An Agent-based Simulation Tool for Evaluating Pooled Queue Performance at Marine Container Terminals

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1 An Agent-based Simulation Tool for Evaluating Pooled Queue Performance at Marine Container Terminals Matthew Fleming University of South Carolina Department of Civil and Environmental Engineering 00 Main Street Columbia, SC 0 Telephone: (0) -0 Fax: (0) fleminmp@ .sc.edu Nathan Huynh (Corresponding Author) University of South Carolina Department of Civil and Environmental Engineering 00 Main Street Columbia, SC 0 Telephone: (0) - Fax: (0) huynhn@cec.sc.edu Yuanchang Xie University of Massachusetts Lowell Department of Civil and Environmental Engineering One University Avenue Lowell, MA 0 Yuanchang_Xie@uml.edu Length of Paper: Text =,0 words; Number of Figures = ; Number of Tables = ; Total =,0 words Resubmission Date: November, 0 TRB 0 Annual Meeting

2 0 ABSTRACT Truck queuing at marine container terminal gates is one of the main sources of delay at terminals and is an area of concern since delays increase the logistical cost of transporting a container. Previous studies on terminal gates focused on the performance of strategies such as the appointment system and extended gate hours. However, there has yet to be a study that evaluates the performance of pooling trucks into a single queue at the gates. Previous studies on pooling offer mixed opinions on whether or not it is beneficial, but none of these studies have attempted to model the movements of the entities in the queue. In a human system (no vehicles) the movements are not as important since the time to move up one space in the queue is negligible; however, due to the size and weight of the trucks at the gates, the time to move is significant and should be considered. This study used agent based simulation to model the terminal gate system with two different queuing strategies, a pooled queue and non-pooled queues, since analytical solutions are not capable of capturing vehicle movements within the queue. Using a carfollowing model, a realistic representation of how vehicles move within the queue is captured. The developed simulation model was used to evaluate queuing strategies under varying conditions. Results indicate that using a pooled queue yields significantly lower average queuing times and variability in queuing times. Keywords: marine container terminal, queuing, agent-based simulation. TRB 0 Annual Meeting

3 Fleming, Huynh and Xie INTRODUCTION Marine container terminals are a critical link in the supply chain as the majority of goods are imported or exported in containers. Thus, their efficiencies affect the entire supply chain. Container terminals are divided into three general sections: seaside, yardside, and landside. Each of the three areas of the terminal is dependent on each other and all need to be efficient in order to maximize the efficiency of the terminal. One bottleneck often seen at container terminals is at the gates (landside) where trucks arrive to either complete an import transaction or export transaction. Import transactions involve picking up a container from the terminal and export transactions involve delivering a container to the terminal. Once the trucks arrive at the entry gate, they must stop to present transaction information, be inspected, and then be directed to a specific location in the container yard. As with all systems where several parties are involved, there are cases where information may not match or may be missing. These transactions that have documentation issues are referred to as trouble transactions and require special intervention and, therefore, more processing time at the gate than non-trouble (normal) transactions. Trouble transactions are generally a result of documentation, container location, or equipment issues and constitute approximately % of all transactions (). During busy periods of the day, long queues of trucks form at the entry gates and this is partly due to trouble transactions as they require a longer processing time. This is detrimental to both the terminal and the truck drivers. Truck drivers are wasting time and money when idling in the queue and the terminal becomes less competitive if they cannot provide the expected level of service. Consider the typical gate setup at marine container terminals in which all arriving vehicles are directed to a set of lanes and simply join the shortest queue. This setup is shown in Figure a with 0 lanes and the white vehicles representing normal transactions and the red vehicles representing trouble transactions. As can be seen in Figure a, the trouble transactions are preventing the vehicles in the same lane from being serviced. The vehicles directly behind the trouble vehicle must now wait for the trouble transaction, which takes much longer than a normal transaction, to be completed before advancing. Now consider the exact same vehicles at the gates as in the Figure a and change the queuing strategy to a pooled queue system. This setup is shown in Figure b. Using this setup the trouble vehicles are no longer directly preventing any vehicles from being serviced. The negative aspect of using this setup is the queue is now much longer than using separate queues since several queues are now combined into a single queue. This study investigated whether or not it would be beneficial for marine terminals to pool all of the entry lanes into a single lane like the setup at banks, airports, theme parks, etc. To answer this question an agent-based simulation model that incorporates a car-following model to model truck movements within the queue(s) is created. The model is intended to be a tool that can be used by terminal operators and planners to investigate the performance of the pooled queue system as well as the separate queues system at their respective terminals. TRB 0 Annual Meeting

4 Fleming, Huynh and Xie (a) 0 (b) FIGURE Illustration of queuing strategies: (a) separate queues strategy; (b) pooled queue strategy. TRB 0 Annual Meeting

5 Fleming, Huynh and Xie LITERATURE REVIEW The following literature review discusses previous queuing studies on terminal gates as well as investigations on pooled and non-pooled queues.. Previous Studies On Marine Container Terminal Gates There have been a few studies that have addressed queuing at the inbound and outbound gates of container terminals. These queuing studies have focused mainly on investigating the use of the appointment system or extending gate hours (,, ). The two studies most related to this work are discussed in more detail below. Guan () developed a model to measure costs of congestion at the gates, provided alternatives to improve gate operation and investigated ways to reduce gate congestion at the Port of New York. A multi-server queuing model was used to analyze congestion at the gates and to estimate truck waiting cost and an optimization model was developed to minimize the total gate system cost. It is noted that in trying to minimize the total system cost, a balance must be found between the gate operators and the trucks. This is because the trucks want to minimize their waiting time in the system and the gate operators want to keep the gate operating costs (i.e. number of gates) to a minimum while maintaining adequate service to truckers. Guan noted that if the truck inter-arrival times and service times follow an exponential distribution that the M/M/S model can be applied. If the truck inter-arrival times follow a Poisson distribution and the service rate follows an Erlang distribution then the M/Ek/S model can be used. Karafa () used the Paramics simulation software to investigate the appointment system as well as extending gate hours and compare them to the original data. In this study tolls are used at the entrance and exit gates of the terminals to capture the queuing at the gates. The authors found that extending gate hours was the best strategy for this particular terminal. Comparison is made to the work of Dougherty () who did not include gate delays, but used a similar technique and the results show that trucks should expect to encounter most of their delay at the gates and not on the surrounding network. This also shows that when building simulation models of the terminal and surrounding network, the gates should not be omitted from the model as this can lead to underestimating the delay.. Pooled Vs. Non Pooled Queues The question of whether or not to pool multiple queues together into one single queue may seem to be one of the most basic questions one can ask regarding queuing applications; however, this issue is not as simple as it may seem and is still open for discussion in the research community. This is because queuing theory is too restricted to model real world scenarios. There have been a number of studies that have investigated pooling using numerical approximations (,,, 0) and most made comparison to independent separate queues. However, as noted by Rothkopf and Rech (), traditional comparisons of a standard M/M/ queue against an M/M/s system will always show that pooled queue is beneficial in terms of waiting time. However, it is noted that these basic queuing theory calculations do not matter in reality because customers will always join the shortest queue and may jockey for position thus the comparison of independent queues are no longer valid since in reality separate queues are not independent. TRB 0 Annual Meeting

6 Fleming, Huynh and Xie One of the less obvious, but important aspects of queuing is the psychological impact of the queuing system on the arriving customer. Larson () discussed some of the psychological impacts of pooling multiple queues together. In his paper, he presented the idea of a situation involving separate queues where an individual joins a queue at a given time and another joins some time later, but begins service before the first individual. The first individual is displeased with the service because a later arriving individual was serviced before them, while the other is pleased by getting serviced earlier. This leads to Larson mentioning that first come, first served is the socially just queue discipline (). Using a pooled queue is exactly this (FCFS) as later arriving vehicles are placed behind others that were already present upon arrival and cannot advance position in the queue until vehicles in front have begun service. Rothkopf and Rech () also noted that they agree with the views of Larson () on the psychology of queuing and that in systems where arrivals cannot jockey for position, which is the case in a terminal setting, pooling may be beneficial. Possible disadvantages of pooling noted in this study are difficulty in choosing servers, difficulty with using specialized servers, and an increase in delay if the previous system segregated jobs by service time. To our knowledge there have been no investigations into whether or not pooling could be beneficial at marine container terminal gates. Previous studies have analyzed such strategies as the appointment system and extending gate hours. However, the simple queuing strategy of using a single lane to serve all of the arriving trucks has yet to be explored. Also, previous studies did not account for trouble transactions, which play a critical role in gate delays. This study used agent-based simulation to evaluate the performance of a pooled queue strategy versus the separate queues strategy. This study also attempted to overcome the shortcoming of queuing theory; that is, lack of consideration of vehicles movements within the queue. This is accomplished by modeling trucks as agents and using a car-following model to simulate the agents behavior. Each truck agent accelerates or decelerates in reaction to the movements of the vehicle that it is following.. METHODOLOGY Netlogo () was chosen as the simulation modeling tool for this study for several reasons. First, being that it is uses a higher level programming language script built on top of Java, which makes it easier and faster to develop models. Second, Netlogo features a built-in animation feature that can be used in either two or three dimensions. Animation allows for quick visual verification that the model is working properly and is excellent for presentation purposes. Third, Netlogo has several useful extension and tools. The most useful of these tools for this study is the BehaviorSpace tool, which allows the user to easily run numerous experiments automatically. BehaviorSpace simply needs the user to input which variables need to be changed and what values to change them to and the tool will run all the combinations of the different variables and output the specified results in either tabular or spreadsheet form.. Components Included In The Simulation Model There are several key components of the gate system that are included in the simulation model:. Gate System Layout,. Truck Arrival Information, TRB 0 Annual Meeting

7 Fleming, Huynh and Xie Gate Service Information, and. Vehicle Interactions. Each of these components will be discussed in detail as to how they were included in the model in the subsequent sections along with the assumptions and simplifications. Some assumptions and simplifications were necessary to make the model tractable... Gate System Layout Input requirements include the number of gates and the number of servers operating. For the purpose of this study the model allows for any number of gates with the assumption that there is always a server operating each gate. However, the model could be easily changed to accommodate the real world scenario where the terminal may not have a server operating each gate. This assumption also means that the model assumes there is an inspection crew for each gate, which again may not be the case in the real world. The model also assumes that all arriving vehicles are directed to a set of gates to complete the necessary transactions... Truck Arrival Information One of the more important components of the simulation model is the hourly truck arrival pattern. Using the data presented in Figure a, an average hourly arrival pattern can be gathered. By averaging the arrival volumes for each hour over the day period we can get an average hourly arrival pattern which is shown in Figure b. When implementing the hourly arrival pattern shown in Figure b, the assumption was made that the arrival rate being generated was the peak arrival rate, which in Figure b is 0 AM. Given that the peak arrival rate was being generated for all hours, it was necessary to eliminate a certain percentage of these vehicles for the non-peak hours in order to reproduce the arrival pattern shown in Figure b. For example, if the simulation model is in the first hour ( AM) then we want to keep vehicles out of the peak vehicles or approximately % of the peak vehicles. TRB 0 Annual Meeting

8 Fleming, Huynh and Xie (a) Transactions AM AM AM 0AMAMAM PM PM PM PM (b) FIGURE Hourly arrival pattern: (a) Sample terminal hourly arrivals (); (b) Simulation input: hourly arrival pattern. The peak hour arrival distribution was assumed to be exponentially distributed and the model allows the user to enter the mean inter-arrival time that is desired. Exponentially distributed inter-arrival times correspond with terminal data collected by Guan (), however one could use another distributions if they wish... Gate Service Information The data used for the service time distributions was collected by Huynh et al. () using webcams located at the terminals. In this study there were 0 observations for normal transaction service times. The data was fitted using Arena Input Analyzer, Minitab, and Easy Fit and all three software reported the best fit distribution to be lognormal with a mean of. and standard deviation of 0.. Netlogo does not include a command for creating a lognormal distributed random variable; however, a lognormal distribution can be created from a normal distribution with a simple transformation using Equations and (). TRB 0 Annual Meeting

9 Fleming, Huynh and Xie ln ln () () From Equations and, using the mean,, and standard deviation,, of the dataset a lognormal distribution can be created using exp (normal (, )). Data was also collected by Huynh et al. () for trouble transactions, but the data was limited as there were only observations. Limited data still gives a rough idea of the trouble transaction distribution and parameters. Arena Input Analyzer showed that the gamma distribution provides a reasonable fit for the trouble transaction times. The parameters for this gamma distribution are an offset of 0, shape parameter of. and a rate parameter of.. These distributions were used to determine the service time of each vehicle depending on whether the vehicle was a normal transaction or trouble transaction... Vehicle Interactions/Movements Within Queues The vehicle interactions modeled in this study simply considered how vehicles followed each other within the queue. It was not necessary to consider lane changing because in reality trucks are likely unable to change lanes when in the queue due to the size of the trucks, lack of maneuverability, and the close proximity of neighboring vehicles. To simulate how vehicles follow one another, a car-following model was used. The car-following model chosen for the simulation model created in this study was the Intelligent-Driver Model (IDM) (). The IDM is composed of the following equations:, (), () The parameters presented in the Equations and are defined in Table along with the values used in the simulation model. TABLE IDM Parameters. Parameter Symbol Definition Value Maximum acceleration.0 ft/s Maximum deceleration. ft/s Desired velocity mph Safe time headway.0 second Jam distance (bumper to bumper) 0 ft Jam distance 0 ft Acceleration exponent Vehicle length 0 ft This particular car-following model was chosen because unlike most other car-following models, it requires little calibration, has intuitive parameters, and has been shown to be a TRB 0 Annual Meeting

10 Fleming, Huynh and Xie 0 reasonable fit to real data. In a study comparing the IDM, full velocity difference model, full velocity acceleration difference model, and the optimal velocity model against real world urban traffic data collected using GPS the IDM was found to significantly outperform the other models (). An advantage of the IDM is that it is more robust and adaptable to different vehicle types and drivers without having to do extensive model calibration as would be the case using most other car-following models.. Netlogo Model Setup Screenshots of both the pooled queue and separate queues models are shown in Figure. The red vehicles are troubled transactions, the ones with yellow containers are export transactions, and the vehicles without containers are import transactions. The vehicle performance characteristics for all the vehicles are identical. In the pooled queue screenshot (top) the yellow gate is a gate that the vehicles stop at to wait on a service gate to become available. The service gates are red when busy and green when they are available. (a) 0 (b) FIGURE Queuing strategies animation in Netlogo: (a) pooled queue strategy; (b) separate queues strategy TRB 0 Annual Meeting

11 Fleming, Huynh and Xie Simulation Logic The model shown in Figure is updated at a user specified time-step, which was 0. seconds for this study. At each time-step the statuses of the model along with any agents currently present in the model are updated. The model generates vehicles according to the inter-arrival distribution and hourly arrival pattern mentioned earlier. Upon generation, the vehicle selects the shortest queue if using the separate queues strategy. Then, the vehicle is positioned behind the last vehicle in the queue with an acceleration and velocity equal to that of the vehicle it is positioned behind. This is done to generate vehicles in the queue as if they are already following the last vehicle in their respective queue. Since the focus of this study was on the behavior of vehicles in the queue, the driving movements prior to joining the queue are neglected. Vehicles in the queue(s) are updated according to the equations,,, and. The position is first updated according to equation and then equations and determine the acceleration for the position update at the next time-step. Finally, the velocity for the next time-step is updated according to equation. In order to update the vehicles in the queue(s) realistically, they must be updated from front to back at each time-step. So, the vehicles in each queue are updated starting with the vehicle at the front and then working back one by one until the last vehicle has been updated before advancing the simulation time. Vehicles in the pooled queue are updated so that the lead vehicle stops at the yellow gate in Figure a to wait for a service gate to become available. Once a service gate becomes available, the lead vehicle immediately moves to the available service gate. It is assumed that there are no conflicts or delays in the queue-to-gate paths. 0. () () Once vehicles reach the service gate and come to a stop, they begin service. The service time is assigned based on the vehicle s transaction type that was assigned when the vehicle was generated. If the vehicle is a normal transaction (non-trouble) then it is assigned a transaction time based on the user input normal transaction time distribution. Similarly, if the vehicle is a trouble transaction then it is assigned a transaction time according to the user input distribution for that transaction type. Upon completion of service, the vehicle immediately exits the system.. SIMULATION RESULTS Several key performance metrics are used to evaluate the performance of the gate queuing strategy. The ones of most interest in this study are the average and standard deviation of the truck queuing times. The average server utilization is also reported along with the average maximum queue length. These last two statistics would be of more interest to both the terminal operator as well as the terminal planners. The results shown in the Table and Figure used the input distributions and parameters specified in the previous section, ten gates, and five percent of arrivals being trouble transactions. The inter-arrival times were varied to simulate varying demands that could possibly occur in real world scenarios. The inter-arrival times were centered around a mean inter-arrival TRB 0 Annual Meeting

12 Fleming, Huynh and Xie 0 time of 0 seconds, which is approximately the mean inter-arrival time of the terminal data collected by Guan () that corresponded to an exponential inter-arrival distribution. TABLE Inter-arrival Variation Results. Mean Interarrival Time (minutes) Gate Queuing Strategy Mean Total Queuing Time (minutes) Mean Standard Deviation of Total Queuing Time Mean Server Utilization Mean Maximum Queue Length (trucks) 0. Separate Pooled Separate Pooled Separate Pooled Separate Pooled Separate Pooled Separate Pooled Separate Pooled Separate Pooled Separate Pooled Percent Improvement in Queuing Times When Using Pooled Queue TRB 0 Annual Meeting

13 Fleming, Huynh and Xie 0.00 Mean Queuing Time (minutes) Pooled Separate Mean Inter arrival Time (minutes) FIGURE Results for variations in mean inter-arrival time. As seen in Table and Figure, using a pooled queue instead of the separate queue strategy has significant benefit in terms of queuing times and standard deviation of queuing times across all of the inter-arrival times simulated. These are highly desirable results, especially a lower standard deviation as truck drivers would prefer to have more predictable queuing times as it would assist in estimating their time spent at the terminal. In terms of server utilization, pooled queue offers more benefit at a lower inter-arrival time, but it is not a significant improvement. The area of concern when using a pooled queue is the maximum queue length. As the system becomes busier, i.e. a lower inter-arrival time, the maximum queue length for the pooled queue grows rapidly and this could lead to traffic congestion problems on the surrounding network. However, if the infrastructure allows for a significantly long queue to exist, then for the scenarios tested it would be of great benefit to use the pooled queue strategy. The frequency of the unfair situation described by Larson () can be quantified for the separate queues strategy. A sample scenario with 0. minute inter-arrival times was chosen to evaluate the unfair situation. The result of 00 simulation runs of this scenario indicated that approximately % of trucks experienced the unfair situation. Other results of interest were how the pooled queue compared to the separate queues strategy under different percentages of trouble transactions and number of gates. Shown in Figures and are results for variations in percentage of trouble transactions and number of gates respectively. The mean inter-arrival time used for the trouble transaction scenarios were 0. minutes and 0. minutes for the number of gates scenarios. The pooled queue strategy offers a lower mean queuing time for both scenarios. TRB 0 Annual Meeting

14 Fleming, Huynh and Xie 0 Mean Queuing Time (minutes) 0 Pooled Separate Percentage of Arrivals That Are Trouble Transactions FIGURE Results for variations in percentage of trouble transactions. Mean Queuing Time (minutes) 0 Pooled Separate Number of Gates FIGURE Results for variations in number of gates. In addition to the variations of interarrival times, percentage of trouble transactions, and number of gates, the sensitivity of the system to some of the key IDM parameters is of interest. Figure illustrates how the queueing time changes with variations in desired velocity, deceleration rate, and acceleration rate. Results show that the pooled queue is relatively insensitive to these IDM parameters while the separate queues strategy is more sensitive to the TRB 0 Annual Meeting

15 Fleming, Huynh and Xie acceleration rate. The sensitivity of these IDM parameters pale in comparison to the sensitivity of the queuing system parameters (inter-arrival time, percentage of trouble transactions, number of gates) shown in Figures,, and. One of the main reasons behind the pooled queue performing better than separate queues lies in how the queue moves in reaction to gates becoming available. Trucks in separate queues advance one spot in the queue each time a truck in front completes service. However, with the pooled queue strategy, multiple gates can become available rapidly and since all gates are pulling trucks from a single queue, the lead truck may not need to stop as the gates are becoming available. This leads to situations where trucks in the pooled queue can advance multiple spots in the queue before coming to a stop. To investigate this effect, the acceleration and velocity profiles were created for a truck arriving at the end of the pooled queue. Figure shows the acceleration and velocity profiles of the 0 th truck joining the pooled queue. Looking at these profiles, one can notice that there are not stop-and-go cycles, which is the case with the separate queues strategy, and that the velocity peaks are of different values. This is because trucks are advancing multiple spaces within the queue or the entire queue may be moving. This result may not always be the case when using the pooled queue as it is dependent upon the system setup. TRB 0 Annual Meeting

16 Fleming, Huynh and Xie Mean Queuing Time (minutes) Mean Queuing Time (minutes) Mean Queuing Time (minutes) Desired Velocity (miles per hour) (a) 0 Deceleration Rate (ft/s ) (b) Acceleration Rate (ft/s ) Pooled Separate Pooled Separate Pooled Separate (c) FIGURE Sensivity analysis of queuing time with respect to IDM parameters: (a) desired velocity; (b) deceleration rate; (c) acceleration rate. TRB 0 Annual Meeting

17 Fleming, Huynh and Xie (a) 0 (b) FIGURE Sample truck performance profiles while in pooled queue: (a) acceleration profile; (b) velocity profile.. SUMMARY AND CONCLUSION In this study, a simulation tool for investigating the possible benefit of using a pooled queue strategy at marine container terminal gates has been created. Through the use of a car-following model that is incorporated in the agent-based simulation model, the movements of agents (i.e. trucks) within the queue are captured realistically. The model can be applied to any terminal where all arriving trucks undergo either the typical separate lanes setup or a pooled lane setup. TRB 0 Annual Meeting

18 Fleming, Huynh and Xie The model allows the user to have complete control over the number of gates, arrival and service distributions, percentage of arrivals that are trouble transactions, and truck performance characteristics. The comparison results between the pooled queue and separate queues strategies show the pooled queue offers lower average truck waiting time. In addition, pooled queue offers more predictable queuing times, which is highly desirable especially from the truck drivers viewpoint. As mentioned earlier, these results may not always be the case for all terminals; it is dependent on the gate setup and the other user inputs that are available in the simulation model. However, based on the results from this study, terminal operators and planners should consider using a pooled queue at their terminal. The major contribution of the work is the development of a simulation model that can be easily adapted to many real world terminal setups to evaluate the performance of the pooled queue strategy and the insights into how the pooled queue performs in terminal setting. Based on the results from this study, the pooled queue strategy could greatly improve customer satisfaction at terminal gates with lower queuing times and more predictable queuing times. The pooled queue strategy should also help reduce emissions and noise released from the terminals. The model created does have limitations, one of which is that it can be very time consuming to run at lower inter-arrival times. This is due to the fact that a lower inter-arrival time generally means that there are a higher number of trucks (agents) present in the system, which means more computations and therefore longer computation times. For example under a scenario of ten gates, percent trouble transactions, the parameters and distributions specified earlier, and a mean inter-arrival time of 0. minutes the separate queues strategy requires. minutes to complete 00 replications while the pooled queue strategy requires. minutes. Another limitation of the model is that it does not take into account the different driver characteristics. The model assumes that all drivers in the system are identical; however, this is certainly not the case in reality. In reality, drivers have different characteristics such as reaction times and acceleration and deceleration rates. An aspect of the gate system that was not modeled is the queuing that takes place before the container terminal opens. Trucks tend to arrive before operating hours so that they can receive service as early as possible. This can lead to significant queues forming before the terminal opens. This study only considered one specific section of the container terminal, the inbound gates. However, the queuing strategy at the inbound gates can have a significant impact on the surrounding roadway network. As mentioned in this study, the pooled queue can extend to great lengths depending on the efficiency of the current gate system and could therefore lead to the queue spilling over onto the surrounding network. This of course depends on the terminal setting and infrastructure that is in place. Future research should consider extending this model to accommodate a small network and allow analysis of the traffic impact of the gate queuing strategy on the surrounding network. Consideration should also be given to the possible impact of the gate strategy on the other sections of the terminal. As mentioned earlier, all sections of the terminal are dependent on one another. Faster service of trucks at the gates could create a queue in the terminal s container yard if the existing equipment is not capable of servicing these trucks in a timely manner. Additionally, the IDM parameters used in this study were based off engineering judgment and typical values used in design. However, in the actual terminal setting these values may be different. Detailed acceleration and velocity data could be collected in the terminal setting and be used in the simulation model. TRB 0 Annual Meeting

19 Fleming, Huynh and Xie ACKNOWLEDGEMENTS The authors are grateful to Dr. Martin Treiber for his assistance with the Intelligent Driver Model and implementation of it in the developed simulation model. TRB 0 Annual Meeting

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