Estimating Missing Link Volumes in a Traffic Network
VAN DER ZIJPP N J and DE KORT A, Delft University of Technology, The Netherlands
In the Netherlands, authorities keep track of average traffic volumes on motorways. This is done in view of the planning of road maintenance, the observation of traffic performance, the identification of trends and future bottlenecks, etc. Data are stored
In the Netherlands, authorities keep track of average traffic volumes on motorways. This is done in view of the planning of road maintenance, the observation of traffic performance, the identification of trends and future bottlenecks, etc. Data are stored in the form of flow-profiles. These profiles represent average hourly volumes, averaged per month, day and hour of the day.
Actually, traffic can only be counted on 870 of the 6200 links of the Dutch motorway network. These links are referred to as the observed links. For the other links, an estimate of the flow profile should be made. At the moment these estimates are made by multiplying a prior estimate by a growth factor. However the quality of the prior estimates should be .questioned. Also it is envisaged that in the future the set of observed links ~ be modified. It is desirable to be able to judge the effect of such a modification on the quality of the flow profile estimates in advance.
In order to address these problems the transportation planning and traffic engineering section at the Technical University of Delft was asked to develop a method that can be used to estimate flow profiles for unobserved links. Using this method it can be determined to what extent the removal or addition of an observed link influences the error of estimation that applies to the estimates of flow profiles.
Earlier projects were aimed to extrapolate tralfic data in time (BGC, 1988), or to estimate missing data in time series of data (Swaying and De Vries, 1996; De Vries en Praagman, 1995), or to identify road sections with comparable flow patterns (TRANSPUTE, 1994). Contrary to these statistically oriented approaches, this projects uses the spatial dependencies of tr~fAe flows as a basis for the estimation of flow profiles. This implies that the link volumes are considered as sums of route flows. This provides a basis to identify relations between observed and unobserved flows or better, to express the unobserved flows in the observed ones.
Although this problem is relatively unknown in literature, it is strongly connected to the well-known problem of estimating Origin-Destination (OD) matrices from traffic counts. The estimation of an OD matrix from traffic counts under the assumption of certain route choice proportions automatically implies an estimate of all link flows in the network, including the unobserved ones. Another approach is to maximize entropy under the constraints of the given flow observations. In (Sherali et. AI, 1994) an approach is described minimizing the total traveled distance on a network under the constraint of the. observed flows. The minimization was performed with Linear Programming techniques.
When modelling the spatial interconnection of network flows, a prior OD matrix provides important information. For the Dutch context such a matrix can be imported from the National Mobility Model (in Dutch: the 'Landelijk Model Systeem', Rijkswaterstaat & Hague Consultancy Group, 1990). A main characteristic of the problem is however that the flow profile s consist of estimates per hour, type of day and month, whereas the available OD matrix only distinguishes between peak and offpeak, and between weekday and non-weekday.
In view of the above it was concluded that none of the methods known from literature can be applied directly to the current problem. This paper investigates three possible approaches. The approach elaborated in more detail, is the derivation of local OD matrices for small subnetworks that contain the unobserved link, followed by the estimation of the flow profile for this link based on the flows observed on its surrounding links.
Association for European Transport