregressive integrated moving average (ARIMA) [25–27], machine learning [28], fuzzy logic [29, 30] and neural networks [31–33]. These methods often suffer from high computational complexity either due to the stationery requirements or a large number of estimated parameters and may not be adaptive to the change in traffic patterns [34]. Smith and Demetsky [35] conducted comparisons of historical average, timeseries, nonparametric regression and artificial neural network (ANN), and found that the nonparametric regression model significantly outperformed the other models and was easier to implement. Even so, nonparametric regression models require large amount of historical data and training process. Moreover, in the scenario where matches are not enough good in the historical database, the nonparametric regression may fail to output reliable prediction.
In order to improve the prediction accuracy, several models were proposed based on realtime traffic data [36, 37]. Very recently, a traffic flow prediction method for signalcontrolled city street network has been proposed in [38]. However, some input variables required by this model are usually difficult to obtain in real transportation systems. Furthermore, the speeddensity fundamental diagram [39] adopted by this model may not hold in urban traffic networks, as the dependency of travel speed on the traffic flow in urban areas is not significant [40] and may demonstrate multivaluedness and instability [41, 42]. For a single urban link, the speed on this link is not only dependent on flows on the link itself but also on other conflicting links [43, 44].
Despite the varying degrees of accuracy that have been achieved by these prediction models, they can hardly be effectively applied to realize dynamic route guidance that helps prevent congestion from happening. These models are fundamentally macroscopic or mesoscopic, and therefore, it is not easy to accommodate the effect of traffic lights and other traffic management measures such as dynamic route guidance and congestion pricing. Besides, some of the models are based on classic traffic flow theory that is originally established for highways and does not necessarily hold on urban links. In this paper, we adopt a microscopic modeling approach to compensate the demerits of existing modeling approaches, and develop effective traffic prediction models to facilitate congestion prediction and construct proactive RGS based on such prediction.
3 The proposed prediction models
3.1 Problem definition
The goal of our problem is to predict the traffic amount on a road link in urban traffic network based on realtime traffic information. The traffic amount on link i in time interval k, denoted as X_{ i }(k), is defined as the number of vehicles on link i at the beginning of time interval k. Although conventionally transportation researchers have been focusing on the parameter of traffic flow, or traffic volume, defined as the number of vehicles passing an observation point per unit of time (usually 1 h) [45], we believe that traffic amount is a better target for our problem than traffic flow or volume, as high traffic amount is a direct indicator of traffic congestion. Besides, it is feasible to count the traffic amount on urban links, whereas the same task can hardly be done on highways.
Suppose in an urban network there is a centralized traffic control center that periodically conducts traffic amount prediction and generates route guidance based on the prediction. The control center considers the traffic network as a discretetime system and adopts the rolling horizon approach [46] to conduct the prediction. In other words, the time horizon is divided into discrete traffic prediction time intervals whose length is τ seconds, and traffic prediction is performed repeatedly every τ seconds and at the beginning of each time interval. In practice, the traffic control center needs to carefully decide on the value of τ to ensure effective and feasible prediction. If τ is too long, the prediction output cannot facilitate timely traffic management. On the other hand, if τ is too short, the new round of prediction is not meaningful, as new traffic data will not have become available at the traffic control center. Suppose there are traffic sensors (e.g. loop detectors and probe cars) on all road links and each sensor provides a traffic data at given time interval τ_{ A G }, we define the shortterm traffic amount prediction problem as follows:
Definition 1
Given the observed traffic data on all the links during time interval k, find the traffic amount on a link i during time interval k+1.
We adopt a microscopic modeling approach to take into consideration of the impact of traffic signal and drivers’ route choice on traffic flow. Compared to conventional mesoscopic modeling based on traffic flow theory, our modeling approach can not only effectively capture the sudden change in traffic flow pattern, but easily be integrated to traffic management measures such as adaptive traffic signaling and dynamic route guidance.
Before presenting the details of the two proposed urban traffic prediction models, we first clarify the assumptions for the models here. We assume that the number of vehicles on each link at an initial time equals zero. The traffic amount is assumed to stay constant during each prediction time interval. The traffic data aggregation period interval τ_{ A G } is equivalent to the prediction interval τ. Moreover, we assume that the split rate of traffic flows at the intersections and the departure/arrival traffic amount on each link are obtained beforehand, e.g. via vehicle tracking [47, 48], vehicular route prediction [49] or even by collecting drivers’ feedback on their route choice [50].
3.2 Model1: prediction based on spatiotemporal correlation
where ${\widehat{X}}_{i}(k+1)$ is the predicted traffic amount on link i in time interval k+1, X_{ i }(k) and ${X}_{{(i1)}_{u}}\left(k\right)$ are the detected traffic amount on link i and its u th upstream in time interval k, ${\widehat{Q}}_{i,\text{in}}\left(k\right)$ and ${\widehat{Q}}_{i,\text{out}}\left(k\right)$ are the predicted traffic amount that enters and leaves link i respectively, X_{dep,i}(k) and X_{arr,i}(k) are the departure and arrival traffic amount on link i, ${\gamma}_{{(i1)}_{u}\to i}\left(k\right)$ is the split rate of traffic amount that travels on the u th upstream of link i in time interval k and will enter link i afterwards, ${\gamma}_{i\to {(i+1)}_{d}}\left(k\right)$ is the split rate of the traffic amount that travels on link i and will enter the d th downstream link in time interval k afterwards. The ${\delta}_{{(i1)}_{u}\to i}\left(k\right)$ is the adjustment factor for the traffic flow from the u th upstream link to link i in time interval k, and ${\delta}_{i\to {(i+1)}_{d}}\left(k\right)$ is the adjustment factor for the traffic flow from link i to its d th downstream link. The adjustment factors take into account the effect of traffic lights on traffic dynamics.
where N_{ i }(k) and o_{ i }(k) are the measured traffic count and occupancy (the percentage of time the detector is occupied by vehicles) on link i in time interval k, respectively, and L_{eff} is the average effective vehicle lengths (EVLs) of the traffic stream, which is the average vehicle length plus the detector length. In practice, L_{eff} has been assumed to be constant; for example, the Washington State Department of Transportation uses L_{eff}= 20 to 25 ft [53]. If no loop detector has been installed on road links, it is still possible to estimate the realtime vehicle speed using telecommunication technologies [54, 55].
3.3 Model2: prediction based on spare road capacity
where L_{ v } and L_{ g } are the average vehicle length and the minimum gap between vehicles, respectively.
where ${\overline{X}}_{{(i1)}_{u}}\left(k\right)$ and ${\overline{X}}_{i}\left(k\right)$ are the average traffic amount on the u th upstream link and link i respectively in time interval k, ${C}_{{(i1)}_{u}}$ and C_{ i } are the capacity of the u th upstream link and that of link i. It is worth noting that the capacities used in Equations 13 and 14 are in fact the queuing capacity [56] of a road defined as the number of vehicles that can be stored on the road in a queue. When this storage capacity is exceeded the queue will spill back onto the upstreams of this road and often block intersections.
The main difference between Model1 and Model2 lies in the prediction of inflow and outflow traffic amount. Model1 considers the propagation of traffic on successive links, which is adaptively adjusted according to the realtime traffic conditions. In contrast, Model2 predicts the actual inflow/outflows by taking the maximum flows that is possible on the concerned link during that time interval as reference. As is shown in Equation 13, the predicted inflow of link i is the minimum of the following two values: (1) the maximum inflow of link i and (2) the sum of the maximum outflow of the direct upstream links adjusted by the split rates and occupied road capacity. Similarly, as is shown in Equation 14, the predicted outflow of link i is the sum of the minimum of the following two values: (1) the maximum inflow of a direct downstream link and (2) the maximum outflow of link i adjusted by the split rates and occupied road capacity.
4 Applying prediction models to RGS
We apply the proposed urban traffic amount prediction models to a typical centralized RGS to construct the proactive RGS. The proposed RGS operates in three phases: (1) detecting and predicting congestion, (2) selecting vehicles for rerouting and computing alternative routes and (3) pushing route guidance to drivers. The RGS also adopts the rolling horizon approach; that is, the time horizon is divided into discrete time intervals, and the three phases are conducted at the beginning of each time interval repeatedly. It is worth noticing that the control time interval τ_{ c } of the RGS is equivelent to the prediction time interval τ. Each of the phases is described in detail below.
4.1 Detecting and predicting congestion
where α∈[0,1] is a predefined congestion threshold value.
4.2 Selecting vehicles and computing alternative routes
When congestion is detected or predicted on a road, vehicles that satisfy the following two requirements will be selected for rerouting: (1) they are on up to the lhop upstream of the congested or willbecongested link and (2) they intend to use this link afterwards. The selection level, denoted as l, needs to be properly chosen to mitigate congestion without triggering secondary congestion on popular alternative routes [7]. The service provider then computes the shortest alternative route for selected vehicles using the Dijkstra algorithm based on current travel time on each road.
4.3 Pushing route guidance to vehicles
When the service provider completes the computation of alternative routes for all selected vehicles, it pushes the guidance to each of the vehicles. Vehicles are expected to switch to the guided alternative routes and continue their travel.
5 Performance evaluation
The purpose of the evaluation is to clarify the answers to the following questions
5.0.0.0 With respect to the prediction models

How to decide on the prediction interval τ? How does τ affect the accuracy of the prediction models?
5.0.0.0 With respect to the proactive RGS

How to decide on the congestion threshold α? How does α effect the system performance of an RGS?

How does proactive route guidance affect the performance of a traffic network on its system level? How does control/prediction interval affect the ultimate system performance?

How many vehicles are involved in rerouting? Is the impact of rerouting the same on rerouted and nonrerouted vehicles?
We adopt an opensource and highly portable microscopic traffic simulator, SUMO [11], to run simulations and collect real traffic data. The route guidance function is realized by employing Traffic Control Interface (TraCI) [57]. TraCI provides an access to a running road traffic simulation in a realtime mode so that we can change the route of a vehicle on the run. The default setting in SUMO 0.15.0 is used to configure vehicles. The vehicle length is 5 m, the minimal gap between vehicles is 2.5 m, and the Krauss model [58] is used as car following model. We use different network topology and traffic demand depending on the purpose of the evaluation, which will be described in detail in each of the following subsections.
5.1 Accuracy of proposed prediction models
The local topology of link 23572355 ♯ 2
Link ID  Length  Max. Speed  Relation 

(m)  (m/s)  
23572355 ♯ 2  109  14  Link i 
24665807 ♯ 1  125  14  Upstream of i 
24665807 ♯ 0  134  14  Upstream of i 
23572355 ♯ 1  98  14  Upstream of i 
23585509 ♯ 0  103  14  Downstream of i 
23572355 ♯ 3  121  14  Downstream of i 
where K is the total number of prediction intervals, X(k) are the values collected from the simulations in SUMO, while $\widehat{X}\left(k\right)$ are the predicted values. The reason for adopting two measures is that a combined evaluation based on both measures can compensate for the potential disadvantages of each single measure and thus provide a better picture of the errors. On the one hand, MAE is scaledependent so that it cannot be compared across estimation series on different scales [61]; on the other hand, SMAPE is scaleindependent, but it is favorable for overestimation. An observation on the difference between the trend of SMAPE and MAE could roughly indicate whether an estimation model tends to yield overestimation. It is also worth noting that we do not adopt the widely used measure Mean Absolute Percent Error (MAPE) [62] here, as this measure yields biased evaluation when real value is close to zero [62].
We conduct prediction every 10, 60, 180, and 300 s, which are equivalent to the aggregation period of traffic data. We run the simulations five times under different seed values, and acquire five sets of real traffic data. For each value of prediction interval, the prediction is conducted over each of the five sets of data and prediction errors are calculated after each prediction. The average values of the prediction errors over the five repetitions are taken as the final results, and the 95% confidence interval is also calculated.
Figure 1 shows that Model1 has the smallest errors among the three prediction models regardless of τ. It significantly reduces MAE by 52% and SMAPE by 41% compared to the baseline Shift Model in the best case (τ=10 s). Model2 also reduces MAE by 30% (τ=10 s) and SMAPE by 28% (τ=300 s) compared to the Shift Model in the best cases. In the studied scenario, Model1 gains its maximum advantage when τ=10 s, which is in the same magnitude as the link travel time. As the prediction interval further increases, the advantage of Model1 decreases, whereas the advantage of Model2 increases. When τ=300 s, the accuracy of the two proposed models is very close. We can infer that Model1 may work better when τ is on the same magnitude as link travel time, while Model2 may be more suitable for longer τ.
In practice, the aggregation period of traffic data ranges from 20 or 30 s [63] to 5 min. The prediction model should be chosen depending on the data aggregation period. For example, if the traffic data is aggregated in less than 1 min, Model1 should be used to perform the prediction; otherwise, Model2 would be a better candidate to yield accurate prediction. In addition, it is worthy of mentioning that the prediction accuracy could be influenced by other factors, such as the characteristics of traffic demand, the topology of the traffic network, the route choice decision made by drivers with or without guidance, the configuration of traffic signal, etc. Hence, the ultimate requirement on the prediction accuracy could be greatly dependent on the specific applications. We also confirmed that the proposed models are not biased [64].
5.2 Performance of RGS with traffic prediction
We compare the performance of the following five cases.

RGS + Model1: A proactive RGS that generates route guidance based on traffic prediction using Model1.

RGS + Model2: A proactive RGS that generates route guidance based on traffic prediction using Model2.

RGS + Modelshift: A proactive RGS that generates route guidance based on traffic prediction using the existing Shift Model.

RGS: A reactive RGS that generates route guidance based on current traffic condition without prediction.

NoRG: No route guidance is provided; thus no rerouting is performed.
We run each simulation five times under different seed values, and take the average values as the final results. In the figures, we also indicate 95% confidence intervals. The selection level l is set to 3, as it produces good results with moderate computation [7]. The penetration rate is 100%; that is, all vehicles are subscribed to the route guidance service and thus can periodically receive route guidance. The compliance rate is set to 100% so that all the drivers are supposed to follow the guidance. The RGS generates route guidance every τ second, which is equivalent to the traffic prediction interval.
We first analyze the performance of the RGS under the impact of the congestion threshold α that is set to three fixed values 0.6, 0.7 and 0.8. In order to evaluate the operating efficiency of the route guidance, we use average travel time as the levelofservice measure. Compared with other similar measures such as travel speed, travel time is not only intuitive to travelers, but also can be easily interpreted in economic terms, which is critical to quantifying the cost and benefit of transportation investments.
6 Conclusions
In this paper, we proposed two urban traffic amount prediction models based on the propagation of traffic flow and the spare road capacity, respectively, for applying the proposed models to a route guidance system (RGS) to reduce average travel time. We evaluated the prediction accuracy of the proposed models by comparing their performance with the Shift Model under varied prediction interval using the real data collected in the traffic simulator SUMO. The results demonstrated that both models significantly reduce prediction error up to 52% and 30% in the best cases compared to the existing Shift Model. In addition, we found that the performance of Model1 peaks when the prediction interval is in the same magnitude as the link travel time, while Model2 demonstrates superiority when the prediction interval is longer. We also evaluated the impact of proactive route guidance by comparing the performance of an RGS with traffic amount prediction (proactive route guidance) to that of an RGS without prediction (reactive route guidance). Simulation results confirmed that the proactive route guidance helps greatly reduce average travel time by up to 70% compared to the reactive ones, and the proposed traffic prediction models can further reduce average travel time by up to 14% in comparison with the existing Shift Model. Moreover, proactive route guidance leads to less number of reroutings for each rerouted vehicle. We also discovered that nonrerouted vehicles could benefit more from route guidance than rerouted vehicles do. In the next step, we intend to propose more efficient route scheduling and routing mechanism in RGS with the objective of pushing the system performance to its optimal.
Declarations
Acknowledgements
The authors would like to thank the anonymous reviewers for their valuable comments and suggestions on this paper.
Authors’ Affiliations
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