Demiryolu ağında trafik sayımlarından O-D matrisi tahmini

Başlık çevirisi mevcut değil.

Tez No: 75589
Yazar: ZEYNEP AĞCI
Danışmanlar: PROF. DR. HALUK GERÇEK
Tez Türü: Yüksek Lisans
Konular: İnşaat Mühendisliği, Civil Engineering
Anahtar Kelimeler: Belirtilmemiş.
Yıl: 1998
Dil: Türkçe
Üniversite: İstanbul Teknik Üniversitesi
Enstitü: Fen Bilimleri Enstitüsü
Ana Bilim Dalı: Ulaştırma Ana Bilim Dalı
Bilim Dalı: Belirtilmemiş.
Sayfa Sayısı: 113

Özet

İçerikte yolculuk matrisi tahmini için ucuz bir yöntem olan trafik sayımlarının kullanım olasılığı geleneksel yöntemler yoluyla tartışılmıştır. Böylesi tahmin için üç grup tanımlanmıştır. Birincisi, yolculukların çekim tipi modelini izlediğini ve problemin gözlenen sayımlardan modelin parametrelerini kalibre ederek azaltılacağını varsayar. Bu teknik çekim modelini varsayılan formuna bağlı olarak lineer ya da non-lineer regresyon çözümlerine yöneltir. İkinci grup yöntemler Wardrop'un birinci ilkesini baz alarak şebeke dengeleme yaklaşımıyla O-D matrisini tahmin eder. Üçüncü grup gözlenen akışlarla oldukça uyumlu yolculuk matrisinin entropi maksimizasyon yolunu izler. İlk grupta yer alan lineer modellerden çekim modeli 1995 yılı verileri baz alınarak uygulama yapılmıştır. Çekim modeli, zonların nüfusları ve mesafeleri baz alınarak uygulanmıştır. Yöntem VMAT ulaşım paket programı üzerinde denenmiştir. İlk aşamada her O-D çifti arasındaki yolculuk olasılığı tanımlanmıştır, ikinci aşamada eldeki trafik sayımlarından veri dosyası elde edilmiştir. Son aşamada ise, rota olasılıkları ve her bölgedeki trafik sayımlarından en muhtemel yolculuk matrisi oluşturulmuştur. Ancak bu denemelerde genelleştirilmiş maliyet değil sadece mesafe esas alınmıştır. Sonuçta, her yaklaşımın avantajları tartışılmış, teknikleri ve uygulama alanları tanımlanmıştır. Eldeki veriler kontrol edildiğinde hangi noktaların yetersiz kaldığı açıklanmıştır.

Özet (Çeviri)

Following a review of conventional methods for estimating a trip matrix, the possibility of using cheaper methods based on traffic counts is discussed. Threee broad groups of models for such estimation have been identified. Counting traffic is a relatively cheap and non-disruptive way of collecting data about a transport system. There is a good case for using counts to increase our knowledge of the system. In general though, they do not provide enough information to determine uniquely the trip matrix which has generated them. The first one assumes that trips follow a gravity type pattern and the problem is reduced to calibrating the parameters of such a model from the observed counts. Depending on the assumed form of the gravity model this technique leads to linear or non-linear regression solutions. The second group of models attempts to estimate the O-D matrix through a network equilibrium approach based on Wardrop's first principle. The third group follows an entropy maximising approach in which the most likely trip matrix compatible with the observed flows is sought. The use of an entropy maximising approach enables one to estimate the most likely trip matrix consistent with the information available (counts). The use of this approach for the proportional asssignment case is described in this paper. Then, the way in which other information can be used to improve the estimated trip matrix is discussed. A particular application of this problem is updating of an old origin destination matrix. Finally, the problem for the equilibrium assignment case is discussed and a simple solution is presented. Finally, the advantages of each approach are discussed and the most promising technique and areas of application are identified. OBJECTIVES In this paper, a model is described that will under certain circumstances yield the most likely origin-destination matrix which is consistent with measurements of link traffic volumes. Given knowledge of the proportionate usage of each link by the traffic between each zone pair, the model parameters scale each element of a prior estimate of the origin-destination matrix up or down so that the measurements of link traffic volumes are reproduced. The fitted values are shown by example to be invariant to the application of uniform scaling to the prior estimates. A Newton model fittingprocedure is outlined. In reality, measurements of link traffic volumes are random variables and the proportionate usage of links by the traffic for each zone pair is not known with certainty. An expression is derived for the variances and covariances of the logarithms of the fitted values in terms of the variances and covariances of the measured link volumes, taking the proportionate usage of links as given. The expression permits the calculation of asymmetric confidence intervals for the elements of the fitted origin-destination matrix. For a large number of applications the existence of a reliable and relatively inexpensive method for estimating O-D matrices would be very valuable. For example: - modelling transport demand in towns - modelling assessment and design of traffic management schemes in rural and urban areas - cross-checking other methods - updating old O-D matrices - modelling rural or inter urban transport demand in sparsely populated areas. - modelling transport demand where other data is non existent, unreliable or out of date as perhaps in developing contries. At this stage we are almost exclusively concerned with journeys by railways, as are all the methods reviewed here. The plan of this report is as follows: The remainder of this section one briefly reviews current methodologies for the estimation of O-D matrices. This is followed by a discussion of some basic concepts like trip generation, distribution and assignment models. The Section is closed with a comment on the practical and theoretical problems of estimating a trip matrix from counts. Section two reviews the first group of techniques, namely linear models. Section three discussed an extension of these into non-linear models. Section four describes methods based on the assumption of equilibrium assignment and Section five discusses entropy maximising models. Finally Section six compares the theoretical and practical implications of these four groups of models and makes some recommendations for practical applications. INTRODUCTION Conventional methods for collecting origin-destination information form, for example, home or roadside interviews tend to be costly, labour intensive and timedisruptive to the trip makers. The problem is even more acute in developing countries, where rapid changes in land use and population shorten the 'shelf-life' of data. The need for developing low cost methods to estimate the present and future O-Dmatrices is apparent. Traffic counts can be seen as the result of combining a trip matrix and route-choice pattern. As such, they provide direct information about the sum of all O-D pairs which use the counted links. Traffic counts are very attractive as a data source because they are non-disruptive to travellers, they are genarally available, they are relatively inexpensive to collect, and their automatic collection is well advanced. The idea of estimating trip matrices or demands models from traffic counts deserves serious consideration and the last decade has seen the development of a number of approaches attempting just that. Consider a study area which is divided into N zones inter-connected by a road network which consists of a series of links and nodes. The trip matrix for this study area consists of N2 cells, or (N2-N) cells if intra-zonal trips can be disregarded. The most important stage for the estimation of a transport demand model from traffic counts is to identify the paths followed by the trips from each origin to each destination. The variable paij İs used to define the proportion of trips from zone i to zone j travelling through link a. Thus, the flow (Va) in a particular link a is the summation of the contributions of all trips between zones to that link. Mathematically, it can be expressed as follows: Va = ?TijPaij 0?paij ?1The variable pa can be obtained using various trip assignment techniques ranging from a simple all-or-nothing to a more complicated equilibrium assignment. Given all the paij and all the observed traffic counts (Va), there will be N2 unknown Tij/s to be estimated from a set of L simultaneous linear equations, where L is the total number of traffic counts. In principle, N2 independent and consistent traffic counts are required in order to determine uniquely the trip matrix T. In practise, the number of observed traffic counts is much less than the number of unknowns Tij/s. Therefore it is impossible to determine a unique solution to the matrix estimation problem. In general, there will be more than one trip matrix which, when loaded onto the network, will reproduce (satisfy) the traffic counts. There are two basic approaches to resolve this problem; structured and unstructured methods. In the structured case, the modeller restricts the feasible space for the estimated matrix by imposing a particular structure which is usually provided by an existing travel demand model, for example a gravity or direct- demand model. The unstructured approach relies on general principles like maximum likelihood or entropy maximisation to provide the minimum of additional information required to estimate a matrix. These two general approaches will be discussed, but first we must consider the relationship between route choice and model estimation.Conventional techniques for collecting origin-destination (O-D) information (home and roadside interviews, number plate surveys, and so on) tend to be expensive in terms of time, disruption, labour and other photography, imply sampling, data collection and coding errors in addition to seasonal, daily and hourly variations. The possibility of being able to estimate (and update) trip matrices from readily available and/or low cost data is particularly attractive. The author has developed a model to estimate an O-D matrix from traffic counts based on an antropy maximising framework. Under suitable conditions it can be said to estimate the most likely trip matrix consistent with the information contained in the traffic counts and a prior (or old) matrix if available. The model requires the assumption that it is possible to identify the O-D pairs using each counted link independently from the matrix estimation process. This may be a reasonable assumption whenever congestion does not play the main role in route choice. If this is not the case, the model needs modification. This model reports on validation tests with the model using both simplistic and capacity restrained route choice models. The data set used covered the central area of Reading in the UK. Two extensions to the congestions network case are discussed and evaluated. One of them, based on independent path flow estimation, was found to perform better than any other route choice model within the adopted framework. The final section of this paper presents some general conclusions about the use of the model. There has recently been considerable interest in methods for estimating the most likely origin-destination (O-D) matrix (sometimes referred to as a trip table) from measurements of traffic volumes on the links in a network. Although it is possible to obtain O-D information directly by surveying trip makers (using, for example, household, workplace or roadside interviews), this tends to be both costly and labor intensive. By contrast, measurements of traffic volumes on links in a network can be made relatively inexpensively and, when automatic traffic conters are used, very little labor is required. Moreover, it is not necessary (as it is, for example, in the case of a roadside interview) to stop vehicles, so the associated risk of causing a disruption to traffic (possibly also resulting in a modification of its distribution) is avoided. Some early approaches to the inference of an O-D matrix from measurements of link traffic volumes have been reviewed by WILLUMSEN. JÖRNSTEN AND NGUYEN have described an approach based on equilibrium traffic assignment which subsequently formed the basis of a program developed by the U.S. DEPARTMENT OF TRANSPORT. VAN ZUYLEN AND WILLUMSEN have developed closely related models for the estimation of an O-D matrix, Van Zuylen using information minimization and Willumsen entropy maximization. The associated problem of inferrring turning movements within an isolated junction given measurements of traffic volumes on the approach roads has also received attention (BEIL, CREMER AND KELLER, HAUER ET AL.). However, this problem is qualitatively different since only for an isolated junction is it generally true that flows entering and leaving the network can be measured by traffic counts.A further model for the inference of an O-D matrix from link traffic volumes, originally suggested by VAN ZUYLEN in order to overcome anomalies encountered with earlier models, is given a probabilistic derivation. This new model, unlike the earlier models, generates an estimated O-D matrix that is always invariant to the application of uniform scaling to the prior estimates. In common with the earlier models, a matrix of route choice proportions is required to be known. In practise, such a matrix may be hard to obtain. In the absence of direct observations, an assignment algorithm will have to be used. This problem has been discussed elsewhere. Making use of the matrix of route choice proportions, some proporties of flow within a complex network, namely linear dependency and correlation, are examined. Linear dependencies are used to reduce the number of model parameters to be fitted. A Newton model fitting procedure is described, and some results concerned with the convergence of the procedure are given. An expression for the approximate variances and covariances of the logarithms of the fitted values (the estimated origin-destination movements) is derived assuming that route choice proportions are fixed but allowing link volumes to be random variables. The expression takes correlations between link volumes into account. Following POTTS AND OLIVER, the transport network is characterized by a graph of nodes connected by either directed or undirected links. Geographical areas which generate or attract traffic are represented by zone centroids, which are connected to the nodes of the graph by centroid connectors. Nodes which are not connected in this way to zone centroids are referred to as intermediate nodes. The level of resolution of the representation of the transport network can be adjusted to fit the available data. For example, when information about turning movements at junctions is available, these movements can each be represented by a link in the graph. It is therefore possible to associate with each movement within the transport network about which there is some information a particular link in the corresponding graph. A small number of models has been suggested to estimate an origin-destination trip matrix from network data. Most of the models reduce the problem to that of calibrating a generalised gravity model from observed link follows; see for example Low (1972), Holm et al (1976). This approach produces a gravity model whose parameters are such that a measure of the difference between observed and synthesised link flows is minimised. A survey of these methods can be found in Willumsen (1978). But a gravity model, even a very flexible one, may not be a sensible assumption about travel behaviour in certain cases. A typical example of this is an inner city, or any other study area, where an important proportion of the trip length takes place outside its boundaries. This paper discusses a family of models, based on an entropy maximising approach, which I claim provides a better basis for the estimates of an O-D matrix. A main problem in traffic planning lies in the forecasting or up-dating of origin- destination flow surveys. The expenditure of the survey necessary for the traffic matrix is not only great in time but is also financially great. For this reason such surveys are very rarity repeated in cycles of a few years. That is why a traffic surveymatrix for a specific area will be used for several years or, in some cases for more than a decade, as an important basis for planning. To overcome this problem a method of up-dating based on estimation, which, depending on the prepared data, is flexibly applicable. The estimation method is based on“Minimum Information Principle”which can be generally applied and is not only restricted to traffic matrices. The method can also be combined with the section models of the modal-split and route- choice (traffic assignment). It must be recorded that the traffic distribution obtained by the well-known“Detroit model”method represents a special case of the estimation method achieved by the“Minimum Information Principle”. In this model, a new matrix is established, through a certain distribution of the matrix by an iterative proportional adaptation, from which only the vektors of the originating and terminating trips are known. In the following section the model example of the traffic matrix for the city of Graz has been taken to explain this method. DISCUSSION The main advantages and disadvantages of each group of models will be discussed here. We will consider applications in three types of areas - Inter urban or rual areas - Free standing urban areas - Sub or inner areas inside an urban area. We shall discuss each group of models in term but we must admit, from the outset, that little can be said about the relative accuracy of the proposed methods of estimating a trip matrix. In effect, very few tests have been made with real data and in these cases all comparisons have been made against observed link flows and not against a“real/observed”O-D matrix. Nevertheless, something can be said about the most promising models and areas of application form theoretical considerations. In particular we shall discuss each model in terms of - the conditions under which the assumptions are likely to be acceptable - the amount of extra data (in addition to traffic counts) required - internal consistency - their eventual use for forecasting purposes and not just short term estimation of a trip matrix- their flexibility for incorporating information already available about trip making behaviour. A MODEL is developed in this paper that yields the most probable set of O-D movements that are consistent with a set of link flows if the probabilities obtained from the prior estimates are corrected. In practise, the prior estimates might be based on an old survey that may not correctly reflect current probabilities. If this is so, or if there is no basis on which to obtain prior estimates (in which case a uniform value has to be adopted), it seems unlikely that the model will yield the most probable set of O- D movements consistent with link flows. As demonstrated, at least some of the fitted values may be sensitive to changes in the prior estimates. In practise, traffic counts are likely to be available for a set of links which include some whose volumes are linearly dependent on the volumes of the others within the set. When inconsistency arises, it is possible to remove it by adjusting the observations using a maximum likelihood criteria (see Van Zuylen and Willumsen and Van Zuylen and Branston), thus incorporating the additional information. However, it would in principle be preferable to fit the model directly to the traffic counts. CONCLUSIONS AND FUTURE WORK Faced with the problem of estimating an Origin Destination trip matrix from traffic counts the entropy maximising approach generates a family of models to solve it. These models have the following properties: a) Require a miinimum of extra assumptions and hence are of more general application. b) Always reproduce the traffic counts which in turn must be internally consistent. c) Allow the use of external, past information and experience based guesses. d) Do not pose excessive computing requirements. Work using data collected by TCDD on the central area of Reading has just been initiated. This data provides an excellent test bed as it includes an O-D matrix and simultaneous volume counts. This paper has reported on validation tests for a model for estimating trip matrices from traffic counts. Under suitable conditions the model produces an O-D matrix which is closest to its prior estimate (if any) and is consistent with the observed counts. This ME2 model has some valuable properties: it does not require a full set of counts but makes use of the information contained in those available; it makes efficient use of prior and/or other information, the matrix generated reproduces the observed counts when loaded onto network; and it is fairly modest in computational requirements.Extensions to the model to the congested network case were discussed and tested. An approach which allows both O-D volumes and path flows to vary within link flow constraints was found to be preferable to a less flexible option. A number of tests using data from the central area of Reading have shown the model and its extension to be reasonably robust and reliable. The model did not generate matrices very close to the observed ones but in general their errors were within the range of daily variations of the sampled matrices. The model has now reached a stage in development in which it can be used with confidence to estimate and update O-D matrices using traffic counts.

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