CALIBRATION OF A TRAFFIC MICROSIMULATION MODEL AS A TOOL FOR ESTIMATING THE LEVEL OF TRAVEL TIME VARIABILITY

Transcription

1 Advanced OR and AI Methods in Transportation CALIBRATION OF A TRAFFIC MICROSIMULATION MODEL AS A TOOL FOR ESTIMATING THE LEVEL OF TRAVEL TIME VARIABILITY Yaron HOLLANDER 1, Ronghui LIU 2 Abstract. A low level of day-to-day variations in travel time is a major feature of a reliable transport system. There is a growing need for credible tools that can predict the extent of travel time variability. We present methodology for using a traffic microsimulation model as such tool, through a special calibration procedure. Various issues, relating to the variability of simulation outputs and to the concept of using this variability to replicate observed travel time fluctuations, are discussed. To test the proposed calibration methodology, its ability to reproduce various distributions of travel times is examined. 1. Background Is has been widely agreed in recent years that the reliability of a transport system is a crucial issue in the appraisal and the design of proposed schemes. A reliable transport system is characterized by a low level of unpredictable travel time variability (TTV). Much research work has concentrated on the effects of TTV on system performance and users behaviour, but implementation of these models can only be effective if it is based on a credible prediction of the extent of variability itself. This paper discusses the use of a traffic microsimulation model as a tool for predicting TTV. It is part of an on-going research, carried out in the Institute for Transport Studies at the University of Leeds, that includes development of both demand-side and supply-side models of TTV. 1 Institute for Transport Studies, University of Leeds, 41 University Road, Leeds, LS2 9JT, United Kingdom, yholland@its.leeds.ac.uk. 2 Institute for Transport Studies, University of Leeds, University Road, Leeds, LS2 9JT, United Kingdom, rliu@its.leeds.ac.uk.

2 524 Y. Hollander, R. Liu 2. Predicting the level of travel time variability In the traditional transport literature, tools for predicting TTV gained much less attention than tools for predicting the mean travel time. We bring a review of exiting mathematical tools that explicitly try to model TTV [10, 11 and many others], and show that most of them are aggregate models, in which the extent of TTV is expressed as a function of macroscopic variables such as the mean travel time. Such expressions are calibrated based on empirical travel time measurements, but they usually lack the ability to explain or predict TTV in other circumstances but those that were used for their calibration. In the current paper we propose methodology for a disaggregate prediction of TTV, whose explanatory power derives from the detailed, microscopic modelling of the performance of individual vehicles, drivers and passengers. The concept of microscopic traffic modelling seems naturally fit for predicting TTV, because most of these models take account of the random nature of traffic phenomena, and of the heterogeneous composition of the population of travellers; these are clearly some of the main causes for TTV. At first glance, one might be tempted to think that estimates of TTV can be derived directly from the output of the simulation runs, by simply analyzing the level of variation among the results. We claim that this is not the case; even if a microsimulation model is proved to be able to yield credible estimates of mean travel times, there is no foundation to the assumption that the distribution of model results replicates the real distribution. Using a microsimulation model as a tool for predicting TTV required a purposely-defined methodology for calibration and validation, which focuses on the distribution of model results. 3. Variability in microsimulation outputs Methodologies for calibrating and validating traffic microsimulation models have been discussed in several recent publications [2, 3, 5, 6, 8, 9, 14], but there has not been sufficient emphasis on the use of microsimulation for analysis of the distribution of the results rather than the mean. Some of the existing calibration methodologies do consider the distribution of outputs, when verifying the match between simulated and observed measurements [4, 7, 12]; but we find that some confusion exists between different types of variation. We distinguish between three dimensions of variability in simulation results: Spatial variability, i.e. variation between measurements taken in different places at a single time point. Temporal variability, i.e. variation between measurements taken in the same place at different time points. Stochastic variation of measurements taken in the same place and same time point, between different model runs. We discuss the different causes of each of these types of variability; we illustrate how existing methodologies mainly refer to spatial or temporal variability, while the relevant definition of TTV for many applications is more similar to the stochastic variation. We show that there is a case for using stochastic TTV between model runs to replicate the random element of day-to-day TTV. We also elaborate on the flexibility in determining whether some sources of TTV, such as accidents and roadside activity, are directly

3 Calibration of a traffic microsimulation model 525 modelled; we comment on the way this should be taken into consideration in the discussed methodology. The proposed procedure aims at calibrating a microsimulation model, i.e. adjusting the values of its input parameters, in a way that will make the distribution of travel times, obtained from a series of model runs, a credible estimate of day-to-day random TTV. A main concept in this procedure is that each run of the simulation represents a single day; the procedure tries to assure that the properties of the calibrated model fix the randomness of the model results at a similar level to the actual randomness of the observed transport system. 4. Formulation of the calibration methodology Prior to the detailed discussion of the calibration procedure, we review the required input data. We stress that compared to other calibration procedures of microsimulation models, the proposed procedure does not allow flexible use of other measures of performance but travel times; nevertheless, we clarify that various definitions or scales of travel time measurements are acceptable. To calibrate the microsimulation model we define an objective function that expresses the difference between the observed and simulated travel time distributions. The calibration procedure aims at minimising the value of the objective function. We present the main stages in the procedure. The solution approach is based on the Multidimensional Downhill Simplex Method, attributed to Nelder and Mead [13]. In this method, each feasible set of the parameters we wish to calibrate is represented by a point in a multidimensional space; a simplex is a geometrical figure whose vertices are such points. In each iteration of the solution process the simplex is modified, till we can use any of the vertices as a satisfactory solution. We also illustrate that one of the manipulation types used in the original Downhill Simplex Method is not suitable for a multidimensional problem as the current one. We discuss practical ways to improve the performance of this procedure without using the unsuitable element. It should be noted that the parameter set found by our proposed methodology is not a global optimum; its uniqueness is not guaranteed, as discussed by Adamski [1]. However, given the complicated, multidimensional nature of the calibration of microsimulation models, there is value in improving the parameter set even if the optimum is local. We are aware of many applications of microsimulation models where no systematic calibration whatsoever has been performed. We also propose a subtle extension to the calibration procedure, which involves modifying the overall level of travel demand before each run of the model. Fluctuations in the daily travel demand are one of the causes of TTV; trip matrices and traffic flow data that are normally used as an input for the microsimulation model are mean values, that do not account for this source of variation. If some information is available regarding the magnitude of these fluctuations, using this extension of the calibration methods might improve the explanatory power of the calibrated model. It should be noted, however, that this also complicates the model implementation, since modification of the total demand will also be required before each run of the calibrated model whenever it is used. If the calibration procedure is used with a fixed level of demand, variations in travel time caused

4 526 Y. Hollander, R. Liu by the daily-changing amounts of traffic are treated as part of the unexplained, random TTV; the resulting model is acceptable but its ability to forecast different levels of TTV in situations with different levels of demand fluctuations is reduced. 5. Implementing the methodology Application of the presented calibration methodology is not limited to any particular microsimulation software or model. We demonstrate such application using the DRACULA model, which is widely used in the UK. For the calibration experiments we use a simple network, representing a small section of the urban network in the city of York, England. To examine the ability of the proposed methodology to turn a microsimulation model into a tool for predicting TTV, we create a series of scenarios; in each scenario, day-to-day TTV follows a different distribution. We investigate whether appropriate calibration fixes the TTV between model runs at a level that can be seen as a satisfactory replication of the actual TTV patterns in all scenarios. 6. Conclusions We conclude with a discussion of some insights and findings relating to the following issues: The general fit of traffic microsimulation models as tools for predicting the extent of TTV. The different dimensions of TTV in traffic analysis. Contribution of the proposed method in the relatively new field of traffic microsimulation calibration. The ability of the calibration process to capture differences between different patterns of TTV. References [1] A. Adamski. Intelligent Entropy-Based Traffic Control. Proceedings of the 9 th Mini- Euro Conference: Handling Uncertainty in the Analysis of Traffic and Transportation Systems, Bari, Italy, [2] J. Barcelo and J. Casas. Methodological Notes on the Calibration and Validation of Microscopic Traffic Simulation Models. Proceedings of the 83 rd TRB annual meeting, Washington, D.C., [3] M. E. Ben-Akiva, D. Darda, M. Jha, H. N. Koutsopoulos and T. Toledo. Calibration of Microscopic Traffic Simulation Models with Aggregate Data. Proceedings of the 83 rd TRB annual meeting, Washington, D.C., 2004.

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