 Proceedings of Engineering and Technology Innovation , vol. 3, 2016, pp. 34 - 36 34 Mitigating Initialization Bias in Transportation Modeling Applications Wonho Suh * Department of Transportation and Logistics Engineering, Hanyang University, Ansan, Korea . Received 30 January 2016; received in revised form 14 February 2016; accept ed 08 March 2016 Abstract Traffic simulat ion model is a useful tool to evaluate real world transportation solutions in a risk free environ ment. Traffic simu lation model requires some form of initia lization before their outputs can be considered meaningful. Models are typically init ialized in a particula r, often “empty” state and therefore must be “warmed-up” for an unknown a mount of simu- lation time before reaching a “quasi-steady-state” representative of the systems’ performance. The portion of the output series influenced by the arbitrary init ia lization is refe rred to as the in itia l transient and is a widely recognized proble m in other areas, but less emphasized in the tran s- portation application. After reviewing methods of accounting for the initia l transient bias, this paper selects and evaluates three techniques; two popular methods from the genera l simu lation fie ld, Welch’s and MSER method, and one from the current state of the practice in the transpo r- tation application, Vo lu me Ba lancing. VISSIM models were created to compare the selected methods. After presenting the results of each method, advantages and criticis ms of each are discussed as well as issues that arose during the imple mentation. It is hoped that this paper in- forms the current practice in transportation ap- plication as to how to account for the in itia l transient in order to continue facilitating mean- ingful and reliable results. Ke ywor ds : traffic simu lation, in itia lizat ion bias, Simulation analysis 1. Introduction Traffic simu lation mode ling has become an increasingly vital instrument for the transport a- tion analysis. Traffic simu lation modeling pro- vides the flexibility to manipulate conditions that could influence network operations in a risk-free environ ment, allow ing for co mple x network ana lysis, testing assumptions and pos- sible outcomes to determine their potential for imple mentation [1]. There a re a nu merous means to employ traffic simulat ion modeling to aid in the analysis and decision ma king process. Thus, it is e xtre me ly impo rtant that the simula - tion output is both meaningful and reliable. One area often overlooked in transportation is guidelines to govern the init ialization of tra ffic simulation models [2]. The simulat ion start-up problem is of sig- nificant interest and has been widely studied in simu lation re lated fie lds [3]. When a model is initia lized in a condition uncharacteristic of steady-state of the real-world condition it is attempting to represent bias may be introduced in the simulation’s output. The bias can in turn lead to inaccurate results and possibly faulty conclusions [3]. There are two categories of methods for mitigating the initia lization bias problem. The most common approach is truncation, or dis- carding the initia l data influenced by the starting conditions. The second approach is intelligent initia lization, o r starting the model in a state with a high probability o f be ing equilibriu m/steady state. However, it is not always convenient or even practical to start the simulat ion in steady state [2]. More importantly, determin ing equilibriu m a priori in a tra ffic simu lation model can be difficult and arbitrary. For e xa mp le, determining a priori how many vehic les to queue at each signal, where to place all the vehicles on a link, and what init ial speed may be nearly impossible in many instances. The need to eliminate initia lization bias, also known as the start-up problem, is a wide- ly-recognized challenge with simu lation analy- * Corresponding author. Email: iamwonho@gmail.com Proceedings of Engineering and Technology Innovation , vol. 3, 2016, pp. 34 - 36 35 Copyright © TAETI sis [3]. Th is occurs because non -terminating simu lations do not have predefined run lengths or in itia l conditions. The simulat ion processes must be initia lized arb itrarily, wh ich creates bias in steady-state parameter estimates. Although methods of re moving init ialization bias e xist, there is currently no largely accepted method that performs suitably in all applicat ions. Add i- tionally, there is an overall negligence of the initial transient problem in practice [2]. The purpose of this paper is to exa mine and evaluate the effectiveness of several techniques used for eliminating initia lization bias fro m transportation applications. 2. Method Methods used to mitigate init ialization b ias attempt to inform the treatment of data affected by the initial transient for discrete, stochastic simu lation models. And as a result these methods seek to provide more accurate, mean- ingful and re liab le results for simu lation output. The methods can be grouped into the following categories as described by Robinson [4]: graphical, heuristic, statistical, in itia lizat ion bias testing, and hybrid methods. 2.1. Graphical Methods The most common methods to identify the initia l transient are graphical procedures [4]. Graphica l procedures consist of a visual inspec- tion of the output time series to determine the e xtent of the initia l transient. A major advantage of the graphica l method is its simp licity and the reliance on few assumptions. A disadvantage is that these methods are typically highly subjec- tive and the truncation points could vary based on the analyst’s judgment. Fish man’s and Welch’s method are two are exa mp les of graphical methods. 2.2. Heuristic Methods Heuristic methods provide definitive rules or formulas to determine the length of the warm-up period [4]. The advantages of these methods are lack of user specific subjectivity, eas e of im- ple mentation, and only a few assumptions are generally needed. Marginal Standard Erro r Ru le (MSER), Conway’s Rule , Crossing of the Means Rule , and Replicated Batch Means are catego- rized as Heuristic methods. 2.3. Statistical Methods Statistical methods rely on statistical princi- ples to determine the wa rm-up period [4]. Dis- advantages tend to include the comple xity of these procedures, constraining assumptions, and increased computing time . Randomization Test, Welch’s Regression-Based Method, N-Ska rt, and Automated Simulat ion Analysis Procedure (ASAP) fall into this category. 2.4. Initialization Bias Testing The goal of in itia lizat ion bias testing is to determine if bias is present in the data due to the initia l transient. The ma jority of these metho ds build upon the work of Schruben [4]. The esti- mates of the mean and variance are used to compute a test statistic which is co mpared to an appropriate F distribution [ 5]. Hypothesis test- ing is performed with the null hypothesis that no initia lization bias e xists. These procedures can also be used in union with previously described methods to determine if in itia lizat ion bias has been successfully removed. 2.5. Hybrid Methods Hybrid methods are typically a co mbination of two methods, usually in itia lizat ion bias tes t- ing method and either a graphica l or heuristic method. These methods are typically co mple x and can require large amounts of data [4]. 3. Results and Discussion Hoad et al. performed a comprehensive re- view on the e xisting methods of estimating the length of the warm-up period and found 42 methods for detecting the extent of the wa rm-up period [6]. These methods were evaluated and graded based on the following crite ria : accuracy and robustness of method, simp licity o f the method, ease of potential automat ion, generality, number o f para meters required, and co mputation time [7]. The list was then narrowed down to six methods for further evaluation. Graphica l methods were e xc luded due to their need for human intervention and their subsequent inabil- ity to be automated. Of the six methods, MSER substantially outperformed the rest while the other methods either severely underestimated the truncation point or required an e xtre me ly large number of computational resources. Proceedings of Engineering and Technology Innovation , vol. 3, 2016, pp. 34 - 36 36 Copyright © TAETI As the research team looks to info rm trans- portation analysts as to how to mitigate init ia li- zation bias, the team investigated detailed anal- yses of three available truncation methods. The methods selected were We lch’s Method, due its simp lic ity and use in practice, MSER, for its effectiveness in identifying the truncation point and use in industry, and the volume method that is currently being use in a couple of traffic ap- plications . It was found that Welch’s Method and MSER method provide co mparable results for the truncation points for when the simulation model has reached steady-state. The results from imple menting these procedures indicate that 1) Welch’s Method would be easy to imple ment in practice and 2) MSER method, which selects the truncation point by selecting the point that minimizes the width of the confidence interval about the truncated sample mean, provides co n- sistent results with possibility to be fully aut o- mated. For the M SER method the truncation point can be determined based on each replicate run, while Welch’s approach gives a single trunca- tion point that is determined fro m and can be applied to all replications. The MSER method has the potential to be a robust and useful tool since it can be included in large automated rep- lication process without human interpretation. 4. Conclusions The goal of this research is to explore d if- ferent methods of mit igating in itia lizat ion bias for transportation applications. The in itia liza - tion bias proble m has often been neglected in practice and when unaccounted for it can yie ld inaccurate, unreliable and less meaningfu l re - sults. Throughout the process of imp le menting in- itia lizat ion bias minimization procedures, sev- eral issues arose. Overall, it is also important to have the analyst involved in the decision so that the decision can be made acco rding to the ob- jective of the study and the application model. Acknowledgement This work is supported by a grant NRF-201 4R1A 1A2054793 and Transportation & Logist- ics Research Progra m 15CTAP-C097344 of Ko rean government. References [1] D. Ni, “A fra me work for new generation transportation simulation,” Proc. IEEE, Winter Simu lation Conference, Monterey, CA, 2006. [2] S. Taylor, “Analy zing methods of mit igat- ing initia lization bias in transportation sim- ulation models ,” Master thesis, Depart ment of Civil and Environ mental Engineering, Georgia Institute of Technology, Atlanta, Georgia, USA, 2010. [3] A. M. Law and W. D. Ke lton, “Simu lation modeling and analysis ,” 4th ed. Ne w York: McGraw-Hill Se ries in Industrial Eng i- neering and Management Science, 2007. [4] S. Robinson, “A statistical process control approach to selecting a warm-up period for discrete-event s imu lation,” European Journal of Operational Research, vol. 176, no. 1, pp. 332-346, Jan. 2007. [5] J. White, K. Preston, M. J. Cobb, and S. C. Spratt, “A comparison of five s teady-state truncation heuristics for simulation,” Proc. Winter Simu lation Conference, Orlando, FL, 2000. [6] K. Hoad, S. Robinson, and R. Davies , “Automating warm-up length estimation,” Proc. Winter Simulat ion Confe rence, Mi- ami, FL, 2008. [7] N. M. 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