EFFECTS OF BYPASS IN SMALL AND NON-CONGESTED CITIES : A CASE STUDY OF THE CITY OF BADAJOZ

Small cities with less than 200,000 inhabitants do not usually suffer from chronic congestion problems. However, private vehicles are used excessively, making it necessary to implement measures to encourage further use of public transport and pedestrian mobility to make it more sustainable. Bypasses improve level of service (LOS) by removing cars from the city center, leading to significant reductions in overall travel time. Most studies so far have been conducted in large cities suffering chronic congestion problems, so the aim of this research is to analyze the effects of bypasses in small and non-congested cities through the construction of a traffic model in Badajoz (Spain), starting with the allocation of the origin-destination travel matrix derived from surveys and traffic counts conducted at the southern and eastern accesses. The traffic model describes the mobility in potentially-capturable future southern traffic relationships and allows insights into different alternatives in the construction of a new high LOS road. This research concludes that small cities with no chronic congestion problems should plan bypasses as close as possible to the city, since they are the most economical, produce greater traffic capture, greater time savings, and eliminate the largest number of CO2 emissions from the urban center. The more distant alternatives have a higher LOS, however, these are longer and more expensive solutions that also capture less traffic and thus eliminate less CO2 emissions.


INTRODUCTION
Greenhouse gas (GHG) emissions and overconsumption of energy resources represent a global problem, which is related both to their causes and consequences [1].
The transportation sector is one of the largest emitters of GHG [2] despite advances in the field of engine technology. This sector accounted for 26% of global energy consumption in 2010, and transportation energy use is expected to increase by 1.1% every year until 2040 [3].
Small cities with less than 200,000 inhabitants do not usually suffer from chronic congestion problems. However, private vehicles are used excessively, making it necessary to implement measures to encourage further use of public transport and pedestrian mobility for greater sustainability. Bypasses improve LOS by removing cars from the city center, leading to significant reductions in overall travel time [4].
Evaluation of bypass influence on reducing air pollution has been carried out in numerous studies [5][6][7]. However, such studies are always carried out for large cities with congestion problems. It is therefore necessary to investigate whether such actions are also valid for smaller cities and to learn how to improve mobility and reduce emissions in urban centers [8,9].
The city of Badajoz currently has a population of approximately 150,000 inhabitants. It is the main urban center in Extremadura, and it has the characteristics of any European average city. Moreover, its geographical location makes it even more privileged for being a border city and the barycenter of three huge European cities: Lisbon, Madrid, and Seville. [10] The road network of Badajoz has a radial infrastructure composed by an ensemble of roads which leave the city and whose axes serve as support for its own growth. The main road (BA-20) passing through Badajoz registers about 132,000 trips daily. Here arises the need for building a new southern bypass, which would allow cars coming from other towns to link with the motorway Madrid-Badajoz and the rest of the communication roads without entering the city center of Badajoz. The so-called Southern Bypass (Ronda Sur) will become an authentic variant of roads which will receive the status of fast track and, together with the motorway of Extremadura, will surround the whole city center of Badajoz [11].
Between 2010 and 2014 an informative study about the Southern Bypass in Badajoz was written, detailing its possible corridors and planning alternatives of the future variant [12] (Figure 1). Alternative 1 is approximately 22 kilometers long. This alternative is the shortest and the closest to the city. It is also the one that was contemplated in the urban planning of Badajoz. Alternative 2 is approximately 30 kilometers long. It runs behind most of the secondary cores making the new route only pick up long distance traffic that does not need to cross the city. Alternative 3 has is approximately 36 kilometers long. It picks up some secondary cores that do not reach alternative 2, and it is outside the protected areas of oak forest that are occupied by this alternative.
On October 6, 2014, the Government of Extremadura approved the informative study [13] selecting the alternative 1. The three alternatives provide a solution to the problems of mobility and pollution existing in the urban center. The selected alternative is the most economical, since it is shorter; however, it is unknown if it is the alternative that captures more traffic and if it is the one that obtains greater savings in terms of travel times and CO 2 emissions.
The aim of this research is to analyze the effects of bypasses in small and non-congested cities by developing a traffic model for the city of Badajoz which provides insight into different alternatives' behavior in the construction of a new high LOS road. The model is able to select the one which captures more traffic and produces bigger savings in travel time and CO 2 emissions, meaning the one which produces better socioeconomic improvement.

METHODOLOGY
Traffic study for the planning of new urban roads is an especially significant chapter, not only because it is necessary to know the number of vehicles that will circulate in each of the planned alternatives, but also as indispensable data to estimate their social and economic profitability [14]. It is very important to have the simulation model and allocation from the very beginning of the planning to have knowledge of the traffic that each of the corridors will capture, creating an extremely valuable auxiliary element for the selection process.
The construction of a traffic model in Badajoz will be done by assigning an origin-destination travel matrix derived from surveys and counts done at the southern and eastern accesses of Badajoz [15,16]. The traffic model describes the mobility in potentially capturable relationships for a future southern bypass and allows the calculation of savings in traveled distance and travel times in relation to the current situation [17].
Activities done in the construction of the traffic model of the city of Badajoz are enumerated below: 1) Traffic characterization of the Southern Bypass of Badajoz starting from the data from the traffic maps of the Ministry of Development and Government of Extremadura [18,19]. in the city center of Badajoz. As a complement, information about network usage was collected through counts with the aim of learning how supply works, and giving information for the utilization of the surveys. A total of 3,759 origin-destination surveys took place at the southern accesses of Badajoz which currently channel the potentially-capturable traffic for the future Southern Bypass.

Selection of locations for surveys and counts
Places with traffic lights were selected so that the survey could take place while every vehicle was stopped. After obtaining a view of the study area, five survey points were selected ( Figure 2  2) Collection and analysis of the information on mobility and traffic at the accesses to Badajoz from south and east, through surveys and counts. 3) Estimation of the average daily traffic (ADT) in specific count locations. 4) Utilization of the surveys carried out and collection of results. 5) Estimation of the origin-destination matrix in the studied area from the surveys done. 6) Creation of the traffic model of Badajoz and its road network. 7) Estimation of the traffic captured by each alternative selected for the Southern Bypass of Badajoz. This estimation derives from the assigning of the traveling matrix to each network, including the alternative which is the object of the evaluation. 8) Estimation of the traffic collected (vehicles-km) and travel time savings (vehicles-hour) for each selected alternative. 9) Estimation of CO 2 emissions saved from the urban center.

Collecting of information about mobility and traffic
Collection of information about transportation demand aims to determine how people move within the study area, in order to estimate mobility. The basic data collected for each trip will in this case be the means of transport, the origin of the trip, and its destination.
[21] recommend generating traffic models from surveys and counts in situ because they are not highly expensive and constitute the most truthful starting point there can be. Therefore, the basic form of collecting data has been through origin-destination surveys done BA -20

Utilization of the surveys
The basic aim of the surveys was to obtain the expressive mobility matrix of the transport demand between each pair of zones considered. In survey utilization, three basic activities can be pointed out:

Counts
Simultaneously with the surveys, a 16-hour vehicle count (from 6:00 to 22:00) of the surveyed traffic was carried out. The results of the vehicle count are shown in Table 1.

Traffic model in the road network of Badajoz
Network assigning models simulate the behavior of a transportation network through the collecting of the traffic loads derived from the travel matrix. This matrix represents the mobility in the study area for a determined year. The traffic which the Southern Bypass will capture is obtained by assigning the 2014 travel matrix to the defined road network, including the 3 bypass alternatives for the future situation.
To be able to make a model of the network, a drawing which guaranteed all the possible coherent itineraries between each pair of centroids (representation of the origin and destination network of a journey) was made [26]. The road network of the study area for 2014 was modeled defining the following parameters for each route: origin knot, destination knot, distance between knots, type of arc, average travel distances, and circulation directions. Cascetta and Ruso [27], and later Russo and Vitetta [28] and Shrewsbury [29], expressed the necessity of adjusting the network (calibration) by checking that the itineraries which allow establishing the modeled network correspond with the reality. This calibration is made calculating the minimum-cost paths (time and distance) from a group of selected centroids and checking them against the real ones used by the users in 2014.
Once it was modeled for the year 2014, the future model was made with the commissioning of the Southern Bypass. It was necessary to include the new arcs which describe each of its 3 alternatives. In Figure 4 there is a representation of the road network in 2014, and in Figure 5 there is a representation of the future network with the commissioning of the Southern Bypass.

Traffic captured by Southern Bypass alternatives
The traffic captured by each of the Southern Bypass alternatives was estimated by assigning the origin-destination travel matrix to the future route network which -Coding of surveys. It consists on translating numeric data and collected information in the survey, the origin-destination coding being of particular interest because it supports the division of the studied area into zones and the defined area codes [23,24]. -Calculation of the expansion coefficients. It is about establishing the necessary conversion coefficient to extrapolate the results of the surveys from a part of the vehicles and users (sample) to the total of vehicles and users (universe). -Collecting of the origin-destination matrix. After coding the surveys, the result is the origin-destination travel matrix which expresses the mobility flow of vehicles classified by type of vehicle and it refers to the universe of vehicles passing through the positions of the survey.

Calculation of the expansion coefficient
Expansion coefficient represents the converting coefficient from the surveyed users (sample) to the total of users (universe) [25]. This expansion coefficient has been calculated for each position of the survey and hour period through the following Equation 1.

Construction of the origin-destination travel matrix in the study area for 2014
The origin-destination travel matrix was obtained through the following process: 1) Travel matrix expansion from the surveys to 2014 ADT estimated. Expansion coefficients described previously were used.  dispersion parameter. Measuring the model from the known values through the surveys and counts, the value of ʎ=0.10 has been adjusted. C 1 -C 2 =0 indicates that the utility of both options is the same, and the election probability of option 1 is 0.5, which corresponds to the situation of indifference against option 2. When the difference C 1 -C 2 acquires increasing positive values, the utility of option 1 increases even more compared to the growth of option 2, and the probability of choosing option 1 tends to unity. When the difference C 1 -C 2 acquires negative values indicating option 2 has better utility than number 1, the probability of choosing option 1 decreases, getting close to zero. The results of these estimations are presented for each of the Badajoz Southern Bypass alternatives in Table 2.

Traffic collected and travel time saving
During the process of assigning, the numbers of vehicles per kilometer (traffic) and vehicles per hour (travel time) used for the movements through the three Southern Bypass alternatives included in the travel matrix were obtained as complementary information. The difference in traffic captured and time saving is obtained when comparing the parameters of each alternative with those from the network in 2014.
It is important to highlight that the socio-economically most feasible alternative will be the one which obtains the highest number of vehicles-km and the least vehicles-hour, since it will be the one that captures more traffic and produces greater time savings. The results are presented in Table 3.
Alternative 1 is the one that collects the most traffic (2.25% more than in 2014); it is also the one that saves more travel time, reducing the situation of 2014 by 1.82%.
includes each of the 3 Southern Bypass alternatives. There are several methods to assign this, such as the "all or nothing" or the stochastic method. The stochastic methods of traffic assignment reveal the variability of the users, their perception of the costs, and the way to simultaneously minimize the distance and the travel time, therefore, the general costs. These methods could be based on a simulation as in Burrell [30], or they could be proportional. The proportional methods are based on a network load algorithm and distribute the trips which arrive to the node among the other entire possible exit knots, contrary to the "all or nothing" assigning method, which assigns all trips to an individual exit node.
In this research, the traffic assigning was carried out using a stochastic proportional method of assigning alternative routes: the Dial method [31]. In this method, two or more alternative routes are assigned between each pair of zones, dividing the existing flow between those itineraries, considering the generalized minimum cost (distance+time) and the generalized cost for each of the itineraries. According to the Dial method, the trips in each origin-destination relationship are divided among the different itineraries through a logit type division model. In Equation 2, the simplest case of a logit model is represented, which is the one that only considers two different options to choose from, considering for each trip the characteristics of the generalized cost. In this case, a similar one to the Ortuzar model is used [32] with the same primary and secondary modal split dispersion parameters (ʎ 1 =ʎ 2 ), which makes it a simple multinomial logit model (MNL) [33,34].
where: p(1) is the probability of the traveler using itinerary number 1; C 1 and C 2 are the generalized costs of itinerary numbers 1 and 2, respectively; ʎ is the  This research analyzes the effects of bypasses in small and non-congested cities by developing a traffic model in Badajoz, starting from the assigning of the origin-destination travel matrix derived from the surveys and counts made at the southern and eastern accesses of Badajoz. The traffic model describes the mobility in potentially-capturable relationships for the

CO 2 emissions
The measurements were made with vehicles of different typology (Fiat 500 1,200 cc gasoline and Opel Astra 1,600 cc diesel) to analyze the difference of impacts between types and to be able to apply them to the fleet of the city of Badajoz ( Table 4). The results are shown in Table 5.
Alternative 1 is the one that captures more traffic and therefore eliminates the largest number of vehicles from the city center and the highest amount of CO 2 emissions.

CONCLUSIONS AND DISCUSSION
Planning new high-capacity roads in small cities, whether they are collective-distributor routes or single variants, requires an effective traffic model which is  These results point to certain policy recommendations for small cities to develop bypasses as close as possible to the city, as it has been demonstrated in this research that it is the alternative that produces greater traffic capture, greater time savings and eliminates the largest number of CO 2 emissions from the urban center. It is also the alternative with the shortest route, therefore the most economical.

ACKNOWLEDGEMENT
The authors would like to acknowledge the Government of Extremadura (Spain) for funding the Informative Study of Badajoz Southern Bypass (Ronda Sur de Badajoz), under which this research has taken place.

RESUMEN
Las ciudades pequeñas con menos de 200,000 habitantes no suelen sufrir problemas crónicos de congestión. Sin embargo, el vehículo privado se usa excesivamente, por lo que es necesario implementar medidas para fomentar un mayor uso del transporte público y desplazamientos peatonales para hacerlo más sostenible. Los bypass mejoran el nivel de servicio (LOS) mediante la eliminación de los automóviles del centro de la ciudad, lo que lleva a reducciones significativas en el tiempo total de viaje. La mayoría de los estudios hasta ahora se han realizado en grandes ciudades con problemas crónicos de congestión, por lo que el objetivo de esta investigación es analizar los efectos de los bypass en ciudades pequeñas y no congestionadas a través de la construcción de un modelo de tráfico en Badajoz (España) comenzando con la asignación de la matriz de viajes de origen-destino derivada de las encuestas y recuentos de tráfico realizados en los accesos sur y este. El modelo de tráfico describe la movilidad en futuras relaciones de tráfico en el sur potencialmente capturables y permite conocer diferentes comportamientos alternativos en la construcción de una nueva carretera de alta LOS. Esta investigación concluye que las ciudades pequeñas sin problemas de congestión future southern variant and allows calculation of savings in travel distances and times in relation to the situation in 2014.
Analyzing the results in Table 3, one might conclude that, from the point of view of the traffic, alternative 1, which is the nearest to the city center, is preferred to alternatives 2 and 3 since it is the alternative with the highest number of vehicles-km (2.25% more traffic) and the one with the lowest number of vehicles-hour (1.82% less travel time). Alternative 1 is also the one that produces greater savings of CO 2 emissions from the city center (Table 5), reaching values that approximate 80% of the sum of the other two alternatives.
In terms of evaluating the performance of the method chosen, it is necessary to note that the "all or nothing" assigning methods and the stochastic methods do not take into account the capacities of the roads, assigning higher amounts of traffic to specific stretches which might not have that required capacity. The assigning method per stretches with capacity restriction takes this issue into account [37,38]. However, due to the fact that Badajoz is not a city with severe traffic jam problems, the use of models which contemplate the restriction of capacity is not necessary, and the use of simpler methods which do not take this into account seems more adequate, such as the Dial method used in this research.
The chosen method should be used only in small cities which have no traffic jam problems. This is because in cities with traffic jam problems the application of the expansion coefficient constant to obtain the O/D matrix would produce a lot of errors [39,40]. Moreover, as shown previously, there is the possibility of errors in traffic assignment considering the lack of capacity on the roads.
It is also necessary to emphasize that there are authors who use zoning-distributing models of gravitational demand, which are more economical since they do not require surveys and have proven to be sufficiently precise [41][42][43][44][45].
All these determinants make each assigning method suitable for a specific field of application in relation to the characteristics of the assigned network and the problem to analyze and evaluate. In interurban networks, the "all or nothing" and stochastic methods are usually used (Dial method). In urban networks, the capacity restricting methods per stretch are used and, to a lesser extent, the Burrel method. In interurban corridors, with alternative itineraries (toll motorway or important variants), the delivery curves are used [46,47]. This method consists on supposing that between each pair of zones there are at least two alternative ways with their own characteristics of time, distance, and level of service. The journeys by the first or the second itinerary are distributed taking into account the already-established delivery curves, which define the percentage by either itinerary according to time