Journal of Data Science 2(2004), 231-244
Estimating Vehicle Speed from Traﬃc Count and Occupancy Data
Martin L. Hazelton University of Western Australia
Abstract: Automatic vehicle detectors are now common on road systems across the world. Many of these detectors are based on single inductive loops, from which data on traﬃc volumes (i.e. vehicle counts) and occupancy (i.e. proportion of time during which the loop is occupied) are available for 20 or 30 second observational periods. However, for the purposes of traﬃc management it is frequently useful to have data on (mean) vehicle speeds, but this is not directly available from single loop detectors. While detector occupancy is ...view middle of the document...
Data collection is typically done by inductive loop vehicle detectors embedded in (or lying on) roadways. A single detector loop provides information on traﬃc volumes (i.e. vehicle counts over an observational period) and occupancy (the proportion of an observational period during which the loop senses
Martin L. Hazelton
the presence of a vehicle). However, an increasing number of ITS (intelligent transport system) initiatives aimed at congestion relief require estimates of (average) vehicle speeds, often as a precursor to estimating travel times. A prime example from the United States is SWIFT (Seattle Wide Area Information for Travelers). Accurate estimation of vehicle speeds is therefore a signiﬁcant problem for traﬃc engineers. Furthermore, given the widespread use (and relatively low cost) of single loop inductive detectors, methods for obtaining speeds from the count-occupancy data produced by these detectors are of particular interest. See Persuad and Hall (1989) and Dailey (1992, 1999) for related comments. Data from loop detectors is (typically) not available at an individual vehicle level, but rather aggregated over pre-set time intervals (often of 20 or 30 second durations). Given information on vehicle lengths, one can hope to compute an estimated speed based on the total length of vehicle passing the loop, and the time it takes to do so (calculated from the occupancy). While single loop detectors do not provide vehicle length data, large exogenous data sets of vehicle lengths are available. Most estimation procedures proposed to date have been based on an application of ﬁrst order method of moments at each time interval. The recent work of Dailey (1999) improved on this relatively crude methodology by incorporating a second order correction, and applying a Kalman ﬁlter to smooth mean speeds from consecutive intervals. In this paper we take a novel approach to the problem of speed estimation, concentrating on modelling at the level of individual vehicles. This avoids bias due to aggregation which is inherent in earlier techniques. We also allow for measurement error in the recorded occupancies, a feature of the data that is widely recognised (see Coifman, 1999, for example) but has been ignored in published work on speed estimation. Modelling at a disaggregate level means that we are confronted with a great deal of missing data – namely the speeds and lengths of each individual vehicle. Markov chain Monte Carlo (MCMC) methods provide powerful tools for estimation in the presence of missing data. See Diebolt and Ip (1996), for example. We use these techniques to obtain Bayesian estimates of the mean vehicle speed over each time interval. The paper is structured as follows. In the next section we describe our basic model. Details of our MCMC algorithm are given in section 3. Issues regarding the block structure of this algorithm and its relation to the mixing rate (see Gamerman, 1997) are discussed. In section 4 our...