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ISSN : 1598-7248 (Print)
ISSN : 2234-6473 (Online)
Industrial Engineering & Management Systems Vol.19 No.1 pp.228-241
DOI : https://doi.org/10.7232/iems.2020.19.1.228

# Traffic Information Sign Location Problem: Optimization and Simulation

Chompoonoot Kasemset*, Chawis Boonmee, Masahiro Arakawa
Department of Industrial Engineering, Faculty of Engineering, Chiang Mai University Chiang Mai, Thailand
Department of Architecture, Design, Civil Engineering and Industrial Management Engineering Nagoya Institute of Technology Nagoya, Aichi, Japan
*Corresponding Author, E-mail: chompoonoot.kasemset@cmu.ac.th
May 8, 2019 October 3, 2019 November 6, 2019

## ABSTRACT

Traffic congestion is a critical problem in many big cities when expansion of traffic systems is implemented to catch up with the increasing demand for road transportation. The policy to shift routes to avoid traffic congestion is one policy that can be supported by traffic information systems. A traffic information sign is one of the solutions that provide traffic information to drivers (users) for selecting routes. Infrastructure for physical signs needs investment, so the optimal number and location of signs should be appropriate for maximizing the effectiveness in reducing traffic congestion. Firstly, a mathematical model for the location of traffic signs was proposed in this study. Then optimal solutions were evaluated using simulation tests. Application of the proposed method is presented for solving the case study of Chiang Mai University’s traffic network. The optimal solutions were to assign two signs on roads with high departure flows and high possibility to change directions. The simulation results present ranges of the probability for changing directions that can reduce the departure flows at the bottleneck gate. When the flows at the bottleneck gate were reduced, the traffic in this area was shown to be less congested. Moreover, utilizations of gates were more balanced.

## 1. INTRODUCTION

Land transportation is used both in urban and rural areas. Especially in urban areas, many big cities in the world are facing traffic congestion problems, such as Los Angeles, New York, and Moscow. The ten most congested cities and countries in the world were reported by Korosec (2018) on the website of Fortune. Costs of traffic congestion can be categorized into two parts: (i) direct costs related to the value of fuel and time wasted, and (ii) indirect costs related to freight and business fees from company vehicles idling in traffic. Those fees are then passed on to households through higher prices, according to INRIX (2018).

Traffic congestion occurs when the expansion of a transportation system cannot cover the rapid increase in travel demand. Transportation demand management (TDM) is the concept that aims to modify travel behaviour to reduce congestion instead of expanding transportation systems as in classical theories like transportation system management (TSM). Intelligent Transportation Systems (ITS) is one supporting tool used during the implementation of TDM. ITS products such as smart cards and advanced traveller information systems (ATIS) could influence the nature of the travel demand. ATIS can inform people of current conditions and encourage them to alter their route, mode, or time of departure (Winters, 2000). Traffic information sign is one of the ATIS forms used to provide real-time traffic status (or information) to drivers. Traffic information signs can support drivers for route selection. Shifting a trip from a more congested route to a less congested one is the concept of balancing the load of traffic systems when capacities are limited and expanding the traffic system is not possible. Technologies capable of the instantaneous delivery of current route information need investment to set up the infrastructure; thus, the optimal number of signs and the effectiveness should be pre-determined for budget proposals.

Existing literature reviews related to traffic signs and traffic congestion mostly address traffic sign timing. Among those research studies, both optimization and simulation are adopted to obtain solutions. A small number of works have been conducted on traffic information signs. Although, research related to traffic information systems is plentiful, these research studies mainly focus on system and hardware development. The first contribution of this research is to propose the application of optimization and simulation techniques for traffic information sign location problems to reduce traffic congestion. The optimal location of signs was obtained by formulating and solving a mathematical model. Then the solutions were tested using simulations to study the effectiveness of the sign locations under uncertain situations by simulating the real traffic system. The second contribution is to present the application of the proposed method by solving the case study of Chiang Mai University.

The remainder of this paper is organized as fol-lows: Section 2 presents preliminaries. Section 3 presents the proposed mathematical model. Section 4 presents a case study of Chiang Mai University with results from optimization and simulation. Finally, conclusion and discussion are given in Section 5 and 6.

## 2. PRELIMINARIES

This section presents the related papers on traffic management. Many researchers have attempted to emphasize this area in order to solve traffic problems. Comprehensive reviews of traffic management were conducted by de Souza et al. (2017) and Hoogendoorn et al. (2014). Addressed by de Souza et al. (2017), the main cause of traffic congestion was from physical bottlenecks (40%). The other causes were traffic incidents (e.g. accidents), bad weather conditions, working zones, poor traffic signal timing and special events (25%, 15%, 10%, and 5%, respectively).

Internet of Things (IoT) is one solution consid-ered in traffic management research. IoT is mainly composed of three sections: application, network, and acquisition (Soni and Saraswat, 2017). Literature reviews on IoT application in traffic management were presented by Soni and Saraswat (2017), Tendulkar et al. (2016), and Avatefipour and Sadry (2018). Nowadays, IoT is being applied continually in traffic management systems. Sharma et al. (2018) proposed an intelligent traffic management system for controlling the traffic system in the city. This study applied raspberry pi, Infrared (IR) sensor, and Liquid Crystal Display (LCD) for developing the proposed system in which raspberry pi is the main component that is employed to control all performance multitasking, while an IR sensor is applied to monitor the density of traffic. The corresponding data are made available on the website for displaying the traffic status. Therefore, people can get updated traffic information and can avoid traffic jams in the city using their proposed system. Farheen et al. (2018) proposed an IoT based traffic management system, using main components including Microcontroller, IR sensor, LED display, Global System for Mobile Communications (GSM) module, mobile phones, Personal Computer (PC), and cloud storage systems, for polices to better perform city traffic monitoring.

Not only IoT applications have been employed to solve traffic problems or develop traffic management systems, several other techniques have also been applied. Optimization and simulation techniques are considered to be the major techniques. Kim and Son (2017) proposed the application of agent-based traffic simulation in lane selection behavior modeling. The realistic lane selection model was simulated to study the discretionary lane changing behavior regarding an individual driver’s uncertain perception and reasoning processes. The solutions were proposed and evaluated using agent-based simulation (ABS). Peñabaena-Niebles et al. (2017) presented optimization techniques to improve the performance of traffic signal coordination at intersections during the transition phase. The proposed mathematical model was oriented to describe the transition regarding coordination parameters at all intersections of an arterial road. The objective was to minimize the social cost during the transition phase expressed in function of costs due to delays, fuel consumption, and air emissions. In this study, an ant colony algorithm was applied to find the optimal transition parameters. The proposed method can yield outstanding performance compared with the traditional methods. Nevertheless, some research works have integrated both optimization and simulation techniques in traffic management systems. Hewage and Ruwanpura (2004) developed the special-purpose simulation (SPS) tool for obtaining traffic signal light timing. The proposed simulation model can be used to provide signal light timing for both single junctions and actual road networks with multiple junctions. The traffic system of the University of Mora-tuwa, Sri Lanka, was used to demonstrate and validate the proposed model. Ezzat et al. (2014) applied a simulation technique to the traffic signal timings under oversaturated conditions. A simulation model was developed, and the authors presented the actual traffic network of Alexandria, Egypt. Then the optimization technique was also applied to minimize the total time in the system of vehicles that led to improve the performance of the road network. Udomsilp et al. (2017) proposed traffic data analysis on Sathorn Road with Synchro optimization and traffic simulation that aimed to control the traffic by generating optimal traffic signal timing to reduce delay time at intersections. Other research papers on traffic signal timing and traffic congestion were Li et al. (2016), Panovski and Zaharia (2016), and Singgih et al. (2016).

Most research of traffic management concentrated on traffic congestion has mainly focused on traffic signal timing using simulation or optimization, as well as integrating both techniques. This study aimed to locate the traffic information signs to improve traffic congestion. For traffic information sign application, there were very few research works addressing this. Wang (2018) proposed a model for selecting locations of traffic signs on road intersections. This research was conducted in the context of a mountainous city. The proposed model included driving characteristics analysis to select traffic sign locations.

As mentioned before, a few related research papers were found. One research work was close to what we proposed but in the context of disaster logistics management. Sugiura et al. (2017) proposed a mathematical model for obtaining the optimal location of emergency exit signs when evacuations are needed considering the behavior of evacuees on simple layout models. The optimal sign locations were calculated by the mathematical model, and the researchers evaluated the effectiveness using multi-agent simulation.

Taking this literature review into consideration, this research aimed to present a method to assign traffic information sign locations in a traffic system, which very few research works have considered. Optimization and simulation were applied in this study. The proposed method is presented using the case study of the traffic system of Chiang Mai University.

## 3. PROPOSED MATHEMATICAL MOD-EL

### 3.1 Model Formulation

The proposed mathematical model for the traffic sign location problem was proposed as follows.

Indices:

• i, j = Intersection Node (i, j = 1, 2, 3 … n) when i represents the starting node and j represents the ending node of any arc i-j.

Sets:

• Rk = Set of arc i-j that connecting to be any main route k (k = 1, 2, 3…k).

Parameters:

• Fij = The number of vehicles flowing from i to j.

• Aj = Chance of changing direction at the ending node j.

• N = Maximum number of traffic sign that can be located.

Decision Variables:

Objective:

(1)

s.t.

(2)

$∑ i , j X i j ≤ N$
(3)

$∑ i , j ∈ R k X i j ≤ 1$
(4)

Let i and j represent the intersection in a traffic network. There is the set Rk that contains members as roads (arcs) starting from i and ending at j when every member is connecting together to become main roads. Fij is the number of vehicles flowing from i to j that can be obtained from data collection while Aj is the chance of changing direction at the ending node j when traffic congestion is observed on the arc i-j. Xij is the decision variable as a binary variable used to assign the location of signs. The assigned location should maximize the summation between two terms as (i) the number of vehicles that can reach signs located between i and j, and (ii) the number of vehicles having the possibility to change direction when flowing from i to j as in Equation (1). Equation (2) is to limit the number of vehicles flowing from i to j that should be greater than or equal to the binary variable as Xij for each road from i to j. This equation is to prohibit locating the sign to the road with no vehicle flows. Equation (3) is to limit the number of locations of signs that should be less than or equal to the maximum number of signs that can be implemented. Equation (4) is to limit the number of signs at each main road, which should not be greater than one.

### 3.2 Model Verification and Valida-tion

The small-size numerical example was solved to verify and validate the proposed mathematical model. The traffic system consists of 5 intersections with 2 gates as shown in Figure 1. Fij and Aj are presented as Table 1 and 2. As mentioned above, Fij can be obtained from data collection and Aj can be calculated from the ratio between the number of arcs at node j minus by one as the current way and the total number of arcs at node j.

Then, the set of main route or Rk are presented in Figure 2.

For this problem, R1 to R4 represent four main roads. Each set of Rk has different members that connect together to form main roads. Then, the problem was solved using Lingo software. The results when using only two signs (N = 2) are presented in Table 3.

As the results show in Table 3, the signs should be located on the roads connected to node 3 to 4 and 4 to 3. The two signs are for different directions of vehicle flows. Considering the main road, R1, they are (1,3) and (3,4). Since the flows of (3,4) are greater than (1,3), the sign was located on (3,4). Similarly, for R2, they were (4,3) and (3,1). Thus, the flows of (4,3) are greater than (3,1), so the sign was located on (4,3). The solution from this problem can confirm the appropriateness of the proposed model. Thus, this formulation is applied to the real case in the following section.

## 4. CASE STUDY

### 4.1 Characteristics of the Problem

In this research, the traffic sign location was proposed in a community area. A university campus can be considered as one example of a community area. In this study, Chiang Mai University (CMU), located at the northern region of Thailand, was selected to be studied. The traffic network of the university from a previous work by Kasemset and Thipboonraj (2017) is presented in Figure 3.

As presented in Figure 3, there are five gates usually opened (presented as C1 to C5) during the peak hours (4 PM to 7 PM) with 26 intersections (presented as D1 to D26). Kasemset and Thipboonraj (2017) addressed that five gates can be used to satisfy the demand of departure vehicles when the optimal solution can be derived from the maximum flow formulation. Whereas the study of Kasemset and Suto (2019) presented that the total capacity of five gates satisfied the needs of total departure vehicles only when uncertainty was excluded, the results from multi-agent simulations presented that the capacity of C5 was not sufficient. Considering Kasemset and Suto (2019), the traffic congestion occurred along the road from D5 heading to C5. Moreover, this result coincided with the real situation occurring in the university case study.

A possible solution was recommended: Apply a real time traffic information system for drivers (Kasemset and Suto, 2019). There are many types of real time traffic information systems, but traffic signs with real time information was considered.

To determine the location of the traffic signs for the case study, the proposed formulation was applied and the optimal solution was confirmed by simulation.

### 4.2 Optimization Results

The model formulation proposed in section 3.1 was employed and the parameters used were addressed as Table 4 to 5.

Four main routes are presented as in Figure 4 as follows:

• R1 = {(1, 2), (2, 4), (4, 5), (5, 24)}

• R2 = {(24, 5), (5, 4), (4, 2), (2, 1)}

• R3 = {(5, 25), (25, 9), (9, 10), (10, 11)}

• R4 = {(11, 10), (10, 9), (9, 25), (25, 5)}

The Lingo model for the case study was presented as Figure 5.

From Figure 5, Line [1] to [6] represented sets used in this problem including sets of main roads as R1 to R4 as line [3] to [6]. For the mathematical model proposed in section 3.1, Line [7] is for the objective function explained before as Equation (1). Line [8] to [14] represents the constraints of this problem as addressed as Equation (2) to (4).

The optimal solutions were obtained in three cases when N was varied. The results are presented in Table 6.

From Table 6, the objective value (Z), the sum-mation between the number of vehicles that can reach signs and the number of vehicles having the possibility to change direction when flowing from i to j, was also increased when N was increased. Whereas a definition of the appropriate value of N is still in doubt, the simulation was conducted consequently to help to decide an appropriate N-value.

### 4.3 Simulation Results

The simulation model from Kasemset and Suto (2019) developed using Arena software was employed in this study.

#### 4.3.1 Parameter Setting

As the model was verified and validated as ad-dressed in Kasemset and Suto (2019), the run length was one hour. The initial test of the existing situation was conducted using 15 runs (replications). Considering only the output at gate C5 as the capacity constraint of this traffic system, vehicles departed from this gate as 1,631.07 ± 14.51 cars (95% confidence interval [CI]). 14.51 was the half-width of the output range that could be reduced to estimate the range of output at this gate precisely. Considering the initial half-width, which was 0.89% deviation from the average value, the number of replications can be estimated when decreasing this num-ber to 0.5% as follows.

$n ≅ n 0 h 0 2 h 2 = 15 14.51 2 8.16 2 ≅ 48$
(5)

Equation (5), derived from Kelton et al. (2009), was used to find the appropriate number of replications. n is the number of desired replications that can reduce h0 (initial half-width) to h (desired half-width), when n0 is the number of initial replications. The results from initial runs as 15 replications indicated the minimum appropriate replications as 48 replications, so 50 replications were used in this study.

#### 4.3.2 Results for Existing System (Without Signs)

The outputs of each gate when the simulation tests were carried out for 50 replications are presented in Table 7.

Table 7 presented the simulation results of the existing system (Scenario 0). The total output was 4,576.48 cars per hour. Considering Gate C1, C3, and C5 with the same capacity of 1,500 cars per hour, only the output of gate C5 was over capacity. Thus, the traffic congestion was observed at this gate. For gate C2 and C4, the gate capacities were 750 cars per hour at which the outputs were lower than the capacities.

#### 4.3.3 Test Scenarios and Assumption

The assumption of this research was that the traffic congestion occurred at the road heading to the gate C5 (as mentioned as Figure 3) as from the results of the related study (Kasemset and Suto, 2019). The locations of signs from the proposed mathematical model are presented in Table 8.

#### 4.3.3.1 The First Test for N =1

When only one sign should be employed, the best solution is to locate the sign at the arc connecting node 24 and 5 together as shown in Figure 6. In addition, to validate the result from the proposed mathematical model, the tests were conducted in three scenarios as follows:

• Scenario 1.1: One sign located between node D24 and D5 as X24,5 (Optimal Solution),

• Scenario 1.2: One sign located between node D9 and D10 as X9,10 (Candidate Solution 1), and

• Scenario 1.3: One sign located between Node D4 and D5 as X4,5 (Candidate Solution 2).

From Figure 6, the locations of signs in each scenario were presented with an example of traffic signs with real-time information display between D24 and D5.

A. Scenario 1.1: Optimal Solution as X24,5

The simulation model of the existing system was modified. The flow chart of the modified part is presented in Figure 7.

From Figure 7, when cars depart from D24 and go to D5, drivers can see the sign and make the decision to change direction with the probability X treated as a random variable. The experiments were conducted to find the range of X that can be accepted. Drivers can either change direction to exit at other gates, or head to D25 (entering to the traffic congestion area as referred to in Figure 6).

The simulation results of scenario 1.1 are pre-sented in Table 9.

From Table 9, X should be 65% to 90%, so the departures at C5 are lower than its capacity and the other gates are satisfied. When X is more than 90%, the departures at C3 were over capacity. When the sign was located at X24,5,

• - the departures at C5 were decreased;

• - the departures at C1 and C3 were increased; and

• - X had a positive correlation with the departures at C1 and C3 but a negative correlation with the departure at C5.

B. Scenario 1.2: Candidate Solution 1 as X9,10

The simulation model of the existing system was modified. The flow chart of the modified part is presented in Figure 8.

From Figure 8, when cars depart from D9 and go to D10, drivers can see the sign and make the decision to change direction with the probability Y treated as a random variable. The experiments were conducted to find the range of Y that can be accepted. Drivers can either change direction to exit at C4 or head to D11 to exit at C5 (referred to Figure 6).

The simulation results of scenario 1.2 are pre-sented in Table 10.

From Table 10, Y should be 20% to 25%, so the departures at C5 were lower than its capacity and the departures at C4 were not over capacity. When Y was more than 25%, the departures at C4 were over capacity. Whereas Y was less than 20%, the departures at C5 were not lower than its capacity. When the sign was located at X9,10,

• - the departures at C5 were decreased;

• - the departures at C4 were increased; and

• - Y had a positive correlation with the departures at C4 but a negative correlation with the departure at C5.

C. Scenario 1.3: Candidate Solution 2 as X4,5

The simulation model of the existing system was modified. The flow chart of the modified part is presented in Figure 9.

From Figure 9, when cars depart from D4 and go to D5, drivers can see the sign and make the decision to change direction with the probability Z treated as a random variable. The experiments were conducted to find the range of Z that can be accepted. Drivers can either change direction to exit at other gates or head to D25 (entering the traffic congestion area as referred to in Figure 6).

The simulation results of scenario 1.3 are pre-sented in Table 11.

From Table 11, Z should be 70% to 80%, so the departures at C5 were lower than its capacity and the departures at C3 were not over capacity. When Z was more than 80%, the departures at C3 were over capacity. However, Z was less than 70%, so the departures at C5 were not lower than its capacity. When the sign was located at X4,5,

• - the departures at C5 were decreased;

• - the departures at C3 were increased;

• - Z had a positive correlation with the departures at C3 but a negative correlation with the departure at C5.

The results of scenario 1.1 to 1.3 are concluded in Table 12.

From the mathematical model, when N = 1 the location at X24,5 is the best location of the traffic real information sign.

From the simulation results, location of X24,5 is the best location because this location can help in shifting the departures from C5 to C1 and C3 with a wider range of the probability of changing direction compared to other locations that have only one alternative for shifting the departures with a narrow range.

The solution from the mathematical model and simulation coincided; when N = 1, the location of X24,5 was the optimal solution. When considering the simulation results, the effect of location X24,5 was the same as the location X4,5 when the shifted departures were assigned to C3. However, the better option of X24,5 was 2 alternative gates as C1 and C3. Thus, X4,5 is not reasonable to be considered when X24,5 is selected. As a result, the simulation experiments were not conducted for N = 3.

Considering the location of a sign at X24,5, the probability X has effects on increasing the departures at C1 and C3 outputs, reducing the departures at C4 and C5 outputs, and no effect on the departures at C2.

#### 4.3.3.2 The Second Test for N = 2

When only two signs should be employed, the best solution is to locate the sign at the arc connecting (i) node 24 and 5, and (ii) node 9 and 10 as shown in Figure 10. The tests were conducted as four scenarios, which are presented in Table 13. The simulation results for N = 2 are presented in Table 14.

From Table 14, every scenario can help in im-proving the situation of gate C5. The departures were shifted from C5 to other gates—C1, C3, and C4. Some discussion can be drawn as follows.

• - X% affects C1 and C3 outputs (positive corre-lation).

• - C2 output does not rely on X% and Y%.

• - C4 output is dependent on X% (negative correlation) and Y% (positive correlation).

• - C5 output is dependent on X% and Y% (negative correlation).

## 5. DISCUSSION

The simulation results of N = 1 support locating the sign at X24,5, which is the same solution as from the proposed mathematical model. The range of the probability to change the direction, X, should be 65% to 90%. With this range, the departures at C5 were lower than its capacity and the departures at other gates were lower than their capacities, as well.

The simulation results of N = 2 (as in Table 14), when the signs were located at X24,5 and X9,10, presented better improvements than N = 1 (as shown in Table 9) in terms of the decreasing of the departures at C5. When load balancing was considered, the results of utilization were presented in Table 15 (N = 1) and Table 16 (N = 2).

Considering Table 15 and Figure 11 (left) for N = 1, the average utilization of the gate and range were reduced. The results can be interpreted that using one sign at X24,5 can balance system load (departures of the systems).

Likewise, considering Table 16 and Figure 11 (right) for N = 2 (sign located at X24,5 and X9,10), system load can be balanced and better than when N = 1.

When comparing N = 1 and N = 2, in terms of both decreasing departures at C5 and load balancing, N =2 was better than N = 1. Thus, when N is limited to a maximum of 2, N = 2 is preferred.

Less X% is affected on increasing average and reducing range of % utilization; this presented the better spanning of load considering all gates.

## 6. CONCLUSION

This research work presented the method for locating traffic signs using optimization and simulation techniques. When traffic congestion occurs, traffic signs can lead drivers to avoid congested areas. A mathematical model was proposed for locating traffic signs to maximize the number of vehicles that can have access to the signs and the number of vehicles that can change the direction to avoid the traffic congestion. After the optimal location was set, simulations were applied to confirm the effectiveness of the sign under uncertain situations.

The proposed method was applied to the case study of Chiang Mai University. The optimal solutions were derived in two cases: using one sign and two signs. After that, the simulation tests were conducted for two cases to find the minimum probability for drivers to change direction. The simulation results presented that using two signs was more effective than using one sign. The probability of changing the direction for the first sign location (X24,5) should be 65 – 90% and the second sign location (X9,10) should be 20 – 25%. Within these probability ranges, the number of departures at C5, which before had traffic congestion, can be reduced to be less than its capacity. Moreover, the average utiliza-tion of all gates can be increased with a smaller utiliza-tion range, which was presented by the shift-ing/balancing of the departures at all the gates.

Due to the proposed mathematical model, two influencing parameters are introduced as Fij (the number of vehicles flowing from i to j) and Aj (the chance of changing direction at the ending node j). There are some important observations when this procedure is applied as follows.

(i) Factors behind the development of transport local systems addressed by Rodrigue (2019) include environmental, historical, technological, political, and economic factors. A change in these factors affects vehicle flows or Fij, but these changes are foreseen and preparations can be provided due to slow change. These factors should be considered during the planning period—both long (more than 10 years) and intermediate (5-10 years) range planning. When changes of these factors are noticed, the location of signs can be re-optimized by choosing new locations promptly. In this situation, the proposed model can still be used by adjusting Fij by either estimating Fij using simulation or considering it as an uncertainty parameter; this would require modifying the proposed model to be a stochastic model.

(ii) As Aj is the chance of changing direction at the ending node j when traffic congestion is observed on the arc i-j; this parameter is important for locating the traffic information sign. A low value of Aj means less chance to avoid traffic jams; conversely, a high value of Aj means that drivers have more alternatives to avoid traffic jams. Thus, traffic information signs should be located at the roads (arc) with high Aj, so the traffic flow can be reduced at the roads with traffic congestion.

In real application, this study provided the location for setting up the advanced traveller information systems (or ATIS) using traffic information signs. The effectiveness of signs was evaluated, but the probability of changing direction also has an influence on the reduction of traffic congestion. Since only appropriate ranges were proposed, this parameter cannot be exactly derived from simulation. To evaluate the probability of changing direction caused by signs, a driver survey should be conducted. If the results of the survey presented indifferent probability values compared with the simulation results, real implementation of signs can be accepted.

The system design for traffic information signs is one task that can be considered for further study. In-formation system development can be both information flow design and infrastructure and device selection. As Internet of Thing (IoT) is advanced technology in information systems, IoT can be considered in developing traffic information systems. Moreover, real-time traffic information can be displayed on intelligent traffic information signs, as well.

## ACKNOWLEDGMENT

This research was supported by the Hitachi Scholarship Research Support Program 2018, Hitachi Global Foundation and the Department of Industrial Engineering, Faculty of Engineering, Chiang Mai University, Thailand.

## Figure

Traffic network for the numerical example.

Main route sets.

Traffic Network Representation of CMU (Kasemset and Thipboonraj, 2017).

Four main routes for the case study of CMU.

Lingo model for the case study of CMU.

Locations of signs for the test of N = 1.

Logical flow for Scenario 1.1.

Logical flow for Scenario 1.2.

logical flow for Scenario 1.3.

Locations of signs for the test of N =2

% Utilization of each gate for N = 1 (left) and N = 2 (right).

## Table

Fij for the small-size problem

Aj for the small-size problem

Xij for the small-size problem

Fij for the case study problem

Aj for the case study problem

Optimal solutions for the case study problem.

Simulation results for the existing system (without signs)

Optimal sign location

Results of scenario 1.1 (unit: cars/hour)

Results of scenario 1.2 (unit: cars/hour)

Results of scenario 1.3 (unit: cars/hour)

Results comparisons for scenario 1.1 to 1.3.

Scenarios for N =2

Results of scenario 2.1 to 2.4 (unit: cars/hour)

% utilization of each gate for N =1

% utilization of each gate for N =2

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