Eduardo Mucelli

Rezende Oliveira

Aline Carneiro

Aline Carneiro Viana

Routine-based network deployment for data offloading in metropolitan area

published or not. The documents may come

I. INTRODUCTION

WiFi offloading seems to be a viable solution to the recent boost up of mobile data consumption that is straining 3G cellular networks in metropolitan areas. [START_REF] Barbera | VIP delegation: Enabling VIPs to offload data in wireless social mobile networks[END_REF], [START_REF] Lee | Mobile data offloading: how much can wifi deliver?[END_REF], [START_REF] Thilakarathna | Performance of content replication in mobitribe: A distributed architecture for mobile ugc sharing[END_REF]. The idea consists in shifting the traffic from cellular networks to WiFi inexpensive ones. Carefully deploying WiFi hotspots can both be cheaper than upgrade the current cellular network structure and can concede substantial improvement in the network capacity [START_REF] Lee | Mobile data offloading: how much can wifi deliver?[END_REF]. Nevertheless, one question remains: how WiFi hotspots should be deployed? The following factors make the answer to this question a challenge task.

The expansion of metropolitan areas increased the possibility of moving around [START_REF] Seto | A metaanalysis of global urban land expansion[END_REF]. This fact together with the increase of smartphone use results in highly dynamic links, which may significantly affect the performance of the network [START_REF] Judd | Efficient channel-aware rate adaptation in dynamic environments[END_REF]. Moreover, people may use different transportation modes, which significantly impacts their trajectories: e.g., a person riding a bike or walking can decide the path to follow contrarily to someone inside a bus. Finally, it is also important to take into account the space-time interaction between people and urban locations, a key point for an efficient network planning. Such considerations can reveal fundamental insights in terms of network usability. Popular sites for instance, are the source of the most of the traffic on the network [START_REF] Kim | Extracting a mobility model from real user traces[END_REF].

In order to consider these issues, this work tackles the WiFi hotspot deployment problem in a metropolitan area by leveraging mobile users' context, i.e., their trajectories and scenario interaction. Our objective is to define what are the best places to receive WiFi hotspots in order to maximize the coverage on an urban scenario. This is a convenient solution for both cellular operators and users: The former can see the traffic being shifted to inexpensive networks while the latter can take advantage of higher data rates and less monetary costs than using cellular networks. We claim that unplanned deployment of hotspots may lead to both under-utilized and over-utilized network areas.

To the best of our knowledge, [START_REF] Wang | Efficient wifi deployment algorithms based on realistic mobility characteristics[END_REF] proposes the only approach to deploy hotspots that considers user mobility characteristics. Our proposal differs from this one in the following main points. First, we consider an urban scenario, which presents significantly higher complexity than the campus scenario considered in [START_REF] Wang | Efficient wifi deployment algorithms based on realistic mobility characteristics[END_REF]: i.e., higher densities, many popular areas, diverse types of mobility (imposed by a variety of transportation modes), bigger area, etc. Second, our objective is not to provide continuous coverage: In an urban scenario, this is prohibitively expensive since it would require the deployment of hotspots over the whole area, where most of them may be under-utilized. Finally, our approach is not restricted to the consideration of only one popular area: In an urban scenario, diverse popular areas may exist and their features may vary according to space-time issues. Some other related works provide solutions for data offloading but not related to hotspot deployment e.g., delegating the data offloading for people's devices [START_REF] Barbera | VIP delegation: Enabling VIPs to offload data in wireless social mobile networks[END_REF], [START_REF] Han | Mobile data offloading through opportunistic communications and social participation[END_REF], [START_REF] Thilakarathna | Performance of content replication in mobitribe: A distributed architecture for mobile ugc sharing[END_REF].

To accomplish our objective, we study the mobility context of people in a metropolitan area of a major city and identify a set of locations to well deploy WiFi hotspots (cf. Section II). Our strategy (cf. Section III ) is methodologically structured as follows. First, we create a time dependent graph to represent the interaction between people mobility and locations suitable to receive a hotspot. Then, we measure how much coverage a location can contribute to. For this, we use a metric herein proposed to rank which locations are suitable to support more: Better positioned hotspots are likely to provide better coverage, and therefore, are likely able to offload more data (cf. Section IV ).

Through extensive experiments on a real-life trace, we evaluate the performance of our routine-based network deployment in terms of network coverage, by varying the number of hotspots deployed. We also compare our solution with an unplanned deployment. The results reveal that with, on average, 16% of deployed spots, our strategy provides about 75% of coverage time, contrarily to 73% of deployed spots in the unplanned deployment case (cf. Section V). Finally, Section VI concludes this work.

978-1-4799-3083-8/14/$31.00 c 2014 IEEE II. RATIONALE Before presenting our strategy for hotspot placement, we provide in this section the insights considered in our solution and discuss our system model.

A. General view

People are routinary semi-rational entities, they have regular circles of actions guided by their decisions but unexpected situations may interfere on their directions [START_REF] Hamermesh | Routine[END_REF]. A person may change their itinerary due to a traffic jam, problems on the public transportation, etc. When choosing an itinerary, people tend to use the shortest-path to reach their destination, also known as "desire line". The desire line is the shortest line between origin and destination, and expresses the way a person would like to go, if such a way were available [START_REF] Throgmorton | Desire lines: The chicago area transportation study and the paradox of self in post-war america[END_REF]. Furthermore, the people's itinerary is characterized by its confinement, i.e., despite of choosing the shortest-paths, people will roam close by their main physical address [START_REF] Brockmann | The scaling laws of human travel[END_REF].

Inspired by these observations, our hotspot deployment proposal considers people context described by how they move. For this, we consider a real dataset describing movements in a large metropolitan area of almost two hundred people and several transportation modes.

In general terms, we want to investigate the possibility of providing a better networking service for people based on their context: i.e., their trajectories and scenario interactions. Specifically, in the work herein proposed, we are going to instantiate such service as a data offloading architecture. Therefore, our main question is: how to provide a contextaware data offloading architecture based on the people's daily trajectories?

B. System model

Our system model represents a fairly real urban scenario composed of 182 people and their routes. Besides, we use data describing more than two hundred thousand real locations in a metropolitan area. Urban scenario: In this work, we are using GeoLife dataset on its latest version [START_REF] Zheng | Geolife: A collaborative social networking service among user, location and trajectory[END_REF]. GeoLife is considered to be unique in the literature. This is due to the fact that it provides a rich view of people mobility using 11 different transportation modes in an urban area for a long period of time. It provides geolocalized and timestamped points from 182 people during a 4 year span, from 2007 to 2011, mostly in Beijing. For each person, the dataset provides a set of geolocalized points ascendingly sorted by timestamp, i.e., a GPS trajectory. Trajectories: A trajectory represents how people moves around and is described as a set of points representing GPS coordinates periodically collected. In GeoLife dataset, people may move around building their trajectories using at most ten different transportation modes such as taxi, bike, run, bus, walk, train, subway, car, boat, and motorcycle. People and points of interest: People move, build their trajectories, and carry mobile devices capable of WiFi communication and able to receive GPS information. While walking by, people may "interact" with points of interest, e.g., bar, bus station, supermarket, etc. Those points of interest describe more than mere locations in the map but they reflect a social aspect: e.g., students are frequently going to meet their colleagues in a coffeehouse close to the university they attend to. Indeed, this represents a routinely behavior that involves not only people but also their interaction with points of interest in a city. In our scenario, points of interest are geolocalized physical venues, e.g., bank, cafe, school, stadium, train station, university, etc. Coverage: While moving around, a person passes by many points of interest and sometimes, may stop by. We consider that the interaction between a person and a point of interest lasts as long as the former is inside the interaction range of the latter. The interaction range is defined as the WiFi range on a urban scenario. Taking into account the interferences caused by buildings, vehicles, or any other obstacle, we consider a interaction range of 50 meters in our experiments: we consider that if a person is, at most, 50 meters from a point of interest they are able to wirelessly communicate and consequently, the latter covers the former. It is important to enhance that initially a point of interest is not compulsory considered as a hotspot but as potential place to receive a WiFi hotspot structure.

III. PROPOSAL

This section presents how mobility is mapped into a time dependent weighted graph and introduces our hotspot placement strategy.

A. Graph creation

Let S be a set of n points of interest S = {s 1 , s 2 . . . s n } uniquely identified by their geographical position: ∀s (x,y) ∈ S, where (x, y) is a pair of coordinates of a point of interest s. Since we are using real data traces containing GPS-based positioning, x and y are respectively, latitude and longitude. Fig. 1(b) illustrates a set of spots of interest presented as stars on map. Initially, we assign all points of interest with a hypothetical range illustrated as dashed circles 1 .

Our graph G(V, E) represents the interaction between people and the urban scenario. The graph should provide a simple and easy-to-see representation of people's mobility. While walking, people create trajectories and their interactions with the urban scenario may point out important places to start planning the deployment of a network infra-structure. Fig. 1(b) illustrates the three trajectories created by three hypothetical people (A, B, and C) and their respective interactions with points of interest. Let P i be a set of all geographic coordinates on the trajectory of a person i, i.e., P i = {p 1 , p 2 . . . p o }. A vertex v ∈ V is created on the same coordinates of the point of interest if the latter covers at least one person passing by. Note that a point of interest that does not respect this condition is not considered as vertex in the graph. A vertex coverage of a person i by point of interest s with a range r is expressed as ∀p ∈ P i , ∃ p | (p xs x ) 2 + (p ys y ) 2 ≤ r 2 , i.e., i is inside s's circular range. An edge e ∈ E is created between two vertices if their corresponding points of interest sequentially cover a person during its trajectory. Fig. 1(c) shows the graph when three people are covered by points of interest.

B. Hotspot placement strategy

A routine centrality metric herein proposed is calculated on the graph, based on two intuitions: Desire lines and confinement of people's mobility.

Desire lines and Stress Centrality:

In GeoLife dataset, people may move around building their trajectories using at most ten different transportation modes such as taxi, bike, run, bus, walk, train, subway, car, boat, and motorcycle. Therefore, to capture this urban behavior a trajectory is divided into legs. A leg is a subset of points from a trajectory with an unique transportation mode. The concept of "desire lines" states that people tend to choose the shortest-paths to arrive on their destinations. In order to verify that, we have compared the length of each traveled leg against the length of the corresponding shortest path considering the same initial and final points of the original leg. Dividing the length of the original leg by the length of the shortest path allows us measuring how longer the path made by a person is from the shortest path. We have used Google Directions API 2 to compute the shortest path. The API receives the coordinates of both initial and final points and a travel mode, i.e., transportation mode. Then, it returns the shortest path considering the restrictions imposed by the existing routes and obstacles in the city for a specific transportation mode. Note that, we only have considered transportation modes where people have decision control of their paths. This excludes for example, buses, boats or trains.

Legs traveled by walking, running, and biking had their lengths divided by their respective shortest paths computed while using the API in walking mode. Google Directions API indeed has a bicycling travel mode, but at the moment, it does not contain routes in Beijing. Legs traveled by taxi, car, and motorcycle had their lengths divided by results of the API in the driving mode. Fig. 2(a) shows the CDF of the ratio between the original legs length and the Google shortest path, by transportation mode. It is possible to see that regardless of the transportation mode 69% of the legs measure, at most, half longer than the shortest path. This result shows that the 1 Unit disk graph model. users in our scenario tend to choose the shortest paths when traveling.

Considering such feature, vertices are ranked with the stress centrality metric [START_REF] Shimbel | Structural parameters of communication networks[END_REF]. Vertices with high stress are those that lay on most of people's shortest routes and may become well positioned hotspots. Vertices with high stress values are likely to be places for hotspot deployment. Indeed, centrality metrics are widely used in the literature, but not yet explored in the problem we are considering. Confinement and Closeness Centrality: People mobility is generally periodic and confined. Even if people are not using the shortest routes, they are at least not going far from their home location. To check how that premise occurs on our scenario, we have measured how confined the trajectories are. People with confined mobility tend to repetitively visit the same areas. For this purpose, Beijing map was divided into cells of 50 square meters, in a grid shape. Then, we have calculated the number of unique cells (N U C) and total cells (N T C) that each trajectory visited. To quantitatively express the confinement of a trajectory, a metric called Repetitiveness was conceived and is represented as the following:

N T C-N UC N T C * 100
Repetitiveness represents how repetitive is the route described by a trajectory. Fig. 2(b) shows the results for repetitiveness for all trajectories grouped by period of the day. It is possible to see that regardless of the period of the day, trajectories present a considerable amount of repetitivity: 91% of the performed trajectories present at most 50% of the visited cells repeated.

On our proposal, we consider Closeness Centrality metric [START_REF] Sabidussi | The centrality index of a graph[END_REF] as a way to measure how likely a place will be to receive repeated visits. Closeness is calculated based on the geodesic distance between all pairs of vertices on the network. It assigns higher values for vertices closer to the rest of the network, that is, on a city those are probably hospitals, and markets, i.e., places planned to be close to most of the people's trajectories. Centralized computation: The centrality metrics are calculated on a offline centralized manner, i.e., the solution herein proposed may be applied on data previously collected by the interested entity, e.g., a Telecom operator. This premise is reasonable since network deployment planning generally uses historical data as input. The result is a set of points of interest ranked by how good they are in providing people coverage. From that point, the operator needs to decide how many hotspots they are willing to deploy and the trade-off between the monetary cost and the predicted amount of WiFi coverage. Spots ranking: To couple with all the above intuitions, we introduce Routine centrality (ρ), a centrality metric that aims to rank spots based on their potential to offload data:

ρ(v) = C s (v) + C c (v) where v ∈ V , C s is

IV. EXPERIMENTAL SETUP

This section describes technical details from two components of our experimental setup: trajectories and points of interest. General Information: All components are based on geolocalized information, i.e., latitude and longitude coordinates within a 1177 km2 central area in Beijing. Moreover, to better understand specific behaviors inherent from different periods of the day, every day is divided into four periods of 6 hours, from 00:00 to 05:59, from 06:00 to 11:59, from 12:00 to 17:59, and from 18:00 to 23:59. Trajectories: As previously mentioned, a trajectory is a set of geolocalized points describing a route traveled by a person using at least one transportation mode. In GeoLife dataset the average sample rate between each trajectory point falls between 5s and 10s. Furthermore, every point of a trajectory may contain extra information: transportation mode label that describes which transportation mode was used on that point of the trajectory.

Points of interest:

The proposed graph is built based on a set of points of interest in Beijing. Points of interest are places generally present in most of major cities, e.g., bars, universities, supermarkets, etc. In order to be able to points of interest in Beijing, databases of places (e.g., Google Places3 ) were used. Such databases are growing and are the most accurate source of public information about points of interest. To avoid to be biased by the characteristics of one unique database, we have collected data from multiple sources namely Google Places, Nokia Maps, and Foursquare, counting more than 202 thousand real unique points of interest with their respective IDs, latitudes and longitudes. While Google Places and Nokia Maps databases provide information about points of interest collected from city hall, owner of venues, etc, Foursquare provides only information from places where its users checked in, generally places related with leisure and social relationships. For each set of places collected from a source, repeated ones were removed by keeping an unique occurrence of each ID. The set of collected points of interest contains 77919 from Google Places, 119346 from Nokia Maps, and 5059 from Foursquare totalizing 202324 places distributed in 98 categories, e.g., market, library, school, etc.

V. PERFOMANCE EVALUATION

To better understand the results of our proposal, hereafter, we have first studied users' mobility characteristics and then assessed our main results.

A. Characterization

To understand how people explore the regions, central Beijing was divided into square-shaped cells of 50 m 2 summing up 181 thousand cells. First, we have analyzed the inter arrival time (IAT). The IAT of a cell A represents the time between visits of people on A and may show how frequently A is visited. Therefore, this metric also may point out how popular a cell is considering that small values of IAT indicates that a cell is frequently visited and it is likely to be a cell inside a popular area. On the other hand, high values of IAT indicates that a cell is not frequently visited and probably does not belongs to a popular area.

Fig. 3(a) shows a heatmap of cells' mean IATs in central Beijing, and by period of the day. It is important to enhance that cells showed in this figure are a subset of all visited cells: A cell must have been visited at minimum twice, i.e., at least one value of IAT was computed for it to appear in the heatmap (125 thousand cells). Regardless of the period of the day, two conclusions can be made from this figure. First, most of the cells have small IAT values: 85% of the cells present mean IAT less than 1 hour. Therefore, it shows a dynamic city in which lots of people are frequently passing by the cells. Second, a north central area consistently shows a high concentration of activity, which is due to the fact that Microsoft Research Asia headquarter is located there. GeoLife experiment was conduced mostly with Microsoft members that were constantly walking nearby the working place.

As expected, the late night period which comprises from 00:00 to 05:59 shows few activity. Periods from 06:00 to 11:59 and 12:00 to 17:59 show, as expected, the highest levels of activity. That is due to the fact that both comprise the most active hours of the day, i.e., people going from home to work and vice-versa, lunchtime, etc. On both periods, cells along roads that connect the central city with the periphery present high IAT values. It is due to the fact that those roads are used to bring people to the city and then, few hours later, take them back when going to home. This behavior is enhanced on the period from 18:00 to 23:59, a specific road on the north central area has almost 25 hours of IAT. That is due to a specific person that went to the city center one day and came back on the day after using the same road.

Fig. 3(b) shows a heatmap of the total time that people spent (TTS) on the cells by period of the day. Regardless of the period of the day, most of cells present low values of TTS, mainly cells along roads. Indeed, 95.8% of the cells present TTS value less or equal 3 minutes. As for IAT results, Fig. 3(b) confirms that the the mobility in Beijing is very dynamic, i.e., people are mostly passing by than staying still for long periods of time.

Although this dynamic behavior, people's mobility in Beijing presents high repetitiviness. Therefore, people will likely have a chance to be covered for longer periods if considering the aggregation of their several repeated short-period coverage.

B. Routine Centrality

We consider coverage time as the amount of time people were inside the range of a spot. To understand how covered people are while moving, we have measured the total amount of coverage time the hotspots provided. To assess hotspots effectiveness on providing coverage, we have computed the percentage of coverage time. For this, after hotspots are ranked by Routine Centrality, we deploy them accumulatively, e.g., best 1%, best 2% and verified what was the percentage of coverage time they provided: By dividing the total time people have been covered in their trajectories by the time they were uncovered.

Fig. 4(a) shows the percentage of coverage time as a function of the percentage of deployed hotspots according to the rank given by the Routine Centrality. Furthermore, this result is presented on four curves representing the periods of the day. Indeed, every period of the day has its own characteristics, e.g., late night presents less activity and people are concentrated in areas surrounding night clubs, bars, etc., while working hours are likely to have people scattered throughout the city. Periods from 00:00 to 05:59 and from 18:00 to 23:59 have less people and using low percentage of hotspots, 2% and 11% respectively, it was possible to cover about 75% of the time. Periods from 06:00 to 11:59 and from 12:00 to 17:59 present more activity and consequently require more efforts to guarantee high coverage rates. They require 34% and 20% of deployed hotspots to achieve 75% of coverage.

In order to measure how effective our routine-based network deployment approach, we have performed comparison with a simpler strategy that deploy hotspots select at random. Fig. 4(b) shows the percentage of coverage time as a function of percentage of deployed hotspots when selected uniformly at random. On contrary to our proposal, the random deployment provides poor coverage time for people in the city: For all periods, it was needed about 73% of hotspots to provide coverage of about 75%. Finally, our results show that a routine-based spot deployment can provide with lower costs a high percentage of coverage time compared to a random deployment. In addition, the coverage is dependent on the period of the day which make us think in a dynamic strategy. Indeed, in order to save energy certain hotspots could be turned off during some periods of the day in which they would provide low or no coverage. This makes possible a adaptative solution in which each period of the day would have only the best hotspots turned on.

VI. CONCLUSIONS AND NEXT STEPS

In this work, we have presented to the best of our knowledge, the first analyses of a metropolitan-wide hotspot deployment. We have proposed a graph model to represent the relationship between people and the city infra structure. Furthermore, based on common behaviors presented on people's real routines, we have proposed a centrality-based metric to rank points of interest in a city that are capable of providing network coverage. Our results show that with a small quantity of spots it is possible to provide high percentage of coverage time.

As future work, we intend to further investigate the mobility characteristics and aggregate a realistic traffic generation model. Therefore, we are going to be able to evaluate traffic offloading and verify the relation between coverage and the amount of offloaded data.

  Fig. 1. A general view of our proposed methodology.

Fig. 2 .

 2 Fig. 2. (a) CCDF of the length ratio. (b) Repetitiveness of trajectories by period of the day.

Fig. 3 .Fig. 4 .

 34 Fig. 3. (Better visualised in colors) (a) Heatmap of the inter arrival time on the cells. (b) Heatmap of the time spent inside cells. For better visualization, this picture shows only visits lasting at most 30 minutes, i.e., 99% the cells are depicted.

https://developers.google.com/maps/documentation/directions

https://developers.google.com/maps/documentation/places

This work was supported by the EU FP7 ERANET program under grant CHIST-ERA-2012 MACACO.


In the last decade, many paper focused on describing vehicular traffic stream of an arterial on an aggregate level. Unfortunately, among this considerable body of research, only few papers account for bus systems. Our paper tries to fill this gap by investigating two potential methods to estimate macroscopic fundamental diagrams of multimodal transport systems of a signalized arterial. The first approach models endogenously motion of bus by extending the work by the moving bottleneck theory, whereas the second approach proposes to incorporate exogenously effects of buses. The estimated macroscopic fundamental diagrams are then cross-compared to results provided by micro-simulation software that finely reproduce traffic stream. It turns out that mean speeds of vehicles and buses produced by the different methods are similar and consistent. Finally, results of the three methods are expressed in terms of levels of service and confronted with the levels of service of the HCM2010.

INTRODUCTION

Study of mixed traffic streams in cities and arterials is a topic of increasing concerns. A large body of works is dedicated to analyze explanatory variables that characterize dynamics of such networks [START_REF] Herman | A two-fluid approach to town traffic[END_REF][START_REF] Mahmassani | Investigation of Network-level traffic flow relationships: some simulation results[END_REF][START_REF] Geroliminis | Existence of urban-scale macroscopic fundamental diagrams: Some experimental findings[END_REF]. These papers aim to evaluate arterials and city networks performance by using traffic measurements. The largest part of this literature has been directed toward improving techniques to monitor traffic streams [START_REF] Skabardonis | Real-Time Estimation of Travel Times on Signalized Arterials[END_REF][START_REF] Zhang | Link-Journey-Speed Model for Arterial Traffic[END_REF], to measure travel times [START_REF] Liu | Time-Dependent Travel Time Estimation Mode for Signalized Arterial Network[END_REF] or to derived relationships between traffic flow and signal control settings [START_REF] Daganzo | An analytical approximation for the macroscopic fundamental diagram of urban traffic[END_REF]. However, evaluation remains a tedious task because of the complicated traffic behavior especially caused by (i) traffic signals and (ii) bus transit systems traversing arterials. Another approach for a better understanding of arterial traffic dynamics is to resort to accurate models. Indeed, aggregated and parsimonious models often provide valuable insights when analyzing and comparing different traffic situations and transit strategies. Various theories have been proposed to reproduce traffic stream on an aggregate level. Among this existing body of works, models that are adapted to characterize traffic in arterials have to account for (i) traffic signal and (ii) transit systems. Many of these papers are based on the key idea that it exists a macroscopic fundamental diagram (MFD) able to reproduce both free-flow and congested traffic conditions. Earlier studies were devoted to look for such relationship in data of real-world network or arterials. However, evidences of existence of MFD have been exhibited only very recently [START_REF] Geroliminis | Existence of urban-scale macroscopic fundamental diagrams: Some experimental findings[END_REF][START_REF] Daganzo | An analytical approximation for the macroscopic fundamental diagram of urban traffic[END_REF]. On their seminal works, the authors pointed out a major insight: the MFD is an intrinsic property of the network itself and remain invariant when demand changes. MFD is thus a reliable tool for traffic agency to manage and evaluate solutions for improving mobility. (8) furnished a very good example of how MFD can be used to dynamically control signals to prevent congestion. It is thus appealing to estimate an accurate MFD for various urban sites and traffic. In this sense, many papers have been recently directed toward highlighting links between shapes of the MFD and different simulated or measured parameters [START_REF] Buisson | Exploring the Impact of Homogeneity of Traffic Measurements on the Existence of Macroscopic Fundamental Diagrams[END_REF][START_REF] Ji | Investigating the Shape of the Macroscopic Fundamental Diagram Using Simulation Data[END_REF], exploring impact of distributions of vehicles and space on MFD [START_REF] Geroliminis | Properties of a well-defined macroscopic fundamental diagram for urban traffic[END_REF] or investigating bifurcation and instability issues of and MFD [START_REF] Daganzo | Macroscopic relations of urban traffic variables: Bifurcations, multivaluedness and instability[END_REF][START_REF] Gayah | Clockwise hysteresis loops in the Macroscopic Fundamental Diagram: An effect of network instability[END_REF]. Unfortunately, this large body of works does not account for multiple modes. [START_REF] Boyaci | Exploring the Effect of Variability of Urban Systems Characteristics in the Network Capacity[END_REF][START_REF] Boyaci | Estimation of the network capacity for multimodal urban systems[END_REF] have presented the only instance trying to overcome this drawback of representation to the author's knowledge. They introduced a methodology to estimate a MFD for an arterial with mixed-traffic bus-car lanes or with dedicated bus lanes. This work extends for multi-modal networks the Variational theory (VT) proposed in [START_REF] Daganzo | An analytical approximation for the macroscopic fundamental diagram of urban traffic[END_REF]. Impacts of bus stops are incorporated in the estimation method by considering these stops as point bottlenecks that locally reduce capacity. However, a bus has also a major influence on traffic when bus travels at a lower speed than the flow speed, i.e. when bus acts as an active moving bottleneck (MB). ( 16) also propose a MFD estimation method for heterogeneous hyperlinks, i.e. a series of successive links with different traffic signal. Based on the VT, this method directly provides the upper envelop of the MFD. However, the existing methods do not account for buses. Our paper tries to fill this gap by investigating two potential methods to model multimodal transport systems on a signalized arterial. The final goal is to provide an aggregated, parsimonious and effective model to reproduce and then evaluate traffic stream of a multimodal urban corridor. To this end, we resort to the MFD that needs to be accurately estimated by appropriate methods. These methods are build on past research in arterial modeling based on MFD representation as well as past research in accounting for buses in traffic flow as moving bottlenecks. Two different approaches are proposed: (i) to improve the method of ( 16) and (ii) to propose a new estimation process. So, the first method (M1) extends the work of ( 16) by introducing the effect of buses with a temporal and local reduction of the capacity of the arterial when a bus is present. This reduction will influence the shape of the estimated MFD. Consequently, buses are endogenously incorporated in the MFD estimation process. On the contrary, the second method (M2) will exogenously account for impacts of buses. Time-space diagrams of an urban arterial are analytically calculated based on the associated MFD estimated without buses [START_REF] Daganzo | An analytical approximation for the macroscopic fundamental diagram of urban traffic[END_REF]. Bus is considered as a MB [START_REF] Newell | A moving bottleneck[END_REF][START_REF] Leclercq | Moving Bottlenecks in Lighthill-Whitham-Richards Model: A Unified Theory[END_REF] that will modify the time-space diagrams. Then, traffic flow dynamics of arterials can be easily assessed through these diagrams. Finally, results of these two methods are cross-compared with results obtained with micro-simulation software (method M3). This is a convenient way to verify that the level of details of previous methods does not introduce bias in results. We use the software SymuVia that is a Lagrangian discretization of the kinematic wave model. Consequently, M3 is fully consistent with both previous methods. Their results will also be confronted with the multimodal Level of Services (LOS) provided in the HCM2010 [START_REF]Highway Capacity Manual[END_REF] because this corresponds to the current reference for practitioners.

Section 2 briefly specifies the study case. Section 3 presents details of the endogenous approach whereas Section

CASE STUDY

Consider here a hypothetic urban arterial (see Figure 1) composed of n successive links with traffic signal and p lanes. The length of link i is l i and its signal settings are: green g i , cycle c i and offset 𝜹 𝒊 from a common reference. The total length of the arterial is L. Traffic on each link is supposed to obey a triangular fundamental diagram (FD) that only depends on three observable parameters: free-flow speed u [m/s], wave speed w [m/s] and jam density 𝜿 [veh/m] (20-21). Capacity q C [veh/s] and optimum density k C [veh/m] can be easily derived: 𝒒 𝑪 = 𝒖𝒘𝜿/(𝒖 + 𝒘) and 𝒌 𝒄 = 𝒒 𝒙 /𝒖. Notice that all the links share the same FD for sake of simplicity.

Figure 1: study case

In the remaining of the paper, we assumed that the arterial is composed of 11 successive 3 lanes links (l i =200m). Concerning the traffic signal settings, g i is equal to 60s and c i to 90s. For sake of simplicity, we supposed that there is no offset. Finally, u is equal to 15 m/s, w is fixed to 5m/s and 𝜿 to 0.185veh/m (q C = 2.08 veh/s =7500 veh/h). We also assumed that buses travel along the arterial with a lower average speed to mimic existence of bus stops: u b =8 m/s. Consequently, bus stops are not explicitly model in this paper.

ENDOGENOUS APPROACH

The aim of this section is to propose a first method that endogenously estimates MFDs and accounts for traffic signal settings and buses represented as a moving obstruction. This method extends previous works from [START_REF] Leclercq | Estimating MFDs in Simple Networks with Route Choice[END_REF] that defines an accurate estimation method founded on VT for arterials with heterogeneous traffic signal parameters. The extension deals with introducing the impacts of moving bottlenecks into the proposed framework. The detailed presentation of the variational method proposed by [START_REF] Leclercq | Estimating MFDs in Simple Networks with Route Choice[END_REF] is out of the scope of this paper, only the key elements will be recap below. Note that VT was described in Daganzo's seminal papers [START_REF] Daganzo | A variational formulation of kinematic waves: basic theory and complex boundary conditions[END_REF][START_REF] Daganzo | A variational formulation of kinematic waves: Solution methods[END_REF].

The foundation of the variational method comes from [START_REF] Daganzo | An analytical approximation for the macroscopic fundamental diagram of urban traffic[END_REF]. This paper shows that a MFD can be defined by a set of cuts {C j }. A cut corresponds to a line in the (k,q) plane parameterized by its y-intercept r j and its slope v j , i.e. q=r j +kv j . Cuts are associated to moving observers that moves into the considered arterial with a constant speed v j . Such observers have no dimension and are not influenced by traffic signals. r j corresponds to the maximal passing rate that such an observer can encounter depending on the FD and the signal settings. In practice, to piecewise-linearly estimate a MFD one only have to define a set of discrete values {v j } and determine the associate r j values. [START_REF] Daganzo | An analytical approximation for the macroscopic fundamental diagram of urban traffic[END_REF] propose to only focus on practical cuts to estimate r j . Practical cuts correspond to specific paths of the moving observer that can only experiment speeds u and 0 when mean speed v j is positive or w and 0 when mean speed v j is negative. These paths are constructed in practice by assigning a speed u (or w) to observers when moving into a link and then delaying them at green signals with different constant values ε j . The mean speed v j is then calculated afterwards and only depends on ε j . This method has been applied in [START_REF] Boyaci | Exploring the Effect of Variability of Urban Systems Characteristics in the Network Capacity[END_REF][START_REF] Boyaci | Estimation of the network capacity for multimodal urban systems[END_REF] but suffers from a limitation that is not compatible with further introducing buses. Indeed, in unregular cases (heterogeneous signal timings or presence of moving obstructions), this method only provides an upper bound for r j . Thus, cuts do not necessarily tightly define the MFD. (16) blows up with this limitation by generalizing the concept of practical cuts. Instead of focusing on particular paths into the arterials, they define a sufficient but minimal variational graph that encompasses the practical cut paths but also all the other optimal paths associated to a mean speed v j in order to properly estimate r j even in heterogeneous cases. To be precise, two variational graphs have to be constructed to deal with free-flow (v j ≥0) and congested cuts (v j <0). We will only present how to define the free-flow graph (the congested graph can be obtained by replacing u by w and considering the arterials in the reserve direction). This graph is composed of three kinds of edges, see Figure 2a: a. the red phases of all traffic signals; b. the green phases of all traffic signals; c. the paths with speed u that start from the ends of all red times of each signal and propagate until another edge (a). Vertices should be added anytime such a path crosses edges (b) and (a).

The proof of sufficiency can be found in [START_REF] Leclercq | Estimating MFDs in Simple Networks with Route Choice[END_REF]. Cuts j are defined by all the paths into the variational graph that have the same initial and final points, i.e. the same speed v j . The associated r j corresponds to the least-cost between these initial and final points. Note that cost rate associated to edges (a) (b) and (c) are respectively 0, q c and 0 (costs associated to edges (c) in the congested graph are wκ). Note also that in regular cases (identical traffic signal settings, constant offset and no buses) only one initial point has to be considered because the network is periodic. In unregular cases, r j values have first to be calculated for different origin points and then averaged for all origin points to properly define cut C j .

Figure 2: Variational method to endogenously estimate the MFD (a) without buses (b) with buses

The above variational method can be easily extended to account for buses. Indeed, [START_REF] Newell | A moving bottleneck[END_REF] and further other authors see [START_REF] Leclercq | Moving Bottlenecks in Lighthill-Whitham-Richards Model: A Unified Theory[END_REF] for a review, shows that the impacts of such vehicles on the global traffic stream can be represented as a moving bottleneck that locally reduces the available capacity. Note that such a bottleneck is said to be active when it really has an influence on the surrounding traffic. [START_REF] Daganzo | On the numerical treatment of moving bottlenecks[END_REF][START_REF] Daganzo | Moving bottlenecks: A numerical method that converges in flows[END_REF] have shown that such a moving bottleneck can also be approximated by a succession of fixed bottlenecks that follows the bus trajectory with a bounded error.

This key result provides a simple way to extend a variational method. Indeed, we can consider that a bus inside a link reduces the available capacity from one lane until it leaves the links. This defines into the arterial time-link regions where the capacity is reduced, see gray shape around the bus trajectory in Figure 2b. This capacity reduction can be taken into account by modifying the costs of the edges that cross such regions. In practice, only cost rates on edge (b) have to be modified and switched to (p-1)/p.q c where p is the number of lanes. Note that introducing buses makes the studied case unregular (bus are introduced according to a given frequency). Thus, several initial points have to be considered. To be sure that the mean value of r j is properly estimated, i.e. that we consider enough initial points, we check that the standard deviation of r j is lower than 10% of its mean value.

Figure 3a presents the resulting free-flow and congested cuts calculated for an arterial and a bus system headway of 3 min. Note that none of the two variational graphs provide the stationary cut corresponding to the minimum capacity observed at the most constraining traffic signals. This cut can easily be added. Red lines in Figure 3a show the only relevant cuts that fully define the MFD. Figure 3b depicts the estimated MFDs for various values of bus time-headway h. It clearly shows that the presence of bus transit systems on the arterials reduces the maximal capacity. Moreover, it is not surprising that the maximal capacity decreases with the increase of h. Figure 3b also reveal that bus has a major effect on the MFD shape in the vicinity of the top of the MFD. Hence, bus is an active MB in this domain of traffic conditions.

EXOGENOUS APPROACH

On the contrary of the previous model, method M2 endogenously encompasses effects of buses. To this end, time-space diagrams are calculated based on the MFD estimated without the presence of buses. This MFD can easily be calculated according to findings of [START_REF] Daganzo | An analytical approximation for the macroscopic fundamental diagram of urban traffic[END_REF] or through the process introduced by method M1. This MFD is displayed in Figure 4. Notice that we use a MFD that is bi-linear in both free-flow and congested situations, for sake of simplicity. However, method M2 can be applied to any piece-wise linear MFD. Figure 4 displays the equilibrium states of traffic flow on arterial that turn out to be of interest throughout the paper. For any equilibrium traffic state A (point of the MFD), the flow and the density are respectively denoted q A and k A . State F corresponds to the limit between maximal free-flow speed u and free-flow speed u f ; C 1 is the full arterial capacity; C 2 corresponds to the change of congested wave speed ; J is the full arterial jam density.

The buses can now be modeled as ordinary MB that traverses arterial at speed u b . Notice that u b is lower than u and u f to incorporate the dwell time du to bus stops. As in [START_REF] Daganzo | A variational formulation of kinematic waves: Bottleneck properties and examples[END_REF], buses are treated as point bottlenecks. When the MB is active, it generates different traffic conditions upstream and downstream of the bus trajectory. The associated equilibrium states are depicted in Figure 4. State D corresponds to the downstream traffic conditions, which is in free-flow situation. The associated flow is assumed to be equal to the capacity of the reduced system (minus one lane) including the effect of signals:

𝒒 𝑫 = 𝒒 𝑪 .
𝒑!𝟏 𝒑 [START_REF] Newell | A moving bottleneck[END_REF][START_REF] Eichler | Bus lanes with intermittent priority: Strategy formulae and an evaluation[END_REF][START_REF] Gazis | The moving and "phantom" bottlenecks[END_REF]. State U describes the upstream condition, which is in congested situation. The associated flow can be completely determined based on the state D and the speed of the MB u b (see Figure 4). According to KWT, interface between states U and D travels at speed u b along the arterial. It is worth noticing that the MB is active for a given traffic state A when passing rate associated to state A is higher the passing rate of state D, i.e. Time-space diagrams can now be calculated. The associated patterns depend on the input flow and the exiting rate of the arterial. Indeed, various levels of the entry demand and the exit bottleneck are tested to mimic all the traffic conditions described by the MFD. Situations can be classified based on three criterions: traffic state conditions, active/inactive MB and propagation of the upstream shockwave generated by the entry of the bus in the arterial. Based on these levels, one can identified five cases that are sum-up in Figure 4. a. case 1: free-flow (FF) state, bus is an inactive MB (r A <r D ), no upstream shockwave; b. case 2: FF state, bus is an active MB (r A >r D ), upstream shockwave moves forward (q A <q U ); c. case 3: FF state, bus is an active MB (r A >r D ), upstream shockwave moves backward (q A >q U ); d. case 4: congested (C) state, bus is an active MB (r A >r D ), upstream shockwave moves backward e. case 5: C state, bus is an inactive MB (r A <r D ), upstream shockwave moves backward.

For each of these cases, many subcases can also be identified based on the bus headway value h. We will only detail the obtained patterns for case 2 and let the reader verify for the remaining cases. Indeed, case 2 is the more generic and easiest situation to explain the framework of our method.

In case 2, the demand inflow q A is comprised between q D and q U and the exiting rate is equal to the maximum capacity C 1 . Because q A >q D , when the bus enters in the arterial, it becomes an active MB and generates state D downstream and state U upstream. Both states are separated by a wave travelling downstream at speed u b . Once the bus has left the arterial, state C 1 is created and propagates upstream at speed w. Figure 5a displays the resulting pattern. This pattern remains valid if the next bus enters in the arterial a time h later when the congestion generated by the first bus has totally been vanished. In that case, the same pattern is observed for all the buses (see Figure 5a, case 2i). Otherwise, state D generated by the entry of the next bus reaches existing state U. It modifies the patterns as depicted by Figure 5b (case 2ii). It is worth noticing that the patterns are periodic after the passage of the second bus (hatched areas in Figure 5). Consequently, it is sufficient to focus on only one pair of buses once the stationary situation has been reached.

Figure 5: Time-space diagram for case 2i (large bus headways) and case 2ii (small bus headways)

We let the reader verify that this work can be easily extended for the other cases. Figure 6 shows the results of the remaining cases. It is important to notice that these time-space diagrams are analytically calculated, i.e. coordinates of every states area are known. Moreover, the patterns are always periodic, which also make the evaluation of the method easier. Consequently, we can calculate the average (in the sense of Edie's definition) flow Q and density K for each pattern and then estimate the MFD. Details of the calculation of Q and K are presented in the final section.

MICRO-SIMULATION

The third method (method M3) proposed in this paper is based on microscopic simulation software. This allows controlling every aspect of the simulated environment and gives also access to vehicles trajectories. The simulation set-up is close as possible to characteristics of the arterial used for both previous methods. The used software, called SymuVia, is based on a Lagrangian discretization of the KWT. Details of the resulting carfollowing law can be found in [START_REF] Newell | A simplified car-following theory: a lower order model[END_REF][START_REF] Leclercq | The lagrangian coordinates and what it means for first order traffic flow models[END_REF]. This car-following law relies on the existence of a triangular FD. We used the same traffic parameters, u f , w, and 𝜿 as in previous methods. Moreover, the model has been refined to take into account bounded acceleration, lane-changing phenomenon and relaxation after lane-changing phenomenon [START_REF] Leclercq | The lagrangian coordinates and what it means for first order traffic flow models[END_REF][START_REF] Laval | Microscopic modeling of the relaxation phenomenon using a macroscopic lane-changing model[END_REF]. Thus, the simulation software is able to accurately reproduce the impacts of the MB on the remaining of the traffic in the arterial.

MFD can now be estimated with the simulated results. We used the trajectories-based approach proposed by [START_REF] Courbon | Cross-comparison of macroscopic fundamental diagram estimation methods[END_REF]. The authors resort to Edie's definitions [START_REF] Edie | Discussion of traffic stream measurements and definitions[END_REF] to calculate flow and density. (34) computes density k and flow q based on the observation of vehicles across a space-time window A:

𝑘 = ! ! ! ! (2) 𝑞 = ! ! ! ! (3)
where l j and t j are respectively the length traveled and the time spent in the area by vehicle j and 𝑨 the area of A. It turns out that such measurements perfectly match MFD definition [START_REF] Edie | Discussion of traffic stream measurements and definitions[END_REF]. In the case of a single pipe, the estimated measurements perfectly match the theoretical MFD. Thus, simulations can be performed for any value of demand. We also add an exit bottleneck to generate congested states. Thereby, the congested part of the MFD will also be appraised.

Time-space diagrams similar to the diagrams of method M2 are obtained. Impacts of the MB are clearly highlighted. It generates lane-changing phenomenon upstream of the MB and reduces the capacity downstream. Figure 8 shows MFDs obtained for various values of bus headway h.

CROSS-COMPARISON

The three methods we proposed aim to reproduce the effects of buses on arterial traffic dynamics. A bus may create a local and temporal capacity reduction, which leads to an increase of travel-time. This increase clearly depends on the demand level qa but also on the bus headway h. It is thus appealing to study the evolution of vehicles and bus mean speed with respect to qa but also to h. Results of the methods are cross-compared based on this indicator but also with LOS of the HCM 2010, which provided a frame of reference.

Calculation of mean speed values

Consistent mean speeds of vehicles and buses have to be calculated to cross-compare the three methods. To this end, we will use instantaneous travel-times. Indeed, formulations that are fully consistent between the three approaches can be found. The centerpiece of these formulations is the definitions of density and flow proposed by (35). Method M1: This is the simplest case. It does not require any extra calculation. Mean speeds of the vehicles 𝑽 𝟏 𝒗𝒆𝒉 are directly derived from estimated MFD and from the fundamental relationship q=k.v. Thus, it turns out that 𝑽 𝟏 𝒗𝒆𝒉 is equal to k/q. Mean speeds of the buses 𝑽 𝟏 𝒃𝒖𝒔 can be calculated in the same way except that 𝑽 𝟏 𝒃𝒖𝒔 cannot exceed the maximal speed of the buses u bus . Figure 9a displays the mean speed values for the range of possible traffic conditions. It is interesting to notice that, in congestion, speed of the buses is not reduced until the speed of the equilibrium state is lower than u bus . It means that even if q is lower that q U , i.e. the MB is not active, the buses are not impacted by the traffic congestion. Method M2: Calculating mean speeds is a more tedious in that case. Edie's definitions have to be adapted to this particular case. It is worth noticing that periodic patterns can be identified for each case (hashed areas in Figure 5 and Figure 6). These patterns are composed of different areas A i where traffic is in equilibrium state. Coordinates of these areas are analytically known such as values of flow and density. It is thus appealing to calculate averaged density K and flow Q based on these patterns. Then, K and Q are calculated as

𝐾 = ! !! . ! ! ! ! ! (4) 𝑄 = ! !! . ! ! ! ! ! (5)
Where A i are the different equilibrium space-time area, k i and q i the respective density and flow. This leads to the averaged speed 𝑽 𝟐 𝒗𝒆𝒉 =Q/K. As previously explained, mean speeds of the buses 𝑽 𝟐 𝒃𝒖𝒔 can be calculated in the same way except that 𝑽 𝟐 𝒃𝒖𝒔 cannot exceed the maximal speed of the buses u bus . Of course, these results depend on the bus headway, the entry demand and the exit rate. Figure 9b depicts the mean speeds of vehicles and buses for the range of possible traffic conditions.

Method M3:

Results provided by method M3 make possible to calculate directly k and q as in Edie's original definitions. As previously explained, trajectories of vehicles are available. Consequently, l j and t j can be easily for h=6 min computed. The main difficulty for method M3 is to use a space-time window consistent with the previous approaches. However, this window cannot exactly match the analytical areas calculated by method M2 otherwise methods M2 and M3 will be redundant. Consequently, we decided to use, in addition to an arterial warm-up time, a very long space-time window (more than ten times the bus headway h). Figure 9c highlights the mean speeds 𝑽 𝟑 𝒗𝒆𝒉 and 𝑽 𝟑 𝒃𝒖𝒔 for the same range of traffic conditions than methods M1 and M2.

Results of the three approaches can now be cross-compared. Figure 10a-d sums up the mean speed values for each method. At a first glance, it is worth noticing that results are close from each other. However, it turns out that differences exist. Indeed, the effects of the MB are observed for different ranges of flow values depending on the used method. Maximal observed capacities are consistent within the different methods with slight differences. Each method includes different modeling Notably, impacts of traffic signals and moving obstructions are noncorrelated with M2, while being correlated with M1 and M3. This surely explains why maximal capacity is bigger when applying M2 because worth cases with high correlations are not reproduced. Higher capacities of method M2 are also due to the fact that the trajectory of the MB is discretized in the framework of method M1. This discretization induces an extra delay in the vehicle travel time calculation according to [START_REF] Daganzo | On the numerical treatment of moving bottlenecks[END_REF][START_REF] Daganzo | Moving bottlenecks: A numerical method that converges in flows[END_REF].

Furthermore, MB can be inactive in method M2 whereas the MB can be active in some part of the arterial in method M1. It explains why the ranges of MB activity differ from one method to another. This also leads to the fact that method M2 underestimates the effects of the bus and provides higher capacities.

One can also see that method M3 furnishes mean speed values lower than the two analytical methods. Lanechanging maneuvers caused by the MB increase the vehicle travel time. Consequently, it also reduces the capacity and explains results of Figure 10a-d. Figure 10e depicts the relative results provided by the three methods from the reference scenario corresponding to the same arterial with no bus. We have calculated the total difference in flow for the whole range of traffic conditions. This aggregated indicator reveals that methods can always be classified in the same order. Method M1 is the most sensitive to the presence of bus whereas method M2 seems to under-estimate impacts of bus. This discrepancy confirms the observations mentioned above. Results of method M3 stands between estimations of both previous methods. Finally, it is worth noticing that estimations tend to converge to the MFD estimated without bus when the headway increases. The results are now confronted to the LOS proposed by the HCM 2010 [START_REF]Highway Capacity Manual[END_REF]. We only focused on the automobile LOS because transit LOS are not consistent with our approach. Indeed, this methodology is applicable for bus system that stops along the arterials and boards passengers. This is not the case in our paper. Then, the automobile LOS measures are computed based on the methodology proposed for urban street segments. Details can be found in [START_REF]Highway Capacity Manual[END_REF].

Speed-flow relationship is calculated for our study case (see Figure 11a). The point is that LOS of the HCM underestimated effects of the traffic signal on the running speed of the vehicles. It is not surprising because correlation between successive traffic signal is not accounted for in this methodology. The second drawback is that the HCM does not provided running speed values for congested situations and especially when spillbacks occur. Our methods clearly fill this gap that is of great importance for city managers.

Then, the HCM running speed thresholds for urban street segments are used to convert mean speed estimated for methods M1 and M2 into LOS letter grades. Figure 11b clearly shows that the grade A is never obtained. Grade D and E corresponds to transient situations. Ranges of mean flow are very small compare to ranges of grade B, C and F. Notice that Figure 11b displays only results of method M1. Similar results are obtained for method M2.

CONCLUSION

By extending past research on MFD estimation methods, this paper shows the potential for using MFD to analytically evaluate performance of an arterial. To this end, we first refine the work of (16) to account for buses in traffic. This method is based on the VT and consists in defining a suitable graph. It provides all the necessary cuts that defined the upper envelop of the MFD. The second approach relies on the analytical study of time-space diagrams. According to Edie's definitions, it has been shown that it is possible to estimate MFDs that account for buses based on the KW theory and the MFD calculated without presence of buses. Finally, we directly estimate MFDs from vehicle trajectories provided by micro-simulation software that is fully consistent with both previous methods.

Then, these three methods have been cross-compared based on estimated mean speed values. The methods furnish average running speed of vehicles and buses for range of all possible traffic conditions (both free-flow and congested situations). It turns out that discrepancy exist in results. Method M1 is the most sensitive to the presence of buses, method M2 always under-estimates impacts of buses whereas results of method M3 falls between estimations of both previous method. These observed differences are easily understandable by the fact that discordances exist between the modeling processes: MB discretization, aggregation of impacts of traffic signal, lane-changing phenomenon, etc. Readers and practitioners can then choose between a detailed and complex method (M1), an analytical method (M2) or micro simulation (M3) to evaluate performance of an arterial. However, M1 presents the best trade-off and turns to be the more appropriate method to estimate accurate MFD.

Finally, methods are compared with the LOS of the HCM 2010. These results are promising, especially in the light of the fact that methods fill the drawbacks of the LOS: congested situations are also appraised. Furthermore, running speed of vehicles estimated by method M1 and M2 are more realistic because effects of successive traffic signal are accounted for. These methods significantly improved the understanding and the evaluation of traffic dynamics of an arterial. One of the next extensions of the methods presented in this paper will be a more realistic modeling of bus systems. Although impacts of buses on traffic are already accounted for, ongoing work is investigating how to incorporate dynamics of motion laws of the bus systems (boarding and alighting of passengers at bus stops). These results can be of great importance to practitioner to manage arterials and bus systems.

  MeetingPaper revised from original submittal.

Figure 3 :

 3 Figure 3: Estimated MFD with method M1: (a) whole sets of cuts for a given headway (h=3min) (b) estimated MFDs for different headways

  r A =q A -u b .k A > r D =q D -u b .k D . Meeting Paper revised from original submittal.

Figure 4 :

 4 Figure 4: MFD of the arterial without bus

Figure 6 :Figure 7 displays

 67 Figure 6: Time-space diagrams for the remaining cases Figure 7 displays MFDs estimated with method M2 for different values of bus headway. The results are not surprising because high headways decrease the capacity of the arterial. For example, the maximal capacity is reduced of more than 8%.

Figure 7 :

 7 Figure 7: MFD estimated with method M2 for different bus headways

Figure 8 :

 8 Figure 8: MFD estimated from simulated trajectories (Method M3)

Figure 9 :

 9 Figure 9: mean speed of (a) method M1 (b) method M2 and (c) method M3

Figure 10 :

 10 Figure 10: Comparison of mean speed obtained with the different methods (a) h=3min (b) h=6min (c) h=12min (d) h=30min (e) Difference in flow.density with a no bus situation Level Of Services (LOS)

Figure 11 :

 11 Figure 11: (a) Comparison of the three methods with HCM 2010 (b) LOS obtained with method M1 for the different headway values

is focused on the exogenous method. Then, Section

is devoted to the micro-simulation of the urban corridor. Finally, Section

proposes to cross-compare the results of the different estimation methods with the multimodal LOS provided in the HCM2010.

ACKNOWLEDGEMENTS

This research was partly founded by the "Région Rhône-Alpes" and supported by the ADViCe project (11-MT-PREDITG02-2-CVS-050).